We evaluate our proposed dataset, Guide3D, through a structured experimental analysis, as follows: i) initially, we assess the dataset’s validity, focusing on reprojection errors and their distribution across the dataset to understand its accuracy; ii) we then explore the applicability of Guide3D in a 3D reconstruction task ; and iii) finally, we benchmark several segmentation algorithms to assess their performance on Guide3D, providing insights into the dataset’s utility.

#Dataset Validation

Our analysis revealed a non-uniform distribution of reprojection errors across the dataset, with the highest variability and errors concentrated at the proximal end of the guidewire reconstructions. Figure 1 shows the reprojection error patterns for both Camera A and Camera B. For Camera A, mean errors increase from approximately 6 px to a peak of 20 px, with standard deviations rising from 5 px to 11 px, indicating growing inaccuracies and variability over time. Significant fluctuations around indices 25 to 27 highlight periods of particularly high error. For Camera B, mean errors exhibit an initial peak of 9 px at index 1, followed by fluctuations that decrease towards the end. The standard deviations for Camera B start high at 11 px and decrease over time, reflecting a pattern of high initial variability that stabilizes later. These patterns are consistent with the inherent flexibility of the guidewire, which can form complex shapes such as loops.

Furthermore, we conducted a validation procedure using CathSim, incorporating the aortic arch model described in next subsection and a guidewire of similar diameter and properties. For sampling, we employed the soft actor-critic (SAC) algorithm with segmented guidewires and kinematic data, producing realistic validation samples. Evaluation metrics included maximum Euclidean distance (MaxED) at 2.880 ± 0.640 mm, mean error in tip tracking (METE) at 1.527 ± 0.877 mm, and mean error related to the robot’s shape (MERS) at 0.001 ± 0.000. These results demonstrate the method’s precision.

#Guidewire Prediction Results

We now demonstrate the capability of the introduced network and highlight the importance of the proposed dataset. We examine the network prediction in the following manner: 1) we first conduct an analysis between the predicted and reconstructed curve by employing piecewise metrics, and 2) we showcase the reprojection error.

Shape Prediction Errors: Table 1 presents the comparison of different metrics for shape prediction accuracy. We quantify the shape differences using the following metrics: 1) Maximum Euclidean Distance (MaxED), 2) Mean Error in Tip Tracking (METE), and 3) Mean Error in Robot Shape (MERS). For all the metrics, the shape of the guidewire, represented as a 3D curve $\mathbf{C}(u)$, is sampled at equidistant $\Delta u$ intervals along the arclength parameter $u$. Therefore, the metrics represent the pointwise discrepancies between the two shapes along the curve’s arclength.

The results indicate that the spherical representation consistently outperforms the Cartesian representation across all metrics. Specifically, the Maximum Euclidean Distance (MaxED) shows a lower error in the spherical representation (6.88 ± 5.23 mm) compared to the Cartesian representation (10.00 ± 4.64 mm). Similarly, the Mean Error in Tip Tracking (METE) is significantly lower in the spherical representation (3.28 ± 2.59 mm) than in the Cartesian representation (6.93 ± 3.94 mm). For the Mean Error in Robot Shape (MERS), the spherical representation also demonstrates a reduced error (4.54 ± 3.67 mm) compared to the Cartesian representation (5.33 ± 2.73 mm). Lastly, the Fréchet distance shows a smaller error for the spherical representation (6.70 ± 5.16 mm) compared to the Cartesian representation (8.95 ± 4.37 mm). These results highlight the advantage of using the spherical representation for more accurate shape prediction.

Shape Comparison Visualization: Figure 2a showcases two 3D plots from different angles, comparing the ground truth guidewire shape to the predicted shape by the network. The network demonstrates its capability to accurately predict the guidewire shape, even in the presence of a loop and self-obstruction in the image. The predicted shape aligns closely with the actual configuration of the guidewire. Notably, the proximal end manifests a more substantial error relative to the nominal error seen at the distal end. Discrepancies from the authentic guidewire shape span from a mere 2 mm at the distal end to a noticeable 5 mm at the proximal end. Impressively, the network evidences its capability to accurately predict the guidewire’s shape using only consecutive singular plane images. Subsequently, the 3D points are reprojected onto the original images, as illustrated in Figure 2b.

#Segmentation Results

We demonstrate Guide3D’s potential to advance guidewire segmentation research by evaluating the performance of three state-of-the-art network architectures: UNet (learning rate: $1 \times 10^{-5}$, 135 epochs), TransUnet (integrating ResNet50 and Vision Transformer (ViT-B-16), learning rate: 0.01, 199 epochs), and SwinUnet (Swin Transformer architecture, learning rate: 0.01, 299 epochs). Performance metrics included the Dice coefficient (DiceM), mean Intersection over Union (mIoU), and Jaccard index, detailed in Table 2. The results indicate that UNet achieved a DiceM of 92.25, mIoU of 36.60, and Jaccard index of 86.57. TransUnet outperformed with a DiceM of 95.06, mIoU of 41.20, and Jaccard index of 91.10. SwinUnet recorded a DiceM of 93.73, mIoU of 38.58, and Jaccard index of 88.55. These findings benchmark the dataset’s performance and suggest potential for future enhancements. Despite these promising results, the presence of loops and occlusions within the guidewire indicates that polyline prediction could significantly improve task utility.

#Discussion and Conclussion

This paper introduces a new dataset, Guide3D, for segmentation and 3D reconstruction of flexible, curved endovascular tools. Extensive experiments demonstrate the dataset’s value; yet several limitations must be acknowledged. Firstly, our dataset lacks clinical real human data due to the complexity and regulatory challenges of acquiring such data. Our standardized platform, however, aims to enable further research, providing a stepping stone towards clinical practice.

Additionally, the dataset primarily focuses on synthetic and experimental scenarios, which may not fully capture the variability and unpredictability of real-world clinical environments. While this controlled setting aids initial algorithm development and benchmarking, further validation with clinical data is necessary to ensure the robustness and generalizability of the proposed methods.

Moreover, the guidewire’s flexibility and the presence of loops and occlusions present significant challenges for segmentation and reconstruction tasks. Our dataset includes these complexities to push the boundaries of current methodologies, but future work should explore more advanced techniques.

Our dataset accommodates both video and image-based approaches, providing a versatile resource to facilitate the translation of these technologies into clinical settings. Our objective is to bridge the disparity between research developments and clinical application by establishing a standardized framework for evaluating the efficacy of various methodologies. Our code and dataset will be made publicly available.

Utilizing the Guide3D dataset, we build a benchmark for the shape prediction task, a critical component in endovascular intervention. Accurate shape prediction of the guidewire is essential for successful navigation and intervention. Here, we introduce a novel shape prediction network designed to predict the guidewire shape from a sequence of monoplanar images. This approach leverages deep learning to learn spatio-temporal correlations from a static camera observing a dynamic scene. Unlike conventional reconstruction methods that require biplanar images, our network uses a sequence of images to extract temporal information, allowing it to map a single image $\mathbf{I}_A$ to the 3D guidewire curve $\mathbf{C}(\mathbf{u})$. By adopting this deep learning approach, we aim to simplify the shape prediction process while maintaining high accuracy. This method has the potential to enhance endovascular navigation by providing real-time, accurate predictions of the guidewire shape, ultimately improving procedural outcomes and reducing reliance on specialized equipment.

#Spherical Coordinates Representation

Predicting 3D points directly can be challenging due to the high degree of freedom. To mitigate this, we use spherical coordinates, which offer significant advantages over Cartesian coordinates for guidewire shape prediction. Spherical coordinates, as represented in Fig. 1a, are defined by the radius $r$, polar angle $\theta$, and azimuthal angle $\phi$. They provide a more natural representation for the position and orientation of points along the guidewire, which is typically elongated and curved.

Mathematically, a point in spherical coordinates $(r, \theta, \phi)$ can be converted to Cartesian coordinates $(x, y, z)$ using the transformations:

This conversion simplifies the modeling of angular displacements and rotations, as spherical coordinates directly encode directional information.

Predicting angular displacements $(\Delta \theta, \Delta \phi)$ relative to a known radius $r$ aligns with the physical constraints of the guidewire, facilitating more accurate and interpretable shape predictions. By predicting an initial point (tip position) and representing subsequent points as offsets in $\Delta \phi$ and $\Delta \theta$ while keeping $r$ fixed, this method simplifies shape comparison and reduces the parameter space. This approach enhances the model’s ability to capture the guidewire’s spatial configuration and improves overall prediction performance.

#Network Architecture

The proposed model (shown in Fig. 1b) addresses the problem of predicting the 3D shape of a guidewire from a sequence of images. Each image sequence captures the guidewire from different time steps $\mathbf{I}_{A,t}$, and the goal is to infer the continuous 3D shape $\mathbf{C}_t(\mathbf{u}_t)$. This many-to-one prediction task is akin to generating a variable-length sequence from variable-length input sequences, a technique commonly utilized in fields such as machine translation and video analysis.

To achieve this, the input pipeline consists of a sequence of images depicting the guidewire. A Vision Transformer (ViT), pre-trained on ImageNet, is employed to extract high-dimensional spatial feature representations from these images. The ViT generates feature maps $\mathbf{z}_t \in \mathbb{R}$. These feature maps are then fed into a Gated Recurrent Unit (GRU) to capture the temporal dependencies across the image sequence. The GRU processes the feature maps $\mathbf{z}_t$ from consecutive time steps, producing a sequence of hidden states $\mathbf{h}_t$. Formally, the GRU operation at time step $t$ is defined as:

The final hidden state $\mathbf{h}_t$ from the GRU is used by three distinct prediction heads, each tailored for a specific aspect of the guidewire shape prediction: the Tip Prediction Head, responsible for predicting the 3D coordinates of the guidewire’s tip through a fully connected layer that maps the hidden state $\mathbf{h}_t$ to a Cartesian anchoring point $\mathbf{p} \in \mathbb{R}^3$; the Spherical Offset Prediction Head, which predicts the spherical coordinate offsets $(\Delta \phi, \Delta \theta)$ for points along the guidewire with a fixed radius $r$; and the Stop Prediction Head, which outputs the probability distribution indicating the terminal point of the guidewire by using a softmax layer to produce a probability tensor $\mathbf{S}$, where each element $\mathbf{S}_j$ indicates the probability of the $j$-th point being the terminal point.

#Loss Function

The custom loss function for training the model combines multiple components to handle the point-wise tip error, variable guidewire length (stop criteria), and tip position predictions. The overall loss function $\mathcal{L}_{\text{total}}$ is defined as:

where $N$ is the number of samples, and $\lambda_{\text{tip}}$, $\lambda_{\text{offset}}$, and $\lambda_{\text{stop}}$ are weights that balance the contributions of each loss component. The tip prediction loss ($\mathcal{L}_{\text{tip}}$) uses mean squared error (MSE) to ensure accurate 3D tip coordinates. The spherical offset loss ($\mathcal{L}_{\text{offset}}$) also uses MSE to align predicted and ground truth angular offsets, capturing the guidewire’s shape. The stop prediction loss ($\mathcal{L}_{\text{stop}}$) employs binary cross-entropy (BCE) to accurately predict the guidewire’s endpoint.

#Training Details

The model was trained end-to-end using the loss from Equation above. The NAdam optimizer was used with an initial learning rate of $1 \times 10^{-4}$. Additionally, a learning rate scheduler was employed to adjust the learning rate dynamically based on the validation loss. Specifically, the ReduceLROnPlateau scheduler was configured to reduce the learning rate by a factor of 0.1 if the validation loss did not improve for 10 epochs. The model was trained for 400 epochs, with early stopping based on the validation loss to further prevent overfitting.

#Next

In the next part, we will validate the effectiveness of Guidewire Shape Prediction dataset and methodology.

We propose the Guid3D Dataset, a comprehensive resource specifically designed to advance 3D reconstruction and segmentation in endovascular navigation. This dataset addresses key limitations in the field, such as the scarcity of high-quality, publicly accessible datasets, by providing a diverse collection of real and synthetic imaging data. Guid3D includes detailed annotations for guidewire and catheter segmentation, alongside multi-view fluoroscopic data that supports accurate 3D modeling. By offering a standardized platform for algorithm development and evaluation, Guid3D aims to bridge the gap between research and clinical practice, facilitating improvements in precision, visualization, and tool tracking during endovascular procedures. Through this dataset, we seek to accelerate innovation in medical imaging, contributing to safer and more effective interventions.

#Data Collection Setup

X-ray System. Our setup employed a bi-planar X-ray system equipped with 60 kW Epsilon X-ray generators and 16-inch image intensifier tubes by Thales, featuring dual focal spot Varian X-ray tubes for high-definition imaging. The system included Ralco automatic collimators for precise alignment and exposure, with calibration achieved through the use of acrylic mirrors and geometric alignment grids.

Anatomical Models. We utilized a half-body vascular phantom model from Elastrat Sarl Ltd., Switzerland, enclosed in a transparent box and integrated into a closed water circuit to simulate blood flow. Made from soft silicone and equipped with compact continuous flow pumps, it replicates human blood flow dynamics. The design is based on detailed postmortem vascular casts, ensuring anatomical accuracy reflective of human vasculature, facilitating realistic vascular simulations.

Surgical Tools. To enhance our dataset, we navigated complex vascular structures using two types of guidewires commonly used in real-world endovascular surgery. The first, the Radifocus™ Guide Wire M Stiff Type (Terumo Ltd.), is made from nitinol with a polyurethane-tungsten coating. It measures 0.89 mm in diameter and 260 cm in length, with a 3 cm angled tip, designed for seeking, dissecting, and crossing lesions. The second, the Nitrex Guidewire (Nitrex Metal Inc.), also made of nitinol, features a gold-tungsten straight tip for enhanced radiopacity in fluoroscopic visualization. It has a diameter of 0.89 mm and a length of 400 cm, with a 15 cm tip, and is generally used for accessing or maintaining position during catheter exchanges. Both guidewires were selected to reflect real-world usage and to diversify the data in our dataset.

#Data Acquisition, Labeling, and Statistics

Using the materials described in Subsection 3.1, we compiled a dataset of 8,746 high-resolution samples (1,024 × 1,024 pixels). This dataset includes 4,373 paired instances, both with and without a simulated blood flow medium. Specifically, it consists of 6,136 samples from the Radifocus guidewire and 2,610 from the Nitrex guidewire, providing a solid foundation for automated guidewire tracking in bi-planar scanner images. Manual annotation was carried out using the Computer Vision Annotation Tool (CVAT), where polylines were created to accurately track the dynamic path of the guidewires. The polyline representation was chosen because the guidewire's structure often results in overlapping sections, making a segmentation mask unsuitable. In contrast, a polyline effectively captures the looping nature of the guidewire, offering greater accuracy.

As shown in Table 1, the dataset includes 3,664 instances of angled guidewires with fluid and 484 without, while straight guidewires are represented by 2,472 instances with fluid and 2,126 without. This distribution reflects a variety of procedural contexts. All 8,746 images in the dataset are accompanied by manual segmentation ground truth, facilitating the development of algorithms that require segmentation maps as reference data.

#Calibration

We extract the camera parameters using a traditional undistortion and calibration method. Undistortion is first achieved with a local weighted mean (LWM) algorithm, using a perforated steel sheet with a hexagonal pattern as a framing reference, and applying a blob detection algorithm to precisely identify distortion points. This approach establishes correspondences between distorted and undistorted positions, allowing for accurate distortion correction.

Following this, a semi-automatic calibration step is performed for marker identification, and the random sampling consensus (RANSAC) method is used to ensure robustness in computing the projection matrix and deriving the intrinsic and extrinsic camera parameters. The calibration process is further refined through direct linear transformation (DLT) and non-linear optimization, utilizing multiple poses of the calibration object to optimize the overall camera setup. Figure 3 illustrates the calibration process.

#Guidewire Reconstruction

Given polyline representations of a curve in both planes, the reconstruction process begins by parameterizing these curves using B-Spline interpolation. Each curve is expressed as a function of the cumulative distance along its path. Let $\mathbf{C}_A(\mathbf{u}_A)$ and $\mathbf{C}_B(\mathbf{u}_B)$ represent the parameterized B-Spline curves in their respective planes, where $\mathbf{u}_A$ and $\mathbf{u}_B$ are the normalized arc-length parameters. The corresponding $\mathbf{u}_B$ for a given $\mathbf{u}_A$ is found using epipolar geometry. Once the corresponding points $\mathbf{C}_A(\mathbf{u}_A^i)$ and $\mathbf{C}_B(\mathbf{u}_B^i)$ are identified, their 3D coordinates $\mathbf{P}^i$ are computed by triangulation, resulting in a set of 3D points $\{\mathbf{P}^i\}_{i=1}^{M}$, where $M$ is the total number of sampled points. This effectively reconstructs the original curve in 3D space.

To retrieve the fundamental matrix $\mathbf{F}$, which describes the relationship between points in Image A ($\mathbf{I}_A$) and Image B ($\mathbf{I}_B$), the condition $\mathbf{x}_B^T \mathbf{F} \mathbf{x}_A = 0$ must hold for corresponding points $\mathbf{x}_A$ in $\mathbf{I}_A$ and $\mathbf{x}_B$ in $\mathbf{I}_B$. Using the projection matrices $\mathbf{P}_A$ and $\mathbf{P}_B$ derived from the calibration process, the fundamental matrix can be calculated as follows:

Here, $\mathbf{e}_B$ is the epipole in Image B, defined as $\mathbf{e}_B = \mathbf{P}_B \mathbf{C}_A$, with $\mathbf{C}_A$ being the camera center of $\mathbf{P}_A$. The skew-symmetric matrix of the epipole $\mathbf{e}_B$ is represented by:

Where $\mathbf{e}_B = (e_{B1}, e_{B2}, e_{B3})^T$, and $\mathbf{P}_A^+$ is the pseudoinverse of the projection matrix $\mathbf{P}_A$. The fundamental matrix $\mathbf{F}$ encapsulates the epipolar geometry between the two views, ensuring that corresponding points $\mathbf{x}_A$ and $\mathbf{x}_B$ lie on their respective epipolar lines.

The matching phase begins by uniformly sampling points along the curve $\mathbf{C}_A(u_A)$ at intervals $\Delta u_A$. For each sampled point $x_A = \mathbf{C}_A(u_A)$, we project the epiline $l_B = F x_A$ into Image B. We then determine the intersection of the epiline $l_B$ with the curve $\mathbf{C}_B(u_B)$, thereby obtaining the corresponding parameter $u_B$ for each $u_A$.

Due to errors in the projection matrices $P_A$ and $P_B$, there are instances where the epiline $l_B$ does not intersect with any part of the curve $\mathbf{C}_B$. To address this, we fit a monotonic function $f_A(u_A) \rightarrow u_B$ using a Piecewise Cubic Hermite Interpolating Polynomial (PCHIP), thus interpolating the missing intersections. The matching process is visualized in Fig. 4.

#Utility of Guide3D Dataset for the Research Community

Guide3D advances endovascular imaging by providing a bi-planar fluoroscopic dataset for segmentation and 3D reconstruction, serving as an open-source benchmark. It enables precise algorithm comparisons for segmentation and facilitates method development in 3D reconstruction through the use of bi-planar imagery. With video data, Guide3D supports video-based methods, leveraging temporal dimensions for dynamic analysis. This enriches the segmentation and reconstruction capabilities, while also aligning with the procedural nature of endovascular interventions. This versatility highlights Guide3D's pivotal role in advancing endovascular imaging.

#Next

In the next part, we will explore Guidewire Shape Prediction methodology.

Endovascular surgical tool reconstruction represents an important factor in advancing endovascular tool navigation, which is an important step in endovascular surgery. However, the lack of publicly available datasets significantly restricts the development and validation of novel machine learning approaches. Moreover, due to the need for specialized equipment such as biplanar scanners, most of the previous research employs monoplanar fluoroscopic technologies, hence only capturing the data from a single view and significantly limiting the reconstruction accuracy.

To bridge this gap, we introduce, a bi-planar X-ray dataset for 3D reconstruction. The dataset represents a collection of high resolution bi-planar, manually annotated fluoroscopic videos, captured in real-world settings. Validating our dataset within a simulated environment reflective of clinical settings confirms its applicability for real-world applications. Furthermore, we propose a new benchmark for guidewrite shape prediction, serving as a strong baseline for future work. The proposal not only addresses an essential need by offering a platform for advancing segmentation and 3D reconstruction techniques but also aids the development of more accurate and efficient endovascular surgery interventions.

#Introduction

Minimally invasive surgery has revolutionized endovascular interventions, offering less invasive options with shorter recovery times. The success of these procedures depends on the precise navigation and manipulation of instruments such as guidewires and catheters. Typically, 2D visualization methods are used for guidance, with monoplanar fluoroscopy being the most common due to its minimal disruption to surgical workflows and relatively affordable cost. However, despite their widespread use, conventional imaging techniques have significant limitations, with one of the primary challenges being the lack of depth perception. This issue complicates the accurate visualization of surgical instruments, increasing the risk of excessive contact with arterial walls, which can compromise patient safety and the effectiveness of the procedure.

In endovascular interventions, depth perception is largely achieved through multi-view imaging systems, such as biplanar scanners, which allow shape reconstruction by combining images from multiple angles and employing epipolar geometry-based reconstruction. However, two major challenges hinder the broader adoption and effectiveness of these systems: (i) the difficulty of accurately segmenting images for successful shape reconstruction, exacerbated by the scarcity of datasets needed to evaluate segmentation methods, and (ii) the limited availability of specialized biplanar scanners in clinical settings due to their high cost. These challenges underscore the critical need for comprehensive datasets to enhance segmentation algorithm accuracy and improve guidewire reconstruction techniques, facilitating the development of more versatile imaging technologies.

In this paper, we introduce Guid3D, a dataset designed to advance 3D reconstruction in endovascular navigation. Guid3D provides a standardized platform for the development and evaluation of algorithms. With a comprehensive dataset that includes manual annotations for segmentation and tools for effective 3D visualization, Guid3D is intended to drive innovation and improvement in endovascular intervention. Furthermore, the inclusion of video-based biplanar fluoroscopic data allows for the exploration of temporal dynamics, such as using optical flow networks. Guid3D seeks to bridge the gap between research innovations and clinical applications, addressing key challenges in endovascular procedures.

#Related Works

#Endovascular Datasets.

Datasets play a crucial role in advancing endovascular navigation by providing essential resources for the development, evaluation, and enhancement of algorithms. These datasets, derived from various imaging modalities such as mono X-ray, 3D ultrasound, and 3D MRI, encompass both real and synthetic images, facilitating diverse applications in the medical field.

Mono X-ray datasets, while prevalent, often fall short in providing the necessary detail required for accurate 3D reconstruction, which is critical for effective surgical navigation. The inherent limitations of 2D imaging techniques make it challenging to fully capture the complexity of anatomical structures during procedures. In contrast, 3D imaging modalities like 3D ultrasound and 3D MRI offer more comprehensive views, enabling better depth perception and improved visualization of surgical tools and surrounding tissues.

Despite the importance of these datasets, there remains a significant gap in the availability of comprehensive, publicly accessible datasets specifically designed for tool segmentation and 3D reconstruction. This scarcity hampers progress in developing robust algorithms capable of accurately interpreting complex medical images. The lack of diverse and high-quality datasets also limits the ability of researchers to train and validate their algorithms effectively, often leading to suboptimal performance in clinical scenarios.

Furthermore, creating high-quality datasets is not merely a technical challenge; it requires collaboration among various stakeholders, including clinicians, radiologists, and data scientists. Such collaboration is essential to ensure that the datasets reflect real-world clinical conditions and include diverse patient populations. Expanding the availability of well-annotated datasets is vital for fostering innovation and advancing the field of endovascular surgery.

#Catheter and Guidewire Segmentation.

The segmentation of endovascular tools, particularly guidewires and catheters, is an evolving field that heavily relies on the availability and quality of datasets. Previous studies have often used synthetic and semi-synthetic data to address the challenges posed by the limited availability of real-world datasets. Researchers have employed manually annotated datasets from 2D X-ray and 3D MRI modalities to train segmentation models. Additionally, the effectiveness of synthetic datasets has been demonstrated in improving model efficiency.

The advent of deep learning techniques, especially U-Net architectures, has significantly enhanced the accuracy of segmentation and tracking for these surgical instruments. This advancement has led to the development of fully automated segmentation frameworks that utilize extensively annotated data and incorporate unsupervised techniques, such as optical flow. However, the absence of a public, standardized dataset for method comparison continues to impede the advancement and assessment of scientific progress in this area.

#3D Reconstruction.

Improving the accuracy of 3D reconstruction in endovascular procedures plays a crucial role in achieving better clinical outcomes by enhancing catheter navigation through advanced visualization and precise tracking. Advances in fluoroscopic imaging technology have led to more accurate positioning of devices. Various algorithms have been developed to facilitate this process, employing techniques such as elastic grid registration and epipolar geometry for 3D reconstruction from biplane angiography. Additionally, automatic catheter detection methods utilizing triangulation and graph-search algorithms have been applied in electrophysiology studies to improve reconstruction outcomes.

Research has demonstrated the importance of accurate 3D models for navigation within both complex and single-view vascular architectures, highlighting the value of biplanar data. However, the limited availability of comprehensive, publicly accessible datasets for the development and validation of algorithms in 3D reconstruction poses a significant challenge to technological progress and clinical application. This situation underscores the critical need for specialized datasets to promote ongoing innovation in the reconstruction of endovascular tools.

#Next

In the next part, we will dive deeply into how to conduct a dataset for 3D shape reconstruction.

In the previous part, we introduce training process and experimental setup. In this part, we validate the effectiveness and efficiency of the proposed method.

#Experimental Results

#Quality Comparison

Table 1 presents a comparison among the baselines FACT, Transflower, EDGE, GDanceR, GCD, and our proposed manifold-based method. The results clearly demonstrate that our model outperforms the baselines across all evaluations on two datasets, AIOZ-GDANCE and AIST-M. We observe that recent diffusion-based dance generation models, such as EDGE or GCD, achieve competitive performance on both single-dance metrics (FID, MMC, GenDiv, and PFC) and group dance metrics (GMR, GMC, and TIF). However, due to limitations in their training procedures, they still struggle with generating multiple dancing motions when faced with a large number of dancers, as indicated by their lower performance compared to our method. This suggests that our approach successfully maintains the quality of dance motions as the number of dancers increases.

#Scalable Generation Analysis

Table 2 illustrates the performance of different group dance generation methods (GCD, GDancer, and Ours) when generating dance movements with an increasing number of dancers. When the number of dancers is increased to 10, GCD appears to run out of memory, which is also observed in GDanceR when the number of dancers increases to 100. Regardless of the number of dancers, our method consistently achieves stable and competitive results. This implies that our proposed method successfully addresses the scalability issue in group dance generation without compromising the overall performance of each individual dance motion.

Figure 3 illustrates the memory consumption to generate dance motions in groups for each method. Noticeably, our proposal still achieves the highest performance while consuming immensely fewer resources required for generating group dance motions (See Figure 4 for illustrations). This, again, indicates that our method successfully breaks the barrier of limited generated dancers by using the manifold.

#Ablation Study

Table 3 presents the performance improvements achieved through the integration of consistency loss and phase manifold. Additionally, we showcase the effectiveness of our proposed approach across three different backbones: Transformer, LSTM, and CNN. Evaluation metrics including FID, GMR, and GMC are utilized. The results indicate that the absence of consistency loss leads to an increase in GMR and a decrease in GMC, suggesting a significant enhancement in the realism and correlation of group dance motions facilitated by the inclusion of the proposed objective. Meanwhile, with out the phase manifold, the model exhibits remarkably higher scores in both the FID and GMR metrics, suggesting that phase manifold can effectively improve the distinction in dance motions while maintaining the realism of group dances, even when the number of dancers in a group is large. In comparing three backbones—Transformer, LSTM, and CNN—we have observed that the chosen Transformer backbone achieved the best results compared to LSTM or CNN.

#User Study

User studies are vital for evaluating generative models, as user perception is pivotal for downstream applications; thus, we conducted two studies with around 70 participants each, diverse in background, with experience in music and dance, aged between 20 to 40, consisting of approximately 47\% females and 53\% males, to assess the effectiveness of our approach in group choreography generation.

In the user study, we aim to assess the realism of sample outputs with more and more dancers. Specifically, participants assign scores ranging from 0 to 10 to evaluate the realism of each dance clip with 2 to 10 dancers. Figure 5 shows that, across all methods, the more the number of dancers is increased, the lower the realism is found. However, the drop in realism of our proposed method is the least compared to GCD and GDanceR. The results indicate our method's good performance compared to other baselines when the number of dancers increases.

#Discussion

While our approach leverages the VAE as a primary solution for generating a manifold, it is important to acknowledge certain inherent limitations associated with this choice. One notable challenge is the susceptibility to issues such as posterior collapse and unstable sampling within the VAE framework. These challenges can result in generated group dance motions that may not consistently meet performance expectations.

One specific manifestation of this limitation is the potential for false decoding when sampling points that lie too far from the learned distribution. This scenario can lead to unexpected rotations or disruptions in the physics of the generated content. The impact of this problem becomes evident in instances where the generated samples deviate significantly from the anticipated distribution, introducing inaccuracies and distortions.

To address these challenges, we recognize the need for ongoing efforts to mitigate the effects of posterior collapse and unstable sampling. While the problem is acknowledged, our approach incorporates measures to limit its impact. Future research directions could explore alternative generative models or additional techniques to enhance the robustness and reliability of the generated results in the face of these identified limitations.

Welcome to the concluding part of our series! In this final installment, we'll delve deeper into the intricacies of the search system that accompanies our proposal. Additionally, we'll conduct a comprehensive evaluation to gauge the overall effectiveness and performance of our solution. Let's explore the various aspects of the search functionality and analyze how it contributes to the success of our proposed system. Let's embark on this journey together as we wrap up our discussion and reflect on the insights gained throughout this series.

#1. Searching and Indexing Method in the CFOR System

To adapt our retrieval system for large-scale datasets, we've developed indexes for the CFOR system to facilitate nonexhaustive similarity search using GPU acceleration. Leveraging the searching algorithm outlined by Johnson et al. (referenced as "billion-scale similarity search with GPUs"), we've implemented it within the CFOR system for retrieval tasks. In searching, the CFOR system enhances accuracy by reducing the search space through additional information such as regions, categories, and attributes. For indexing, the object ontology aids in creating multi-indexing files to minimize search time. Our focus is on similarity search in vector collections using the L2 distance in the k-selection algorithm.

In the realm of searching, we distinguish between exact search (exhaustive search) and compressed search (greedy nonexhaustive search).

• Exact search: Almost all searching algorithms in this type try to compute the full pairwise distance between the query and each data point in the database sequentially or using the index file.
• Compressed-Domain search: Almost all searching algorithms in this type try to compute distance between the query and each data point in the database by applying space transformation, encoding, subspace splitting, or hashing. These methods can help improve searching time by using index files, but they have a trade-off in searching accuracy.

#2. Data

Our fashion retrieval system was built on a subset of approximately 300,000 images of DeepFashion. In the DeepFashion dataset, objects from different aspects are caught in complicated background. The input image in the dataset is annotated with different labels based on details (fine-grained) of input of the current model concern, i.e., rich annotation. The samples given in Figures 1 and 2 show more details about the DeepFashion dataset.

In testing, we employ part of the benchmark data to fine tune the trained models. We ensure that there are no fashion item overlaps between fine-tuning and testing sets. The dataset includes ∼220,000 images of the training set, 40,000 images of the validating set, and 40,000 images of the testing set split. However, in attribute learning, we limited the number of attribute labels used for testing and the number of training images for specific attributes to make an imbalanced attribute dataset so as to prove our proposed methods.

#3. Results and Discussion

In the CFOR system, object ontology is useful in controlling training flow which impacts the performance of object category classification and attribute multitask classification. For object category classification, ontology controls the amount of training data through concepts. For attribute multitask classification, ontology manages local grouping which directly affects the performance of the proposed local imbalanced data solver on the large-scale dataset.

In this section, we will evaluate the effectiveness of different deep networks with the support of ontology on both category classification and attribute multitask classification in the CFOR system to pick out the best architecture for training the system. We will also compare our results with FashionNet.

#Category Classification

We compare the performance between different deep architectures including NASNet, ResNet-18, ResNet-101, FashionNet, NASNet with average pooling dropout (NASNet APD) (proposed by us), and ResNet with average pooling dropout (ResNet APD) (proposed by us). These experiments will be evaluated by top-k accuracy (Figure.3). Our target is to find out the best possible architecture to apply as a core network of the CFOR system. This step can be mentioned as a preparation step before applying the CFOR system for fashion retrieval.

The result of category classification by ResNet-18 APD is higher than 1.23% (at k= 1) after removing nodes and making average pooling in the ResNet-18 architecture (compared with the original ResNet-18 architecture). This increased value is 0.93% with the ResNet-101 architecture (compared with the original ResNet-101 architecture) and 0.02% with the NASNet v3 architecture (compared with the original NASNet v3 architecture). The ResNet-101 APD architecture (the best architecture addressed) outperformed the FashionNet architecture (the best performing architecture in category classification on the DeepFashion dataset versus others such as WTBI or DARN), and the value is 4.6% with k= 3 and 2.58% with k = 5. Based on the above experimental results, the ResNet-101 architecture provides better classification and higher performance compared to others (NASNet and ResNet-18). For this reason, we propose ResNet-101 as the core network architecture for training classification models.

#Attribute Learning

Attribute multitask learning is an important part of the CFOR system. In this section, we evaluate the performance of the proposed local imbalanced data solver with MCC in dealing with the imbalanced attribute data on the large-scale fashion dataset.

Precision is the proportion of relevant instances among the retrieved instances which consider both true positives and false positives in each attribute. However, the number of true positives and false positives is bias because of the imbalanced data problem. Thus, precision can also be affected by the imbalanced data problem. Otherwise, recall, which cares about true-positive labels but not false-positive labels, will be used to evaluate experiments because of its good reflection for fewer data attributes.

Local MTL gets over STL and MTL in 28/35 attributes with a 54.70% recall rate (higher than that in STL (17.06%) and that in MTL (28.70%)). While a single task shows its weakness in fewer data attributes and multitasks get struggled with the serious imbalanced problem and lesser intergroup correlations in fashion data, local MTL can lower their negative influences as well as widen the positive effect of inner-group correlations on attribute learning. Thus, local MTL gets over STL and MTL in 13/15 fewer sample attributes (Figure.4).

Based on the experiment, comparison of chic, solid, and maxi attributes which have equal accuracy between MTL with and without MCC shows that MTL with MCC had higher recall compared to that without MCC in 20/35 remaining attributes. The overall performance increases about 3%. For attributes with fewer data, MTL with MCC had higher recall compared to that without MCC in 9/14 attributes. The overall performance for these fewer data attributes increases 5.14% (see Figure 5 for more details).

#Retrieval in CFOR System Results

In this experiment, we test the retrieval ability of the CFOR system by using MAP from 1 retrieval result for each query (MAP@1) to 30 retrieval results for each query (MAP@30) so as to evaluate the effectiveness. The similarity retrieval experiment will check whether the extracted attributes in retrieved images are matched with ground-truth attributes in query image. The retrieval method will be based on deep features and over 35 attributes. After experimenting in 35 attributes belonging to 5 groups, the starting MAP@5 is acceptable (hovering 0.531) which shows the effectiveness of the searching method. The MAP@30 hovers 0.815, and the trend keeps rising which shows consistency and stabilization of information prediction methods in the CFOR system. A simple visualization of the retrieval process in the CFOR system is shown in Figure.6.

#4. Conclusion

This work presents the coarse-to-fine object retrieval system, a learning framework for e-commerce online retrieval, which is supported to deal with large-scale imbalanced datasets. The framework can impact input and output as well as reconstruct datasets from the coarse-grained level to the fine-grained level and is believed to be an effective method in improving learning performance designed for retrieval. For input reconstruction, the framework based on ontology is used for threading training flow, local grouping in multitask attribute learning, and hierarchical storage and retrieval. For output optimization, we take advantage of MCC to minimize the effect of the imbalanced dataset on multitask attribute learning.

Through extensive experiments, we demonstrate the applicability of object ontology in improving training flow, the effectiveness of different deep networks (ResNet and NASNet) applied on important tasks in fine-grained retrieval, and the usefulness of local multitask attribute learning and an MCC-based imbalanced data solver in attribute multitask learning. The CFOR system is designed to have flexibility so that it can be optimized easily in the future.

In the previous part, we introduct our main proposal Variational Phase Manifold Learning. In this part, we have explore the training process and experimental setup to validate the proposed method.

#Training

During training, we consider the following variational lower bound to mainly train our dance generation VAE model:

In practice, we apply the conditional VAE loss, which is defined as the weighted sum $\mathcal{L}_{\text{cvae}} = \mathcal{L}_{\text{rec}} + \lambda_{\text{KL}}\mathcal{L}_{\text{KL}}$. In particular, the reconstruction term $\mathcal{L}_{\text{rec}}$ measures the motion reconstruction error given the decoder output (via a smooth-L1 loss). The KL divergence term $\mathcal{L}_{\text{KL}}$ compares the divergence $D_{\text{KL}}$ between the posterior and the prior distribution to enforce them to be close to each other.

The conditional VAE objective above is calculated for each dancer separately and cannot capture the correlation between dancers within a group. Therefore, it is essential to impose consistency among dancers and avoid strange effects such as unsynchronized dance. To this end, we propose a group consistency loss by enforcing the latent phase manifold to be similar for the same group, given the input music. Specifically, we first calculate the phase manifold features based on the frequency domain parameters as follows:

where $\mathbf{P}\in\mathbb{R}^{2D}$ is the phase manifold vector that encodes the spatial-temporal information of the motion state. The phase feature may look similar to the positional encodings of transformers in the sense that both use multi-resolution sinusoidal functions. However, the phase feature is much richer in terms of representation capacity since it learns to embed the spatial (body joints) and temporal (positions in time) information of the motion curves, whereas the positional encodings only encode the position of words. Finally, our consistency objective is to constrain phase manifold between dancers within a group to be as close as possible to each other, which is formulated as:

where the first term encourages the network to map different dancers belonging to the same group ($\mathbf{x}^m$ and $\mathbf{x}^n$) into the same set of distributional phase parameters while the second term penalizes the discrepancy in their corresponding phase manifolds. In general, this loss is applied to ensure every dancer is embedded into a single unified manifold that can effectively represent their corresponding group. To summarize, our total training loss is defined as the combination of the VAE loss and the consistency loss $\mathcal{L} = \mathbf{\mathcal{L}}_{\text{cvae}} + \lambda_{\text{csc}}\mathbf{\mathcal{L}}_{\text{csc}}$.

For testing, we can efficiently generate motions for an unlimited number of dancers by indefinitely drawing samples from the learned continuous group-consistent phase manifold. It is noteworthy that for inference, we only need to process the prior network once to obtain the latent distribution. To generate a new motion, we can sample from this latent (Gaussian) distribution and use the decoder to decode it back to the motion space. This approach is much more efficient and has significantly higher scalability than previous approaches that is limited by the number of dancers processed simultaneously by the entire network.

#Experiments

#Implementation Details

Our model was trained on 4 NVIDIA V100 GPUs using Adam optimizer with a fixed learning rate of $10^{-4}$ and a mini-batch size of 32 per GPU. For training losses, the weights are empirically set to $\lambda_{\text{KL}} = 5\times 10^{-4}$ and $\lambda_{\text{csc}} = 10^{-4}$, respectively. The Transformer encoders and decoders consist of 5 layers for both encoder, decoder, and prior Network with 512-dimensional hidden units. Meanwhile, the number of latent phase channels is set to 256. To further capture the periodic nature of the phase feature, we also use Siren activation following the initialization scheme. This can effectively model the periodicity inherent in the motion data, and thus can benefit motion synthesis.

#Experimental Settings

Dataset. In our experiments, we utilize the AIOZ-GDance and AIST-M datasets. AIOZ-GDance is the largest music-driven dataset focusing on group dance, encompassing paired music and 3D group motions extracted from in-the-wild videos through a semi-automatic process. This dataset spans 7 dance styles and 16 music genres. For consistency, we adhere to the training and testing split during our experiments.

Evaluation Protocol. We employ several metrics to assess the quality of individual dance motions, including Frechet Inception Distance (FID), Motion-Music Consistency (MMC, and Generation Diversity (GenDiv), along with the Physical Foot Contact score (PFC). Specifically, the FID score gauges the realism of individual dance movements concerning the ground-truth dance. MMC assesses the matching similarity between motion and music beats, reflecting how well-generated dances synchronize with the music's rhythm. GenDiv is computed as the average pairwise distance of kinetic features among motions. PFC evaluates the physical plausibility of foot movements by determining the agreement between the acceleration of the character's center of mass and the foot's velocity.

In assessing the quality of group dance, we adopt three metrics : Group Motion Realism (GMR), Group Motion Correlation (GMC), and Trajectory Intersection Frequency (TIF). Broadly, GMR gauges the realism of generated group motions in comparison to ground-truth data, employing Frechet Inception Distance on extracted group motion features. GMC evaluates the synchronization among dancers within the generated group by computing their cross-correlation. TIF quantifies the frequency of collisions among the generated dancers during their dance movements.

Baselines. Our method is subjected to comparison with various recent techniques in music-driven dance generation, namely FACT, Transflower, and EDGE. These approaches are adapted for benchmarking within the context of group dance generation, considering that their original designs were tailored for single-dance scenarios. Additionally, our evaluation includes a comparison with GDanceR, GCD, and DanY. All of the mentioned works are specifically designed for the generation of group choreography.

#Next

In the next part, we will explore the effectiveness of the proposal through quantitative and qualitative results.

To provide fine-grained information to the CFOR system, attribute learning is a most important task which should be optimized in both time-processing performance and ability to deal with large-scale imbalanced datasets.

#1. Framework

Local multitask learning is applied to attribute learning. The proposed framework, depicted in Figure.1 and Figure.2 and comprising online and offline phases, consists of three main components. The initial component introduces a local multitask transfer learning model with a loss function designed to leverage inner-group correlations among attributes. The second component presents an imbalanced data resolver based on MCC (Matthews Correlation Coefficient) without any adjustments to the pretrained model or loss function. The third component discusses prior knowledge used for local attribute grouping to facilitate local multitask learning.

The input and output of the learning framework will be images and their attribute vectors, respectively. However, with the local grouping role, the attribute vector’s size will be based on the number of attributes in each group. The dataset should be merged or split based on the local grouping role.

To evaluate the effectiveness of the proposed framework, we apply it in the fashion field and split the dataset into five local groups: fabric, shape, part, style, and texture. Because fashion has lesser intergroup correlations, the shared block should be designed to optimize the effectiveness of inner-group correlations to improve the overall performance. However, in crowd attributes (such as activities, locations, and participants), intergroup correlations should be taken into account to improve performance. Thus, the shared block should be modified to adapt to the context.

#2. Deep Multitask Learning

Our aim is to estimate a number of fashion attributes via a joint estimation model. However, with the dynamic attributes, MTL which supports creating a joint estimation model becomes vulnerable in the training phase due to its nonusability when the number of attributes increases. Thus, the local grouping method can help solve this situation.

#Framework in Detail

In the experiments, the proposed framework processes the query image and generates a confident score vector comprising 7 attribute scores per group across 5 groups, which is then thresholded to obtain binary outputs. The architecture is outlined in detail below.

Figure.1 illustrates the overall structure of the proposed method. For each group, a training set is assumed, consisting of $N$ fashion images, each with $M$ attributes. The dataset is represented as $D = {(X_i, Y_i)}$, where $X_i$ is the image and $Y_i$ is the label encoded as a one-hot vector. Inspired by prior researches, we employ an end-to-end DNN architecture as a shared block to learn joint representations for all tasks. The loss function employed is binary cross-entropy, and the activation function at the output layer is sigmoid, chosen for its simplicity and flexibility in modifying the DNN architecture.

#Network Architecture

NASNet automatically generates network architectures, constructing an optimal model by initially creating architectures on a smaller dataset and then scaling them up to a larger one. Through experiments, the search for the best cells is conducted on the CIFAR-10 dataset, which are subsequently applied to the ImageNet dataset by stacking multiple copies of them, each with their own parameters. The resulting model demonstrates a 1.2% improvement in top-1 accuracy compared to the best human-designed architectures. NASNet proves its effectiveness over previous architectures and offers a transfer learning model trained on a diverse ImageNet dataset. Leveraging the pretrained NASNet model on ImageNet, transfer learning is applied to the DeepFashion dataset to expedite convergence and enhance performance. Additionally, a dropout layer is incorporated with NASNet to mitigate overfitting. While utilizing the NASNet model generation algorithm to tailor a model for the DeepFashion dataset is a promising approach, the time and hardware resources required for NASNet's model generation and training from scratch are significant. Due to hardware limitations, only transfer learning is employed.

We will do experiments on NASNet architectures to find out which one is suitable for each specific task in our CFOR system. In our fashion retrieval experiments, the category classifier task and region classifier task are applied transfer with single-task learning, while fashion attribute recognition is applied local multitask learning. Besides, to adapt to large-scale datasets and reduce the effect of overfitting, we recommend changing the final fully connected layer to the global average pooling layer along with dropout.

#Next

In the next post, we will discover Searching and Indexing Method in the CFOR System as well as the effectiveness of the whole system.

In the previous part, we have explore the introduction about group dance scalability and the what is manifold. In this part, we introduct our main proposal Variational Phase Manifold Learning.

#Task Definition

Given an input music sequence $\mathbf{a} = \{a_1, a_t, ...,a_T\}$ with $t = \{1,..., T\}$ indicates the index of the music frames, our goal is to generate the group motion sequences of $N$ arbitrary dancers: $\mathbf{x} = \{x^1_1,..., x^1_T; ...;x^N_1,...,x^N_T\}$ where $x^n_t$ is the pose of $n$-th dancer at frame $t$. We use the 6D continuous rotation for every joint, along with 3D joint positions and velocities. Additionally, the corresponding 3D root translation vectors are concatenated into the pose representations to involve the trajectory of motion. Previous group dance methods, which generate the whole group at once, cannot deal with the increasing number of dancers and can only create group sequences up to a pre-defined number of dancers, due to the vast complexity of the architecture. In contrast, we aim to generate group dance with an unlimited number of dancers.

#Phase-conditioned Dance VAE

Our goal is to learn a continuous manifold such that the motion can be generated by sampling from this learned manifold. We assume that although different dancers within the same group may present visually distinctive movements, the properties of their motions, such as timing, periodicity, or temporal alignment are intrinsically similar. We aim to learn a generative phase representation for each group of dancer in order to synthesize their motion indefinitely. Our generative model is built upon the conditional Variational Autoencoder architecture, thanks to its diverse generation capability and fast sampling speed. However, instead of directly encoding the data into a Gaussian latent distribution as in common VAE approaches, we model the latent variational distribution by the phase parameters extracted from the latent motion curve, which we call variational phase manifold. The latent phase manifold is well-structured and can well describe key characteristics of motion (such as its timing, local periodicity, and transition), which benefits learning motion features.

The overview of our Phase-conditioned Dance VAE is illustrated in Figure 3. Specifically, the model contains three main networks: an encoder $\mathcal{E}$ to capture the approximate posterior distribution conditioned on both motion and music $q_\phi(\mathbf{z}|\mathbf{x},\mathbf{a})$, a prior network $\mathcal{P}$ to learn the conditional prior given only the music $p_\theta(\mathbf{z}|\mathbf{a})$ , and a decoder $\mathcal{D}$ to learn to reconstruct the data from the latent distribution $p_\theta(\mathbf{x}|\mathbf{z},\mathbf{a})$. The new motion is generated by sampling the frequency-domain parameters predicted by the prior network, which is then passed through the decoder network to reconstruct the motion in the original data space. Furthermore, we adopt Transformer-based architecture in each network to effectively capture long-range dependencies and holistic context of the dance sequence.

#Encoder

The encoder $\mathcal{E}$ is expected to take both the motion and music feature sequence as input, and produce a distribution over possible latent variables capturing the cross-modal relationship between them. To transform the joint input space into a learned phase manifold, we adopt the Transformer decoder architecture where the Cross-Attention mechanism is utilized to learn the relationship between the motion and the music. Accordingly, the output of the encoder is a batch of latent curves (i.e., the activation sequences per channel) that can particularly capture different spatial and temporal aspects of the motion sequence. However, instead of training the model to directly reconstruct the input motion from the extracted latent curves, we further enforce each channel of the latent space to have a periodic functional form (i.e., sinusoidal). This enables us to effectively learn a compact parameterization for each latent channel from a small set of parameters in the frequency domain.

#Generative Variational Phase Manifold

Here we focus on learning the periodicity and non-linear temporal alignment of the motion in the latent space. In particular, given the output latent curves from the encoder $\mathbf{L} = \mathcal{E}(x,a) \in \mathbb{R}^{D \times T}$ with $D$ is the number of desired phase channels to be extracted from the motion, we parameterize each latent curve in $\mathbf{L}$ using a sinusoidal function with amplitude ($\mathbf{A}$), frequency ($\mathbf{F}$), offset ($\mathbf{B}$) and phase shift ($\mathbf{S}$) parameters. To allow for variational phase manifold learning, we opt to predict two sets of parameters $\mathbf{\mu}_{\mathcal{E}} =\{\mathbf{\mu}^A; \mathbf{\mu}^F; \mathbf{\mu}^B; \mathbf{\mu}^S \}$ and $\mathbf{\sigma}_{\mathcal{E}} =\{\mathbf{\sigma}^A; \mathbf{\sigma}^F; \mathbf{\sigma}^B; \mathbf{\sigma}^S \}$, which corresponds to the mean and variance of $\mathbb{R}^{4D}$ dimensional Gaussian distribution:

To do so, we first apply differentiable Fast Fourier Transform (FFT) to each channel of the latent curve $\mathbf{L}$ and create the zero-indexed matrix of Fourier coefficients as $\mathbf{c}=FFT(\mathbf{L})$ with $\mathbf{c} \in \mathbb{C}^{D \times K+1}$, $K =\lfloor \frac{T}{2}\rfloor$. Correspondingly, we compute the per channel power spectrum $\mathbf{p} \in \mathbb{R}^{D \times K+1}$ as $\mathbf{p}_{i,j} = \frac{2}{N}|\mathbf{c}_{i,j}|^2$, where $i$ is the channel index and $j$ is the index for the frequency bands. Correspondingly, the distributional mean parameters of the periodic sinusoidal function are then calculated as follows:

where $\mathbf{f} = (0, \frac{1}{T},\dots,\frac{K}{T})$ is the frequencies vector. At the same time, the phase shift $\mathbf{S}$ is predicted using a fully-connected (FC) layer with two $\arctan$ activation as:

To predict the distributional variance of the phase amplitude and phase shift parameters $\{\mathbf{\sigma}^A, \mathbf{\sigma}^S\}$, We additionally apply a separate two-layer MLP network over each channel of the latent curves. The variational latent phase parameters are sampled by utilizing parameterization trick, i.e., $\mathbf{A}\sim\mathcal{N}(\mathbf{\mu}^A,\mathbf{\sigma}^A)$ and $\mathbf{S}\sim\mathcal{N}(\mathbf{\mu}^S,\mathbf{\sigma}^S)$. In our experiments, we find that sampling the phase frequency $\mathbf{F}$ and offset $\mathbf{B}$ often produce unstable and non-coherent group movements. This might be because the frequency amplitudes of the dancers within the same group are likely to associate with the rhythmic pattern of the musical beats while the offsets capture their alignment, thereby should be consistent with each other. Therefore, we treat those parameters as deterministic by constraining their variance to zero.

Finally, the sampled set of phase parameters $\mathbf{z} = \{\mathbf{A};\mathbf{F};\mathbf{B};\mathbf{S}\}$ are used to reconstruct a parametric latent space consisting of multiple periodic curves to represent each intrinsic property of the motion by:

where $\mathcal{T}$ is a known time window series obtained by evenly spacing the timesteps from $0$ to $T$. Intuitively this curve construction procedure can be viewed as a "quantization" layer to enforce the network to learn to represent the motion features in the frequency domain, which is useful in representing different aspects of human motion such as their timing and periodicity. In the last step, a decoder is utilized to reconstruct the original motion signals from the set of parametric latent curves.

#Decoder

To decode the latent space into the original motion space, previous works have to use a sinusoidal positional encoding sequence with duration $T$ as the proxy input to the sequence decoder. This is because their latent space is only formed by single latent vectors following a Gaussian distribution, which cannot span the time dimension. However, we observe that it usually results in unstable and inconsistent movements, as the proxy sequence is generic and usually contains less meaningful information for the decoder. Meanwhile, our method does not suffer from this problem as our latent space is built on multiple curves that can represent the motion information through time, thanks to the phase parameters. Subsequently, our decoder $\mathcal{D}$ is based on Transformer decoder architecture that takes the constructed parametric latent curve, as well as the music features as inputs, to reconstruct the corresponding dance motions. Here, we also utilize the cross-attention model where we consider the sequence of and music features as key and value along with the sampled latent curves as the query. The output of the decoder is a sequence of $T$ vectors in $\mathbb{R}^D$, which is then projected back to the original motion dimensions through a linear layer, to obtain the reconstructed outputs $\hat{\mathbf{x}}=p_\theta(\mathbf{x}|\mathbf{z},\mathbf{a})$. We additionally employ a global trajectory predictor to predict the global translation of the root joint based on the generated local motions, in order to avoid intersection problems between dancers.

#Prior Network.

Since the ground-truth motion is generally inaccessible at test time (i.e., we only have access to the music), we also need to learn a prior $\mathcal{P}$ to match the posterior distribution of motion from which the latent phase can be sampled. Specifically, We follow the manifold procedure to predict the Gaussian distribution conditioned on the music sequence $\mathbf{a}$, which is then used for sampling the latent phases:

where a Transformer encoder is used to encode the input conditioning music sequence and predict the corresponding $\mathbf{\mu}_{\mathcal{P}}$ and $\mathbf{\sigma}_{\mathcal{P}}$. We implement the prior network similarly to the encoder network, however, we use self-attention mechanism to capture the global music context. Learning the conditional prior is crucial for the conditional VAE to generalize to diverse types of music and motion. Intuitively speaking, each latent variable $\mathbf{z}$ is expected to represent possible dance motions $\mathbf{x}$ conforming to the music context $\mathbf{a}$. Therefore, the prior should be able to encode different latent distributions given different musics.

#Next

In the next part, we will explore the training procedure and experimental setups to validate the effectiveness of the proposed method.

In the previous article, we delved into integrating the contrastive divergence loss function into federated learning, exploring its potential benefits for enhancing model performance and tackling non-IID data issues in autonomous driving contexts. In this follow-up piece, we delve into various federated learning configurations and present experimental findings that support the efficacy of our approach.

#1. Implementation

Dataset: Our experimentation involves three datasets (see Table 1): Udacity+, Gazebo Indoor, and Carla Outdoor. Gazebo and Carla datasets exhibit non-IID characteristics, while Udacity+ represents a non-IID variant of the Udacity dataset.

Table 1: The Statistic of Datasets in Our Experiments.

Network Topology: Our experimentation encompasses three distinct federated topologies, namely the Internet Topology Zoo (Gaia), North American data centers (NWS), and the Zoo Exodus network (Exodus). The primary focus is on the Gaia topology, while supplementary insights from the NWS and Exodus topologies are provided in our ablation study.

Training: Within each silo, model training is executed with a batch size of 32 and a learning rate set at 0.001, facilitated by the Adam optimizer. The local training regimen within each silo precedes the transmission and aggregation of models using the specified global aggregation equation. The training regimen spans 3,600 communication rounds and leverages a simulation environment akin to that described in Nguyen et al. (2022), powered by an NVIDIA 1080 GPU.

Baselines: Our comparative analysis involves several contemporary methods across diverse learning scenarios, including Random and Constant baselines as outlined by Loquercio et al. (2018). Within the Centralized Local Learning (CLL) scenario, we utilize Inception-V3, MobileNet-V2, VGG-16, and Dronet as baseline models. In the context of Server-based Federated Learning (SFL), our comparison extends to FedAvg, FedProx, and STAR. For the Decentralized Federated Learning (DFL) setting, our evaluation includes MATCHA, MBST, and FADNet. Model effectiveness is assessed using Root Mean Square Error (RMSE) and Mean Absolute Error (MAE), while wall-clock time (ms) serves as a metric for training duration.

#2. Qualitative Results

In practice, we've noticed that the initial phases of federated learning often yield subpar accumulated models. Unlike other approaches that tackle the non-IID issue by refining the accumulation step whenever silos transmit their models, we directly mitigate the impact of divergence factors during the local learning phase of each silo. Our method aims to minimize the discrepancy between the distribution of accumulated weights from neighboring silos in the backbone network (representing divergence factors) and the weights specific to silo $i$ in the sub-network (comprising locally learned knowledge). Once the distribution between silos achieves an acceptable level of synchronization, we reduce the influence of the sub-network and prioritize the steering angle prediction task. Inspired by the contrastive loss of the original Siamese Network, our proposed Contrastive Divergence Loss is formulated as follows:

Table 2: Performance comparison between different methods. The Gaia topology is used.

Table above summarizes the performance comparison between our proposed method and recent state-of-the-art approaches. The results indicate that our CDL under the Siamese setup with two ResNet-8 models outperforms other methods by a significant margin. Notably, our approach achieves substantial reductions in both RMSE and MAE across all three datasets: Udacity+, Carla, and Gazebo. Despite not increasing the network's parameter count, CDL introduces a larger model size during training due to the additional sub-network required by the Siamese setup. Additionally, our CDL with ResNet-8 demonstrates superior performance compared to other baselines, particularly in the DFL learning scenario, and to a lesser extent in SFL and CLL setups.

#3. Contrastive Divergence Loss Analysis

CDL Performance Across Various Topologies In practice, training federated algorithms becomes more complex as the topology involves more vehicle data silos. To assess the efficacy of our CDL, we conduct training experiments and compare the results with other baseline methods across different topologies. Table 3 presents the performance comparison of DroNet, FADNet, and our CDL with a ResNet-8 backbone when trained using DFL across three distributed network infrastructures with varying numbers of silos: Gaia (11 silos), NWS (22 silos), and Exodus (79 silos). The table clearly demonstrates that our CDL consistently achieves superior results across all topology configurations. In contrast, DroNet encounters divergence issues, and FADNet exhibits suboptimal performance, particularly in the Exodus topology with 79 silos.

Table 3: Performance under different topologies.

CDL with Various Architectures Our CDL, functioning as a loss function, exhibits versatility across different network architectures when integrated into the Siamese setup, leading to performance enhancements. Figure.1 showcases the efficacy of CDL across diverse networks such as DroNet, FADNet, Inception, MobileNet, and VGG-16 within the Gaia Network framework in the DFL scenario. The outcomes demonstrate CDL's efficacy in mitigating the non-IID challenge across varied architectures, consistently elevating performance.

CDL with IID Data Figure.2 illustrates CDL's efficacy across various data distributions. While CDL is primarily tailored for addressing the non-IID challenge, it also demonstrates marginal performance enhancements when applied to models trained on IID data distributions. Leveraging the Siamese setup, CDL inherits traits and behaviors akin to triplet loss. Given triplet loss's established effectiveness with IID data, it becomes evident that CDL can similarly augment model performance in scenarios where IID data is utilized.

#3. Ablation Study

Figure.3 illustrates the training results in RMSE of our two baselines, DroNet and FADNet, as well as our proposed CDL. The results showcase the convergence ability of the mentioned methods across three datasets (Udacity+, Gazebo, Carla) with NWS and Gaia topology. It is evident that our proposed CDL can attain a superior convergence point compared to the two baselines. While other methods (DroNet and FADNet) struggled to converge or exhibited poor convergence trends, our proposed CDL demonstrates better overcoming of local optimal points and shows less bias towards any specific silo.

#4. Discussion

Although our method exhibits promising results, there are several areas for potential improvement that warrant consideration for future work:

• Our CDL is specifically designed to address the non-IID problem, meaning its effectiveness heavily depends on the presence of non-IID characteristics within the autonomous driving data. Thus, in scenarios where data distributions across vehicles are relatively consistent or lack significant non-IID factors, the proposed contrastive divergence loss may only lead to limited performance enhancements.

• While our proposal has been validated on autonomous driving datasets, real-world testing on actual vehicles has not yet been conducted. Conducting a study involving various driving scenarios, such as interactions with pedestrians, cyclists, and other vehicles, could provide further validation of our method's efficacy.

• Although our approach is tailored for autonomous driving applications, its underlying principles may have applicability in other domains where non-IID data is prevalent. Exploring its effectiveness in areas like healthcare, IoT, and industrial settings could expand its potential impact.

#Conclusion

We presented a new method to address the non-IID problem in federated autonomous driving using contrastive divergence loss. Our method directly reduces the effect of divergence factors in the learning process of each silo. The experiments on three benchmarking datasets demonstrate that our proposed method performs substantially better than current state-of-the-art approaches. In the future, we plan to test our strategy with more data silos and deploy the trained model using an autonomous vehicle on roads.

In this section, we will mention about ontology, fashion ontology, and its related information and present the contributions of object ontology to the CFOR system.

#1. Ontology Definition for CFOR System

As described by Guarino, ontology is a "formal, explicit specification of a shared conceptualization." Typically, ontologies consist of concepts and their hierarchical structure, aiding in organizing information within a domain. A complete ontology typically includes concepts, relations, and axioms. Additionally, ontologies offer several key advantages:

• Describing domain knowledge through a semantic hierarchical tree, with concepts represented as nodes identified by words or phrases.
• Bridging the semantic gap in various tasks, including those in computer vision and other disciplines.
• Enhancing software engineering practices by improving flexibility, reliability, specification, and reusability.
• Supporting multitask problem-solving capabilities.

Any proposed ontology should satisfy two fundamental criteria:

• Wide recognition within the community.
• Feasibility for formalization using mathematical expressions, enabling digitization.

In our approach, we employ ontological engineering to facilitate communication and information sharing across different levels of data abstraction involved in image fashion retrieval, detection, and information tagging.

The object ontology comprises two primary levels: coarse-grained and fine-grained.

• At the coarse level, the object ontology includes regions, categories, or high-level conceptual entities, which leverage global features extracted by deep networks for similarity retrieval. However, these deep features are treated as black boxes, lacking explicit semantic information to aid users in their search process.
• At the fine-grained level, the object ontology encompasses attributes that provide detailed descriptions of objects.

In our experiment, we focus on describing the object "Fashion." The fashion ontology is constructed using prior knowledge and information from the DeepFashion dataset, along with ontology definitions introduced by Guarino. See Figure.1 for an illustration of the fashion ontology.

The fashion ontology developed comprises three primary semantic levels: 1. Regions: Representing areas such as Top, Bottom, and Body. 2. Categories: Specific objects associated with each region, such as dresses or robes for the Body region. 3. Attributes: Describing detailed visual concepts like denim or fur.

To streamline the discussion, our investigation focuses on the object fashion across three regions (Top, Body, and Bottom), select categories within these regions, and their respective attributes.

Within the CFOR system, a query image undergoes processing starting from the coarse level of the object ontology to identify the region and category of the corresponding object. Subsequently, the object proceeds to the fine-grained concept ontology to ascertain attributes. Once all necessary information is obtained, the object undergoes indexing and similarity distance computation to identify similar images in the database, ranked by a cumulative score derived from similarity scores of global features and attribute learning between the query image and target database images. For a detailed illustration, refer to Figure.2.

#2. Fashion Object Ontology

In this section, we introduce the fashion object ontology. Within the fashion domain, we categorize semantic fashion concepts based on regions. Each region encompasses a detailed ontology comprising categories and attributes. To facilitate experiments using the DeepFashion dataset, we extend the fashion ontology within the "Clothes" branch (refer to Figure 9). It's essential to emphasize that the proposed ontology is not specific to any application and should be viewed as a flexible foundation.

The fashion object ontology consists of multiple levels of concepts, with relations between each level to articulate their associations. Two primary relations are employed: 1. "Part of": This relation specifies that the concepts are components of the main concept. 2. "Has a": This relation describes the main concept in detail.

For this study, we concentrate solely on the Clothes branch to ensure equitable comparisons with other methodologies. The Clothes taxonomy comprises 50 distinct categories. A clothing region taxonomy has been established (refer to Figure.3), organizing all clothing categories hierarchically. The first level of this hierarchy represents the most general clothing region, with three primary regions defined: 1. Top (e.g., tee and tank) 2. Bottom (e.g., skirt and jeans) 3. Body (e.g., dress and robe)

#3. Fine-Grained Object Ontology

Fine-grained object ontology is used to describe objects at the attribute level. Semantic information such as attributes can be useful for a customer to retrieve (see Figure.4). It is important to note that the proposed ontology is not application dependent and should be considered as an extensible basis.

Cloth attributes vary across different levels—some attributes, like color, are common across all cloth regions, while others are specific to certain regions or categories. Our ontology is structured into two main parts, each detailed in the following sections: 1. Specific fashion concepts—pertaining to particular characteristics of clothes such as fabric, part, and style. 2. Visual concepts—related to popular visual characteristics like color, shape, and texture, not exclusive to fashion.

Rudd et al. demonstrated in a study that a multitask learning-based model outperforms a combination of single-task learning-based models in face attribute prediction. While this approach shows promising results for fashion attributes as well, there's a significant difference in the quantity of attributes between faces and fashion items. This disparity can pose challenges in scaling the system, such as in training and storage requirements. To address this, we propose applying local multitask learning to attribute learning, providing more flexibility. Further explanation is provided in the subsequent sections.

#Next

In the next post, we will discover Attribute Learning and its correlation with multitask learning.

Generating group dance motion from the music is a challenging task with several industrial applications. Although several methods have been proposed to tackle this problem, most of them prioritize optimizing the fidelity in dancing movement, constrained by predetermined dancer counts in datasets. This limitation impedes adaptability to real-world applications. Our study addresses the scalability problem in group choreography while preserving naturalness and synchronization.

In particular, we propose a phase-based variational generative model for group dance generation on learning a generative manifold. Our method achieves high-fidelity group dance motion and enables the generation with an unlimited number of dancers while consuming only a minimal and constant amount of memory. The intensive experiments on two public datasets show that our proposed method outperforms recent state-of-the-art approaches by a large margin and is scalable to a great number of dancers beyond the training data.

#Introduction

The proliferation of digital social media platforms has significantly increased the popularity of creating and sharing dance videos. This surge in interest has led to the daily production and consumption of millions of dance videos across various online platforms, attracting attention from the research community in fields such as computer vision and computer graphics. Recent advancements in these areas have focused on generating authentic dance movements in response to music, with broad applications spanning animation, virtual idols, virtual metaverses, and dance education. These technologies provide powerful tools for artists, animators, and educators, enhancing creativity and enriching the dance experience for both performers and audiences.

To address these challenges, we propose a novel approach to scalable group dance generation using a phase-based variational generative model, termed Phase-conditioned Dance VAE (PDVAE). Unlike traditional variational autoencoders that operate in high-dimensional motion space and often struggle to capture temporal dynamics, PDVAE leverages phase parameters in the frequency domain to represent the latent motion space. This enables the generation of realistic and synchronized group dance performances without increasing computational and memory costs, even as the number of dancers grows. PDVAE provides a flexible and efficient solution for generating crowd-scale dance animations, with potential applications in diverse fields such as entertainment, virtual reality, education, and media production.

In this work, we aim to advance the state-of-the-art in scalable group dance generation by overcoming the limitations of existing methods and demonstrating the feasibility of generating large-scale, natural, and synchronized dance performances efficiently.

To summarize, our key contributions are as follows: - We introduce PDVAE, a phase-based variational generative model for scalable group dance generation. The method focuses on generating large-scale group dance under limited resources. - To effectively learn the manifold that is group-consistent (i.e., dancers within a group lie upon the same manifold), we propose a group consistency loss that enforces the networks to encode the latent phase manifold to be identical for the same group given the input music. - Extensive experiments along with thorough user study evaluations demonstrate the state-of-the-art performance of our model while achieving effective scalability.

#Related Works

#Music-driven Choreography

Crafting natural human choreography derived from music poses a complex challenge, encompassing the need for synchronization, coherence, and expressiveness between movement and musical inputs. Earlier approaches often relied on music-motion similarity constraints to ensure alignment between the generated dance and the accompanying music. Many of these methods employ heuristic algorithms to stitch together pre-existing dance segments from limited music-dance databases, successfully producing extended and realistic dance sequences. However, such techniques are constrained when attempting to generate novel dance fragments, as they depend heavily on pre-defined segments rather than innovative motion generation .

Recent advancements have focused on utilizing deep learning architectures to map music into dance motions. Various techniques, including Convolutional Networks (CNN) , Recurrent Networks (RNN) , Graph Neural Networks (GNN) , Generative Adversarial Networks (GAN) , and Transformer models , have been explored for dance generation. These models typically rely on inputs such as the current music and a brief history of previous dance motions to predict the next human poses in a sequence. For instance, innovations in multi-modal feature fusion have enabled the simultaneous integration of music and text, producing dance sequences guided by both musical and textual cues .

Despite the progress made by these methods, generating synchronized and coordinated dance movements for multiple dancers remains a significant challenge. Achieving harmony between multiple dancers requires not only temporal alignment but also the consideration of spatial relationships and interactions between performers. This adds complexity to the generation process, making it difficult for current techniques to manage multiple dancers cohesively. Additionally, these methods are often constrained by the limited number of dancers present in their training datasets .

Several recent works have sought to address these limitations. For instance, Perez et al. propose a multimodal transformer combined with a normalizing-flow-based decoder to predict a distribution of possible future poses, offering improved flexibility in motion generation. Feng et al. introduce a motion repeat constraint for long-term generation, allowing their model to generate future frames while taking into account historical dance motions. Le et al. further explore group dance by examining consistency and diversity among dancers, ensuring that generated movements maintain coherence across multiple performers. However, these methods are still limited by the number of dancers depicted in training datasets, restricting their scalability for larger group performances.

Overall, while significant strides have been made in music-driven dance generation, further research is needed to overcome the challenges of scalability and synchronization in group dance synthesis.

#Motion Manifold Learning

Motion manifold learning has garnered significant attention in computer vision and artificial intelligence, primarily aiming to understand the fundamental structures underlying human movement and dynamics. This approach offers the capability to generate human motion patterns, providing insights into intrinsic motion dynamics, managing nonlinear relationships within motion data, and learning contextual and hierarchical representations. Consequently, numerous methodologies have emerged, each contributing distinct perspectives to advance the comprehension and synthesis of human motion.

Holden et al. pioneered motion manifold learning by generating character movements from high-level parameters mapped to a motion manifold, eliminating the need for manual preprocessing while enabling natural, smooth post-generation editing of motion sequences. MotionCLIP introduced a 3D human motion autoencoder aligned with CLIP's semantic space, facilitating semantic text-based motion generation, disentangled editing, and abstract language specification. This approach capitalizes on CLIP's rich semantic knowledge, integrating it within the motion manifold for enhanced control and interpretation of human movement. Sun et al. further advanced this field by employing VQ-VAE to learn a low-dimensional motion manifold, effectively refining motion sequences to improve coherence and continuity.

#Next

In the next part, we will dive deeply into the main proposal that leveragw manifold learning to handle scalability of group dance generation.

In the previous post, we delved into the realm of federated learning in the context of autonomous driving, exploring its potential and the challenges posed by non-IID data distribution. We also discussed how contrastive divergence offers a promising avenue to tackle the non-IID problem in federated learning setups. Building upon that foundation, in this post, we will delve deeper into the integration of contrastive divergence loss into federated learning frameworks. We'll explore the mechanics of incorporating this loss function into the federated learning process and examine its potential implications for improving model performance and addressing non-IID data challenges in autonomous driving scenarios. We unravel the intricacies of leveraging contrastive divergence within federated learning paradigms to advance the capabilities of autonomous driving systems.

#1. Overview

Motivation: The effectiveness of federated learning algorithms in autonomous driving hinges on two critical factors: firstly, the ability of each local silo to glean meaningful insights from its own data, and secondly, the synchronization among neighboring silos to mitigate the impact of the non-IID problem. Recent efforts have primarily focused on addressing these challenges through various means, including optimizing accumulation processes and optimizers, proposing novel network topologies, or leveraging robust deep networks capable of handling the distributed nature of the data. However, as highlighted by Duan et al., the indiscriminate adoption of high-performance deep architectures and their associated optimizations in centralized local learning scenarios can lead to increased weight variance among local silos during the accumulation process in federated setups. This variance detrimentally impacts model convergence and may even induce divergence, underscoring the need for nuanced approaches to ensure the efficacy of federated learning in autonomous driving contexts.

Siamese Network Approach: In our study, we propose a novel approach to directly tackle the non-IID problem within each local silo by addressing the challenges of learning optimal features and achieving synchronization separately. Our strategy involves implementing \textit{two distinct networks within each silo}: one network is dedicated to extracting meaningful features from local image data, while the other focuses on minimizing the distribution gap between the current model weights and those of neighboring silos. To facilitate this, we employ a Siamese Network architecture, comprising two branches. The first branch, serving as the backbone network, is tasked with learning local image features for autonomous steering using a local regression loss $\mathcal{L}_{\rm {lr}}$, while simultaneously incorporating a positive contrastive divergence loss $\mathcal{L}_{\rm {cd^+}}$ to assimilate knowledge from neighboring silos. Meanwhile, the second branch, referred to as the sub-network, functions to regulate divergence factors arising from the backbone's knowledge through a contrastive regularizer term $\mathcal{L}_{\rm {cd^-}}$. See Figure.1 for more detail.

In practice, the sub-network initially adopts the same weights as the backbone during the initial communication round. However, starting from the subsequent communication rounds, once the backbone undergoes accumulation using Equation below, each silo's local model is trained using the contrastive divergence loss. The sub-network produces auxiliary features of identical dimensions to the output features of the backbone. Throughout training, we anticipate minimal discrepancies in weights between the backbone and the sub-network when employing the contrastive divergence loss. Synchronization of weights across all silos occurs when gradients from the backbone and sub-network learning processes exhibit minimal disparity.

where $\mathcal{L}_{\rm {lr}}$ is the local regression loss for autonomous steering.

#2. Contrastive Divergence Loss

In practice, we've noticed that the initial phases of federated learning often yield subpar accumulated models. Unlike other approaches that tackle the non-IID issue by refining the accumulation step whenever silos transmit their models, we directly mitigate the impact of divergence factors during the local learning phase of each silo. Our method aims to minimize the discrepancy between the distribution of accumulated weights from neighboring silos in the backbone network (representing divergence factors) and the weights specific to silo $i$ in the sub-network (comprising locally learned knowledge). Once the distribution between silos achieves an acceptable level of synchronization, we reduce the influence of the sub-network and prioritize the steering angle prediction task. Inspired by the contrastive loss of the original Siamese Network, our proposed Contrastive Divergence Loss is formulated as follows:

where $\mathcal{L}_{\rm {cd^+}}$ is the positive contrastive divergence term and $\mathcal{L}_{\rm {cd^-}}$ is the negative regularizer term; $\mathcal{H}$ is the Kullback-Leibler Divergence loss function

where $\hat{y}$ is the predicted representation, $y$ is dynamic soft label.

Consider $\mathcal{L}_{\rm {cd^+}}$ in Equation above as a Bayesian statistical inference task, our goal is to estimate the model parameters $\theta^{b*}$ by minimizing the Kullback-Leibler divergence $\mathcal{H}(\theta^b_i, \theta^s_i)$ between the measured regression probability distribution of the observed local silo $P_0 (x|\theta^s_i)$ and the accumulated model $P (x|\theta^b_i)$. Hence, we can assume that the model distribution has a form of $P (x|\theta^b_i) = e^{-E(x,\theta^b_i)}/Z(\theta^b_i)$, where $Z(\theta^b_i)$ is the normalization term. However, evaluating the normalization term $Z(\theta^b_i)$ is not trivial, which leads to risks of getting stuck in a local minimum. Inspired by Hinton, we use samples obtained through a Markov Chain Monte Carlo (MCMC) procedure with a specific initialization strategy to deal with the mentioned problem. Additionally inferred from Equation above, the $\mathcal{L}_{\rm {cd^+}}$ can be expressed under the SGD algorithm in a local silo by setting:

where $Q_{\theta^b_i} (x|\theta^s_i)$ is the measured probability distribution on the samples obtained by initializing the chain at $P_0 (x|\theta^s_i)$ and running the Markov chain forward for a defined step.

Consider $\mathcal{L}_{\rm {cd^-}}$ regularizer in Equation above as a Bayesian statistical inference task, we can calculate $\mathcal{L}_{\rm {cd^-}}$ as in Equation above, however, the role of $\theta^s$ and $\theta^b$ is inverse:

We note that the key difference is that while the weight $\theta^b_i$ of the backbone is updated by the accumulation process from Equation above, the weight $\theta^s_i$ of the sub-network, instead, is not. This lead to different convergence behavior of contrastive divergence in $\mathcal{L}_{\rm {cd^+}}$ and $\mathcal{L}_{\rm {cd^-}}$. The negative regularizer term $\mathcal{L}_{\rm {cd^-}}$ will converge to state $\theta^{s*}_i$ provided $\frac{\partial E}{\partial \theta^s_i}$ is bounded:

for any $\mathbf{k}_1$ constraint. Note that, $\mathbf{K}^m_{\theta^s}$ is the transition kernel.

Note that the negative regularizer term $\mathcal{L}_{\rm {cd^-}}$ is only used in training models on local silos. Thus, it does not contribute to the accumulation process of federated training.

#3. Total Training Loss

Local Regression Loss. We use mean square error (MAE) to compute loss for predicting the steering angle in each local silo. Note that, we only use features from the backbone for predicting steering angles.

where $\hat{\xi}_i$ is the ground-truth steering angle of the data sample $\xi_i$ collected from silo $i$.

Local Silo Loss. The local silo loss computed in each communication round at each silo before applying the accumulation process is described as:

In practice, we observe that both the contrastive divergence loss $\mathcal{L}_{\rm {cd}}$ to handle the non-IID problem and the local regression loss $\mathcal{L}_{\rm {lr}}$ for predicting the steering angle is equally important and indispensable.

Combining all losses together, at each iteration $k$, the update in the backbone network is defined as:

where $\mathcal{L}_{\rm {b}} = \mathcal{L}_{\rm {lr}} + \mathcal{L}_{\rm {cd^+}}$, $u$ is the number of local updates.

In parallel, the update in the sub-network at each iteration $k$ is described as:

#Next

In the next post, we will evaluate the effectiveness of Constrative Divergence Loss in dealing with Non-IID problem in Federated Autonomous Driving.

Federated learning has been widely applied in autonomous driving since it enables training a learning model among vehicles without sharing users' data. However, data from autonomous vehicles usually suffer from the non-independent-and-identically-distributed (non-IID) problem, which may cause negative effects on the convergence of the learning process. In this paper, we propose a new contrastive divergence loss to address the non-IID problem in autonomous driving by reducing the impact of divergence factors from transmitted models during the local learning process of each silo. We also analyze the effects of contrastive divergence in various autonomous driving scenarios, under multiple network infrastructures, and with different centralized/distributed learning schemes. Our intensive experiments on three datasets demonstrate that our proposed contrastive divergence loss significantly improves the performance over current state-of-the-art approaches.

#1. Introduction

Autonomous driving represents a burgeoning field wherein vehicles navigate without human intervention, employing a blend of vision, learning, and control algorithms to perceive and react to environmental changes. While traditional approaches heavily rely on supervised learning and data collection for model training, recent efforts, such as those by Bergamini et al., Chen et al., and Wang et al., have proposed various solutions to different challenges in autonomous driving. However, data collection poses privacy concerns as user data is shared with third parties, prompting a shift towards federated learning (FL). FL allows multiple parties to collaboratively train models without sharing raw data, thereby preserving user privacy while enabling autonomous vehicles to collectively learn predictive models from diverse datasets.

Typically, there are two primary federated learning scenarios: Server-based Federated Learning (SFL) and Decentralized Federated Learning (DFL). In SFL, a central node coordinates the training process and aggregates contributions from all clients, enhancing data privacy by transmitting only model weights. However, the reliance on central nodes in SFL can potentially bottleneck the system due to data transmission constraints. In contrast, DFL operates without a central server, employing a fully distributed network architecture. In autonomous driving, several works have explored both DFL and SFL to address different problems such as collision avoidance, trajectory prediction, and steering prediction.

In practical application, both Server-based Federated Learning (SFL) and Decentralized Federated Learning (DFL) approaches exhibit their own advantages and limitations, yet both are susceptible to the non-IID problem inherent in federated learning. The non-IID problem, as described by Sattler et al. and Wang et al., arises when data partitioning across silos exhibits significant distribution shifts. Particularly in autonomous driving, this issue poses significant challenges during the accumulation process across vehicle silos. Each vehicle's unique driving patterns, weather conditions, and road types contribute to differences in data distribution, exacerbating the non-IID problem. For instance, data collected from vehicles on highways may differ substantially from data collected in urban settings. This discrepancy can lead to difficulties in constructing robust and accurate learning models, where reliance on data from a specific context may result in poor performance in others.

Previous studies have tackled the non-IID problem through various approaches such as optimizing the accumulation step, incorporating normalization into the global model, fine-tuning global model weights via distillation, or aligning the distribution between the global model and local ones. These methods typically refine global model weights to adapt to divergence factors arising from diverse distributions across local datasets. However, this optimization process can be challenging due to factors like determining the optimal accumulation step size for each local silo, managing network topology disconnections and bottlenecks, and ensuring consistency between local and global objectives.

In the paper, we introduce a novel Contrastive Divergence Loss (CDL) to tackle the non-IID problem in autonomous driving. Unlike other methods that wait for local model learning before addressing the non-IID issue during global aggregation, our CDL loss directly mitigates the impact of divergence factors throughout each local silo's learning process. This approach simplifies the adaptation of distribution between neighboring silos compared to handling the non-IID problem in the global model. Consequently, each local model becomes more resilient to changes in data distribution, allowing the use of typical accumulation methods like FedAvg for global weights without concerns about non-IID effects on convergence. The intensive experiments on three autonomous driving datasets verify our observation and show significant improvements over state-of-the-art methods.

#2. Related Works

Autonomous Driving: Autonomous driving has emerged as a prominent research area in recent years, with a focus on leveraging deep learning for various tasks such as object detection, trajectory prediction, and autonomous control. For instance, Xin et al. proposed a recursive backstepping steering controller, while Xiong et al. analyzed nonlinear dynamics behavior using proportional control laws. Yi et al. presented an algorithm for self-reconfigurable robots during waypoint navigation, and Yin et al. combined model predictive control with covariance steering theory for robust autonomous driving systems.

Federated Learning for Autonomous Driving: Federated learning offers a privacy-aware solution for collaborative machine learning without sharing local data. It has gained traction in autonomous driving and intelligent transport systems, addressing communication, computation, and storage efficiency. Various works have explored federated learning for autonomous driving tasks such as steering angle prediction and turning signal prediction. However, challenges remain, including non-IID data distribution among participants, which recent works primarily address through accumulation processes rather than local silo optimization.

Contrastive Divergence: Contrastive models have gained attention in federated learning for handling heterogeneity in local data distribution. While contrastive learning has been applied to various datasets, its potential for mitigating non-IID data effects in federated autonomous driving remains underexplored. Most existing works focus on optimizing frameworks in server-based or P2P federated learning, or adjusting the accumulation process, with limited consideration of contrastive loss function behavior in federated autonomous driving scenarios.

#3. Preliminary

We summarize the notations of our paper in Table.1.

We consider each autonomous vehicle as a data silo. Our goal is to collaboratively train a global driving policy $\theta$ from $N$ silos by aggregating all local learnable weights $\theta_i$ of each silo. Each silo computes the current gradient of its local loss function and then updates the model parameter using an optimizer. Mathematically, in the local update stage, at each silo $i$, in each iteration $k$, the model weights of the local silo can be computed as:

where $\mathcal{L}_{\rm {lr}}$ is the local regression loss for autonomous steering. To update the global model, each silo interacts with the associated ones through a predefined topology:

In practice, the local model in each silo is a deep network that takes the RGB images as inputs and predicts the associated steering angles

#Next

In the next post, we will introduce our proposal with contrastive divergence loss.

In previous part, we have discussed about the proposal to deal with fine-grained image classification. In this part, we will verify the effectiveness and efficiency of the proposal.

#1. Experimental Setup

Dataset. We evaluate our method on three popular fine-grained datasets: CUB-200-2011, Stanford Dogs and FGVC Aircraft (See Table 1).

Table 1: Fine-grained classification datasets in our experiments.

Implementation. All experiments are conducted on an NVIDIA Titan V GPU with 12GB RAM. The model is trained using Stochastic Gradient Descent with a momentum of 0.9. The maximum number of epochs is set at 80; the weight decay equals 0.00001, and the mini-batch size is 12. Besides, the initial learning rate is set to 0.001, with exponential decay of 0.9 after every two epochs. Based on validation results, the number of top-k ambiguity classes is set to 10, while the parameters $d_{\phi}$, $\alpha$ are set to $0.1$ and $0.5$, respectively.

Baseline. To validate the effectiveness and generalization of our method, we integrate it into 7 different deep networks, including two popular Deep CNN backbones, Inception-V3 and ResNet-50; and five fine-grained classification methods: WS, DT, WS_DAN, MMAL, and the recent transformer work ViT. It is worth noting that we only add our Self Assessment Classifier into these works, other setups and hyper-parameters for training are kept unchanged when we compare with original codes.

#2. Experimental Results

Table.2 summarises the contribution of our Self Assessment Classifier (SAC) to the fine-grained classification results of different methods on three datasets CUB-200-2011, Stanford Dogs, and FGVC Aircraft. This table clearly shows that by integrating SAC into different classifiers, the fine-grained classification results are consistently improved. In particular, we observe an average improvement of $+1.3$, $+1.2$, and $+1.2$ in the CUB-200-2011, Stanford Dogs, and FGVC Aircraft datasets, respectively.

Table: Contribution (% Acc) of our Self Assessment Classifier (SAC) on fine-grained classification results.

#3. Qualitative Results

Attention Maps. Figure.1 illustrates the visualization of attention maps between image feature maps and each ambiguity class. The visualization indicates that by employing our Self Assessment Classifier, each fine-grained class focuses on different informative regions.

Prediction Results. Figure.2 illustrates the classification results and corresponding localization areas of different methods. In all samples, we can see that our SAC focuses on different areas based on different hard-to-distinguish classes. Thus, the method can focus on more meaningful areas and also ignore unnecessary ones. Hence, SAC achieves good predictions even with challenging cases.

#Conclusion

We introduce a Self Assessment Classifier (SAC) which effectively learns the discriminative features in the image and resolves the ambiguity from the top-k prediction classes. Our method generates the attention map and uses this map to dynamically erase unnecessary regions during the training. The intensive experiments on CUB-200-2011, Stanford Dogs, and FGVC Aircraft datasets show that our proposed method can be easily integrated into different fine-grained classifiers and clearly improve their accuracy.

Extracting discriminative features plays a crucial role in the fine-grained visual classification task. Most of the existing methods focus on developing attention or augmentation mechanisms to achieve this goal. However, addressing the ambiguity in the top-k prediction classes is not fully investigated. In this paper, we introduce a Self Assessment Classifier, which simultaneously leverages the representation of the image and top-k prediction classes to reassess the classification results. Our method is inspired by self-supervised learning with coarse-grained and fine-grained classifiers to increase the discrimination of features in the backbone and produce attention maps of informative areas on the image. In practice, our method works as an auxiliary branch and can be easily integrated into different architectures. We show that by effectively addressing the ambiguity in the top-k prediction classes, our method achieves new state-of-the-art results on CUB200-2011, Stanford Dog, and FGVC Aircraft datasets. Furthermore, our method also consistently improves the accuracy of different existing fine-grained classifiers with a unified setup.

#1. Introduction

The task of fine-grained visual classification involves categorizing images that belong to the same class (e.g., various species of birds, types of aircraft, or different varieties of flowers). Compared to standard image classification tasks, fine-grained classification poses greater challenges due to three primary factors: (i) significant intra-class variation, where objects within the same category exhibit diverse poses and viewpoints; (ii) subtle inter-class distinctions, where objects from different categories may appear very similar except for minor differences, such as the color patterns of a bird's head often determining its fine-grained classification; and (iii) constraints on training data availability, as annotating fine-grained categories typically demands specialized expertise and considerable annotation effort. Consequently, achieving accurate classification results solely with state-of-the-art CNN models like VGG is nontrivial.

Recent research demonstrates that a crucial strategy for fine-grained classification involves identifying informative regions across various parts of objects and extracting distinguishing features. A common approach to achieving this is by learning the object's parts through human annotations. However, annotating fine-grained regions is labor-intensive, rendering this method impractical. Some advancements have explored unsupervised or weakly-supervised learning techniques to identify informative object parts or region of interest bounding boxes. While these methods offer potential solutions to circumvent manual labeling of fine-grained regions, they come with limitations such as reduced accuracy, high computational costs during training or inference, and challenges in accurately detecting distinct bounding boxes.

n this paper, we introduce the Self Assessment Classifier (SAC) method to tackle the inherent ambiguity present in fine-grained classification tasks. Essentially, our approach is devised to reevaluate the top-k prediction outcomes and filter out uninformative regions within the input image. This serves to mitigate inter-class ambiguity and enables the backbone network to learn more discerning features. Throughout training, our method generates attention maps that highlight informative regions within the input image. By integrating this method into a backbone network, we aim to reduce misclassifications among top-k ambiguous classes. It's important to note that "ambiguity classes" refer to instances where uncertainty in prediction can lead to incorrect classifications. Our contributions can be succinctly outlined as follows:

• We propose a novel self-class assessment method that simultaneously learns discriminative features and addresses ambiguity issues in fine-grained visual classification tasks.
• We demonstrate the versatility of our method by showcasing its seamless integration into various fine-grained classifiers, resulting in improved state-of-the-art performance.

#2. Method Overview

We propose two main steps in our method: Top-k Coarse-grained Class Search (TCCS) and Self Assessment Classifier (SAC). TCCS works as a coarse-grained classifier to extract visual features from the backbone. The Self Assessment Classifier works as a fine-grained classifier to reassess the ambiguity classes and eliminate the non-informative regions. Our SAC has four modules: the Top-k Class Embedding module aims to encode the information of the ambiguity class; the Joint Embedding module aims to jointly learn the coarse-grained features and top-k ambiguity classes; the Self Assessment module is designed to differentiate between ambiguity classes; and finally, the Dropping module is a data augmentation method, designed to erase unnecessary inter-class similar regions out of the input image. Figure.2 shows an overview of our approach.

#3. Top-k Coarse-grained Class Search

The TCCS takes an image as input. Each input image is passed through a Deep CNN to extract feature map $\textbf{\textit{F}} \in \mathbb{R}^{d_f \times m \times n}$ and the visual feature $\textbf{\textit{V}} \in \mathbb{R}^{d_v}$. $m, n$, and $d_f$ represent the feature map height, width, and the number of channels, respectively; $d_v$ denotes the dimension of the visual feature $\textbf{\textit{V}}$. In practice, the visual feature $\textbf{\textit{V}}$ is usually obtained by applying some fully connected layers after the convolutional feature map $\textbf{\textit{F}}$.

The visual features $\textbf{\textit{V}}$ is used by the $1^{st}$ classifier, i.e., the original classifier of the backbone, to obtain the top-k prediction results. Assuming that the fine-grained dataset has $N$ classes. The top-k prediction results $C_k = \{C_1,..., C_k\}$ is a subset of all prediction classes $C_N$, with $k$ is the number of candidates that have the $k$-highest confident scores.

#4. Self Assessment Classifier

Our Self Assessment Classifier takes the image feature $\textbf{\textit{F}}$ and top-k prediction $C_k$ from TCCS as the input to reassess the fine-grained classification results.

#Top-k Class Embedding

The output of the TCCS module $C_k$ is passed through the top-k class embedding module to output label embedding set $\textbf{E}_k = \{E_1,...E_i,..., E_k\}, i \in \{1,2, ..., k\}, E_i \in \mathbb{R}^{d_{e}}$. This module contains a word embedding layer~\cite{pennington2014glove} for encoding each word in class labels and a GRU~\cite{2014ChoGRU} layer for learning the temporal information in class label names. $d_{e}$ represents the dimension of each class label. It is worth noting that the embedding module is trained end-to-end with the whole model. Hence, the class label representations are learned from scratch without the need of any pre-extracted/pre-trained or transfer learning.

Given an input class label, we trim the input to a maximum of $4$ words. The class label that is shorter than $4$ words is zero-padded. Each word is then represented by a $300$-D word embedding. This step results in a sequence of word embeddings with a size of $4 \times 300$ and denotes as $\hat{E}_i$ of $i$-th class label in $C_k$ class label set. In order to obtain the dependency within the class label name, the $\hat{E}_i$ is passed through a Gated Recurrent Unit (GRU), which results in a $1024$-D vector representation $E_i$ for each input class. Note that, although we use the language modality (i.e., class label name), it is not extra information as the class label name and the class label identity (for calculating the loss) represent the same object category.

#Joint Embedding

This module takes the feature map $\textbf{\textit{F}}$ and the top-k class embedding $\textbf{E}_k$ as the input to produce the joint representation $\textbf{\textit{J}} \in \mathbb{R}^{d_j}$ and the attention map. We first flatten $\textbf{\textit{F}}$ into $(d_f \times f)$, and $\textbf{E}_k$ is into $(d_e \times k)$. The joint representation $\textbf{\textit{J}}$ is calculated using two modalities $\textbf{\textit{F}}$ and $\textbf{E}_k$ as follows:

where $\mathcal{T} \in \mathbb{R}^{d_{\textbf{\textit{F}}} \times d_{\textbf{E}_k} \times d_j}$ is a learnable tensor; $d_{\textbf{\textit{F}}} = (d_f \times f)$; $d_{\textbf{E}_k} = (d_e \times k)$; $\text{vec}()$ is a vectorization operator; $\times_i$ denotes the $i$-mode tensor product.

In practice, the preceding $\mathcal{T}$ is too large and infeasible to learn. Thus, we apply decomposition solutions that reduce the size of $\mathcal{T}$ but still retain the learning effectiveness. We rely on the idea of the unitary attention mechanism. Specifically, let $\textbf{\textit{J}}_p \in \mathbb{R}^{d_j}$ be the joint representation of $p^{th}$ couple of channels where each channel in the couple is from a different input. The joint representation $\textbf{\textit{J}}$ is approximated by using the joint representations of all couples instead of using fully parameterized interaction as in Eq.~\ref{eq:hypothesis}. Hence, we compute $\textbf{\textit{J}}$ as:

Note that in Equation above, we compute a weighted sum over all possible couples. The $p^{th}$ couple is associated with a scalar weight $\mathcal{M}_p$. The set of $\mathcal{M}_p$ is called the attention map $\mathcal{M}$, where $\mathcal{M} \in \mathbb{R}^{f \times k}$.

There are $f \times k$ possible couples over the two modalities. The representation of each channel in a couple is $\textbf{\textit{F}}_{i}, \left(\textbf{E}_k\right)_{j}$, where $i \in [1,f], j \in [1,k]$, respectively. The joint representation $\textbf{\textit{J}}_p$ is then computed as follows

where $\mathcal{T}_{u} \in \mathbb{R}^{d_f \times d_e \times d_j}$ is the learning tensor between channels in the couple.

From Equation above, we can compute the attention map $\mathcal{M}$ using the reduced parameterized bilinear interaction over the inputs $\textbf{\textit{F}}$ and $\textbf{E}_k$. The attention map is computed as

where $\mathcal{T}_\mathcal{M} \in \mathbb{R}^{d_f \times d_e}$ is the learnable tensor.

The joint representation $\textbf{\textit{J}}$ can be rewritten as

It is also worth noting from Equation above that to compute $\textbf{\textit{J}}$, instead of learning the large tensor $\mathcal{T} \in \mathbb{R}^{d_{F} \times d_{\textbf{E}_k} \times d_j}$, we now only need to learn two smaller tensors $\mathcal{T}_{u} \in \mathbb{R}^{d_{f} \times d_{e} \times d_j}$ in Eq.~\ref{eq:couplecompute} and $\mathcal{T}\mathcal{M} \in \mathbb{R}^{d_f \times d_e}$.

#Self Assessment

The joint representation $\textbf{\textit{J}}$ from the Joint Embedding module is used as the input in the Self Assessment step to obtain the $2^{nd}$ top-k predictions $\textbf{C}'_k$. Note that $\textbf{C}'_k = \{C'_1,..., C'_k\}$. Intuitively, $\textbf{C}'_k$ is the top-k classification result after self-assessment. This module is a fine-grained classifier that produces the $2^{nd}$ predictions to reassess the ambiguity classification results.

The contribution of the coarse-grained and fine-grained classifier is calculated by

where $\alpha$ is the trade-off hyper-parameter $\left(0 \leq \alpha \leq 1\right)$. $\text{Pr}_1(\small{\rho} = \small{\rho}_i), \text{Pr}_2(\small{\rho} = \small{\rho}_i)$ denotes the prediction probabilities for class $\small{\rho}_i$, from the coarse-grained and fine-grained classifiers, respectively.

#Next

In the next post, we will verify the effectiveness and efficiency of the method.

In the previous post, we have discussed about offline phase in details. In this post, we will discover the online phase in details.

#1. States in Online Phase

The online phase of the CFOR system corresponding to the demonstration in Figure.1

#2. Technical Details

The used functions will be described as follows:

• (i) detector(imgQuery): an object in an image is automatically detected by using a trained detector. In this function, we inherit the successful software YOLO (version 3.0) to identify fashion items. Besides, the items identified are also refined by the region identification model, which is trained by “classifyModel” function.
• (ii) infor_extract(states, obj, onto, classifyModels, multitaskModel): for each query object, all attribute learning models trained in function "multitaskModel" and coarse classification models in function "classifyModel" are run. We extract the region ⟶ category ⟶ attributes and necessary features for each stage of the ontology.
• (iii) query_expansion(infor, feat): query expansion based on the mean vector is used for reranking retrieval results.
• (iv) compute_sim_score(database, infor, feat): for each pair of features, asymmetric distance is used to measure the dissimilarity distance between the query and the sample in the database
• (v) ranking(scorelist, database, top__k, GPU_search = True): based on the score between the query and all samples in the database obtained from function "compute_sim_score," ranking is applied; smaller is better.
• (vi)retrieval(indexes, score_list, database, GPU_search = True): the retrieval process contains 3 steps including feature retrieval, fine-grained retrieval, and query expansion. For global retrieval, global features of the query object obtained from function “inforextract” and the features of samples in the database are passed to function "ranking" to get 1st top-_m retrieval results. For fine-grained retrieval, attribute features of the query object obtained from function “inforextract” and the features of samples in 1st top-_m retrieval results are passed to function "ranking" to get 2nd top-k retrieval results. For query expansion, the mean vector is computed from 2nd top-k retrieval results, and each feature of 2nd top-k retrieval results is passed to function "ranking" to get final top-k retrieval results, i.e., query expansion-based reranking.

As described in Figure 1, the online phase of the CFOR system contains three stages which will be put into use in real time. They are given as follows.

#3. Prediction Stage

This stage will take advantage of object ontology and classification models obtained from the offline phase and then makes predictions from coarse to fine for each query image:

Fine-grained information in terms of regions, categories, and attributes provides more options for a customer to give a full semantic query. The object will be predicted from coarse to fine. In turn, the region, category, and attribute will be predicted based on object ontology and a local MDNN. The object retrieval system uses extracted semantic information as the category and attribute to search in detail.

#3. Dissimilarity Measuring Stage

This stage will take advantage of the database as well as the indexing file from the offline phase and a dissimilarity measure to get scores and then rank, rerank, and release retrieval results for each query image. This stage is based on the dissimilarity measure between attribute vectors of query images and database images:

Based on combination of K-nearest neighbour search in terms of L2 distance and asymmetric distance computation, we take advantage of parallel processing by GPU through the Faiss method to compute the distance from the query image to the necessary one in the database. The distance which is also called the score of each image in the database is then sorted to rank the dissimilarity. The smaller the score of the image, the more similar the query. Based on the number of retrieval images required or thresholds, we will have an appropriate cutoff in the score as well as the number of retrieval images. This kind of measurement is used to compute distance for both deep features vectors and attribute vectors.

#4. Dissimilarity Measuring Stage

Query expansion is a technique that can help gather additional relevant information from the input to increase retrieval performance. The information can be relevant images, additional features, description, etc. based on the query expansion algorithms and data. In this stage, we would like to take advantage of the previous retrieval results and then expand the query by using the mean vector to rerank and get reranked retrieval results to improve retrieval performance.

Query expansion based on the mean vector is chosen among many methods, the mean vector computed from features of retrieval results and the features of input help reduce the bias between different considered features. Thus, the CFOR system can eliminate unrelated features; that is, retrieval features have high gap from the mean vector features, which helps reduce outliers and rise the precision score.

Query expansion based on computing mean vector is performed very fast, and it can take advantage of the Faiss similarity searching method as well. Query expansion can remove outliers, thanks to the statistic essence of the mean vector.

#Next

In the next post, we will mention the Fashion Ontology, a CFOR System Testing in Fashion.

In the previous post, we have discussed about offline phase and online phase in overview. In this post, we will discover the offline phase in details.

#1. States in Offline Phase

This phase consisted of three substages:

• Object Ontology Establishment Stage. This stage defines fashion ontology to control the training flow as well as the online retrieval flow which serves as a bridge between high-level concepts (objects and categories), midlevel concepts (attributes), and raw data.
• Learning Stage. This stage exploits deep networks with transfer learning in dealing with the specific tasks including object part learning, category learning, and attribute learning.
• Storing and Indexing Stage. This stage defines a way of storing data as well as making the index list to reduce retrieval or searching time.

From the offline phase, in this section, inherited from previous state-of-the-art methods, we will mention about object part extraction, transfer learning, and its role in the retrieval system as well as data storing. These modules are highly generalized to any object. Other issues including ontology, attribute learning, network architecture, and indexing strategy will be detailed in the following sections.

#2. Loss Function

This function inherited the current state-of-the-art ResNet for classification, and cross entropy loss function is applied for multiclass classification in the category classification model and attribute classification model.

For attribute multitask classification models, the loss function is described as follows:

#3. Technical Details

Object ontology which is designed manually based on professional experience and public dataset for the community. It is organized into the hierarchical semantic tree with three main levels: region level, category level, and attribute level. Regions, categories, and attributes are learned automatically based on the local MDNN. The DeepFashion dataset, the used functions will be described as follows:

• (i)extract_predicates(dta): in a rich-annotated dataset, e.g., DeepFashion, a sample image can be annotated by many labels in different fine-grained levels. For each fine-grained level, the function is used to extract the unique possible labels of samples and then store these labels into a corresponding array. For example, in the DeepFashion dataset, Top, Bottom, and Body are unique labels belonging to one fine-grained level, and thus, they are stored into one array. Similarly, fabric, shape, part, style, and texture labels belong to one fine-grained level and are stored into one array.
• (ii)build_ontology(predicates, prior): this matches the extracted level and its labels from each predicate array into the corresponding stage of the general ontology, i.e., prior. For example, Top, Bottom, and Body belong to one level which is matched with the region stage of the ontology. After the matching is finished, all other unused stages are eliminated from the general ontology to generate the adapted ontology, e.g., fashion ontology.
• (iii)extract_state(onto): from the built ontology, all stages and their labels are searched and stored into arrays which will be used to reconstruct the data. For example, the region stage array contains three classes, and the category stage array contains 50 classes.
• (iv)extract_nes_dta(dta, state, onto): based on the stage and the classes extracted from the “extract_state” function, the whole DeepFashion dataset will be split. Only samples having the labels belonging to the stage are stored as the training set of that stage in the ontology. For example, with the region classification model, only samples labelled Top, Body, or Bottom are used for training.
• (v)classifyModel(architecture, state_dta): in the DeepFashion dataset, based on ontology, there are four classification models: region classification model and category classification model for the Top region, Body region, and Bottom region. These models are retrained from the ImageNet dataset using ResNet-10.
• (vi)multitaskModel(group_state_dta, architecture, Matthrew_coef = True): for each group state in terms of the fine-grained attribute level, a multitask classification model is built, e.g., fabric attribute group classification model and style attribute group classification model. These models are retrained from the ImageNet dataset using NASNet v3. Besides, the attribute learning and the usage of MCC are mentioned for an imbalanced data solver.
• (vii)indexing(state_sta): indexing files are created that will be used for run-time retrieval. The method is based on the nonexhaustive compressed-domain search with GPU.
• (viii)build_storage(onto, states): storage structures are automatically created based on built-in object ontology and extracted states.
• (ix)infor_extract(states, dta, onto, classifyModels, multitaskModel): for each sample in the database, all attribute learning models trained in “multitaskModel” function are run and then all possible attributes which are higher than thresholds are extracted.
• (x)feat_extract(dta, onto, classificationModels, multitaskModel): for each sample in the database, the features of the pre-softmax layer in four models trained in “classifyModel” function are obtained.
• (xi)structure(storage, feat_dta, info_dta, indexFiles): the database is automatically built based on extracted features, extracted information, index, and storage structure.

#3.1. Object Part Extraction

For the aforementioned reasons, foreground objects should be extracted from background regions efficiently and accurately before entering the retrieval step. The target of object extraction is to filter the necessary specific subjects. This also improves the efficiency of the following modules as well as increases the overall system performance. There are many successful object detection methods. Among them, YOLO shows the state-of-the-art results. In our system, we inherited the successful software YOLO (version 3.0) to identify fashion items.

#3.2. Transfer Learning

Transfer learning is one of the best methods to reduce training time, especially with complicated architectures such as ResNet or NASNet. The key issue is the initial parameters. In the first step of the training process, we have to generate these parameters with some unsupervised learning methods. However, the initial one will be far from the optimal one. In transfer learning, we will reuse the trained parameters on a large and diverse dataset (such as ImageNet dataset). By this way, our training process will be easier to meet convergence. Thus, it reduces the training time.

Transfer learning can be applied in different ways based on the size of the dataset and data similarity. There are four scenarios in total. First, if the data size is small while data similarity is high, we use the pretrained model as a feature extractor. Second, if the data size is small and data similarity is low, we freeze the top layers and train the remaining layers of the pretrained model. Third (ideal situation), if the data size is large and data similarity is high, we can retrain the model by using the weights initialized in the pretrained one. Fourth (worst situation), if the data size is large and data similarity is low, transfer learning cannot be applied, and we have to train our model from scratch. In our fashion example experiments, while DeepFashion is a large dataset and ImageNet (dataset used for transfer learning) is a high diversity one, we can use all of the initialized weights from the pretrained model.

According to our approach, transfer learning will be applied in region, category classification as well as attribute learning along with ResNet and NASNet architectures, respectively. It can also be used in global deep feature extraction to improve the overall retrieval performance.

#3.3. Data Storing

Features extracted from the category classification task and attribute learning will be stored in a hierarchical semantic tree based on object ontology. All features belong to a leaf of object ontology and will be stored in one file. In case of the expansion of large-scale data, the mentioned files can be indexed and split with a corresponding mapping key for each image. The folders will be organized based on object ontology in which each name corresponds to each concept. To clarify, data storing for the proposed ontology is defined as follows (see Figure below for an example of data storing):

• (i) All files are stored in a folder named “database,” which is denoted as the “Object” node.
• (ii) Based on ontology, “Object” node contains 3 nodes at the “Region” semantic level. Thus, we have 3 smaller folders: “Top,” “Body,” and “Bottom.”
• (iii) At the next stage of ontology, we have the “Category” semantic level. Thus, we have 50 folders representing all nodes of “Category.”
• (iv) Finally, we have the “Attribute” semantic level standing for the leaf node state in ontology. At this state, all features belong to the same “Region” and “Category” and are stored in one file.

#Next

In the next post, we will mention the online phase in details.

In the previous post, we have discussed about the imbalance data problem annd the overview of the object retrieval system. The CFOR system is organized into two main phases: offline phase and online phase. In this post, we will discover the overall of the online phase and offline phase of the proposal.

#1. Overview of Offline Phase

This phase is designed to generate object ontology, database, indexing file and region detection model, category classification model, and attribute classification model.

• Object ontology is designed manually based on professional experience and public dataset for the community. It is organized into a hierarchical semantic tree with three main levels: region level, category level, and attribute level.
• The database is generated to store the preextracted features, regions, categories, and attributes of all images in the dataset. It supports to reduce the online retrieval time and provides the necessary semantic information for each retrieved image.
• The indexing file which is created to support fast mapping in the online phase of the CFOR retrieval system is the key to perform the retrieval task at runtime.
• Regions, categories, and attributes are learned automatically based on the local MDNN. Detection models and classification models are created to extract or predict semantic information of the query image and dataset such as regions, categories, and attributes.

#2. Overview of Online Phase

This phase of the CFOR system is designed to run the retrieval process including object detection, semantic information extraction, and query expansion and retrieval.

In the object detection stage, we use the trained object detector to detect objects in the query image. In the semantic information extraction stage, the built-in object ontology and classification models are used for extracting the necessary semantic information of each identified object. The extracted semantic information and deep global features of each detected object passed through the searching system along with the indexing file to quickly compute the score between the query object and the sample in the database. Retrieval is applied to rank and export the most similar images to the query object and their relevant information. Query expansion is optional and used to increase the retrieval performance with a trade-off for retrieval time.

The power of mutually supporting object ontology, local MDNN, and imbalanced data solver in the CFOR system: Figure.1 shows the operation of the CFOR system with the interaction of the three main modules object ontology, a local MDNN, and an imbalanced data solver to optimize the learning strategy and improve the overall retrieval performance on large-scale datasets.

Object ontology supports conducting the training flow (with a local MDNN) and retrieval flow (from the coarse-grained level to the fine-grained level) to save computational costs in the training stage and retrieval stage on large-scale datasets. Training flow also paves a way for applying transfer learning which may improve the convergence rate of deep networks. Object ontology which could transform the global imbalance of data into local imbalance of data based on fine-grained groups makes the imbalanced data problem easier to deal with.

Deep multitask NN supports to link the object ontology to the raw data effectively at the category level and attribute level by exploiting inner-group correlations and intergroup correlations. The object ontology supports to update the system at the local level with parallel processing based on the local MDNN. Therefore, CFOR is updated in a flexible manner on large-scale datasets with many variations.And the proposed imbalanced data solver based on MCC which addresses data imbalance has contributed effectively to increasing the quality of object ontology implementation without adjusting network architecture and data augmentation.

Algorithm and demonstration of the CFOR system: an online phase and offline phase (Figures 2 and 3) are used to analyze tasks in the CFOR system. These phases will be demonstrated in detail in this section.

Besides, the CFOR system can be put into use as a general solution for retrieval. To evaluate the performance of the proposed system, fashion objects with attributes are selected in experiments.

#Next

In the next post, we will mention the offline phase in details.

In the previous post, we have discussed about multitask learning and object retrieval system. In this post, we will discover imbalance data problem and the main proposal.

#1. Imbalanced Data Problem

Imbalanced data are the problem in machine learning in which the class distribution is not uniform between the classes. Usually, they are composed of two types of classes: the majority classes (positive) and the minority classes (negative). Recent research in machine learning shows that using an uneven distribution of class examples during learning can cause learning algorithms with misleading performance (bias). It means a classifier with high accuracy in the majority, but it gives poor accuracy in the minority class. In the case of attribute learning, an imbalance occurs if the number of instances in some attributes varies significantly in quantity compared to other attributes. To deal with this situation, in general, adjusting the distribution of classes is an essence of many popular methods to handle imbalanced data problems.

• Data sampling: sampling-based methods such as upsampling, downsampling, or data augmentation are considered to be a solution for imbalanced data problems. In addition to making data more balanced, they can help reduce training time (downsampling) or make the learning process more efficient (upsampling). The best approach we know is SMOTE which can solve the situation by automatically generating additional data (upsampling) based on the original dataset. However, these methods increase overfitting when training (upsampling) or losing (downsampling) data. Data augmentation is proved to be robust in dealing with imbalanced training data. However, this method takes up a lot of training resources, and it is difficult to find a proper augmented dataset which is large enough to train. And it is very difficult (or impossible) to augment data to balance the attributes in datasets because each object usually has many attributes.

  Figure 1. A simple data sampling

• Architecture, loss function, and metric configuration: other methods exploit network architectures, loss functions, or metrics to address the imbalanced data problem when training. The methods (at the algorithm level) enhance the existing classifier by adjusting algorithms to recognize the smaller classes. Internal techniques provide general solutions for the imbalanced data problem because these are not specific to particular problems. These approaches show better performance compared to data sampling; however, they are often difficult to implement as well as configure in the future. Therefore, they are not always the best choice in dynamic retrieval systems in which the attributes have a large variety.Threshold and output-based configuration: instead of generating more data or making changes in the model, these methods find the best thresholds based on output. The essence of these methods is to use scores that show the probability to indicate which test sample is a member of a class in producing several learners by changing the threshold for class members. These methods are particularly effective in resolving imbalanced data problems without changing the configuration in the model. Moreover, they also do not reduce data or increase overfitting. SVM is proposed to find these thresholds. However, Boughorbel et al. proposed Matthews’ correlation coefficient (MCC) to deal with imbalanced data in classification. Although SVM shows better performance, MCC consumes less resources and processing time compared to it. Based on the methods of many other researchers, we found a solution for multitask learning that is suitable to retrieval systems using the end-to-end DCNN for training and MCC for estimating thresholds to get final outputs.

#2. Materials and Methods: CFOR System

The CFOR system is very complicated but easy to understand. We focus on the main points of the CFOR system.

CFOR is an object retrieval system integrated by object ontology, a local MDNN (NASNet and ResNet), and an imbalanced data solver (MCC) to improve the performance of the large-scale object retrieval system from the coarse-grained level (categories) to the fine-grained level (attributes) (see Figure below).

Query Image. For traditional content-based image retrieval systems, with query images, one is just able to retrieve the images ranked on visual similarity to query image. It is very difficult (or impossible) for users to provide semantic information to the system based on query images. But the interesting thing is that, in our CFOR system, this challenge has been solved. The semantic information of the query image is extracted automatically by the category and attribute classification system, and users can use the extracted semantic information during the retrieval process.An example is how users can query “Asian face” with only a query image; here, “Asian race” is semantic information. The traditional retrieval methods cannot meet this requirement because of the curse of semantic gap. And the CFOR system can recognize “Asian race” and use it to retrieve. Another example for “Fashion” object based on our CFOR system is described in Figure 3.

From the query image, based on fashion ontology, the detector quickly identifies the region (Top and Bottom; see Figure 4).

After that, the user selects the region (Top; see Figure 5); the CFOR system quickly identifies the category related to the Top region (category: Blazer). Later, specific concepts and visual concepts are extracted according to Blazer, and users can select some of them (or all of them) to retrieve. For user-friendly interaction, only extracted regions, categories, and attributes are shown. Other information such as global deep features, attribute vector, ontology, or group of attributes which are used as searching input of the system will not be displayed. In such a way, users can order the CFOR system at the semantic level, and they can achieve the results that match both the content and semantics of the query image.

#Next

In the next post, we will mention the online phase and offline phase of the proposed retrieval system.

Object retrieval plays an increasingly important role in video surveillance, digital marketing, e-commerce, etc. It is facing challenges such as large-scale datasets, imbalanced data, viewpoint, cluster background, and fine-grained details (attributes). This paper has proposed a model to integrate object ontology, a local multitask deep neural network (local MDNN), and an imbalanced data solver to take advantages and overcome the shortcomings of deep learning network models to improve the performance of the large-scale object retrieval system from the coarse-grained level (categories) to the fine-grained level (attributes). Our proposed coarse-to-fine object retrieval (CFOR) system can be robust and resistant to the challenges listed above. To the best of our knowledge, the new main point of our CFOR system is the power of mutual support of object ontology, a local MDNN, and an imbalanced data solver in a unified system. Object ontology supports the exploitation of the inner-group correlations to improve the system performance in category classification, attribute classification, and conducting training flow and retrieval flow to save computational costs in the training stage and retrieval stage on large-scale datasets, respectively. A local MDNN supports linking object ontology to the raw data, and an imbalanced data solver based on Matthews’ correlation coefficient (MCC) addresses that the imbalance of data has contributed effectively to increasing the quality of object ontology realization without adjusting network architecture and data augmentation. In order to evaluate the performance of the CFOR system, we experimented on the DeepFashion dataset. This paper has shown that our local MDNN framework based on the pretrained NASNet architecture has achieved better performance (14.2% higher in recall rate) compared to single-task learning (STL) in the attribute learning task; it has also shown that our model with an imbalanced data solver has achieved better performance (5.14% higher in recall rate for fewer data attributes) compared to models that do not take this into account. Moreover, MAP@30 hovers 0.815 in retrieval on an average of 35 imbalanced fashion attributes.

#1. Introduction

Nowadays, object retrieval is facing some challenges and has some advantages.

Query format plays a very important role in large-scale object retrieval systems. Thus, the query format should be user-friendly and satisfy user requirements in practice.

Two query formats are popular these days: image-based format and text-based format. The text-based query format is being used widely in many searching systems. However, in many cases, it is very difficult to use query text to express the content that human would like to retrieve because words have some limitations in expressing visual information. Instead, a query image is worth more than thousand words; it allows customers to search objects without typing, and the most important thing is that it can retrieve the results based on content. Nevertheless, the limitations of the query image in expressing semantic information could decrease the overall retrieval performance. Thus, the query image and retrieval image with useful related information (regions, categories, fine-grained attributes, etc.) will be the interesting points that we have to focus on to improve the performance of the coarse-to-fine object retrieval system.

Object retrieval systems should meet the requirements of retrieving from large-scale datasets not only at the coarse level but also at the detailed level (or attribute level). For example, in face retrieval systems, facial attribute retrieval is often required. In fashion retrieval systems, fashion attribute retrieval is an indispensable requirement. In person reidentification systems, in the reidentification stage, besides using the global features of the whole human body, attribute vectors of the face and clothes are also being exploited effectively. In crowd attribute recognition systems, the useful attribute set consisted of location, participants, and activities.

Objects often have multiple attributes, and there are methods to retrieve objects at the attribute level from large-scale datasets without manual annotation. In attribute recognition, the traditional methods often waste a lot of time in selecting hand-crafted features for each attribute group during the trial-and-error process but do not always achieve the desired results. In recent years, the deep convolutional neural network (DCNN) has demonstrated high performance in many tasks in computer vision such as detection, classification, recognition, and retrieval. And without exception, the DCNN is also used for attribute learning, with only one network architecture, and the DCNN model can learn to recognize many attributes.

The performance of the DCNN-based attribute learning model will not achieve high rate if the set of attributes plays the same role in the network architecture at the output level and imbalanced data are unresolved. To exploit the inner-group correlations in coarse-grained groups or fine-grained groups, the DCNN often is revised to the deep multitask NN. The performance of classification will be improved if the elements of fine-grained category groups or fine-grained attribute groups could share similar learning features, so the slope of their error surface will become more uniform and the deep multitask learning algorithm can easily reach the global optimum effectively.

Object ontology plays an important role in category classification, attribute classification, and conducting training flow and retrieval flow to save computational costs in the training stage and retrieval stage on large-scale datasets, respectively. Thus, based on our experience in researching objects related to attributes such as face, cloth, person (reidentification), crowd (monitoring), and fast filters in large-scale object retrieval, we would like to introduce an object ontology as a hierarchical semantic tree with three levels: region, category, and attribute levels. The attribute level consisted of visual concepts and specific concepts. Visual concepts support linking common visual attributes to arbitrary objects.

We introduce an object ontology based on popular large-scale standard datasets in science community, so we hope that our ontology can meet the criterion “widely recognized in community.” And for criterion “realization,” we have proposed the local MDNN to support linking object ontology to the raw data. However, if object ontology could not be linked with high quality, it could not function effectively. And we have proposed the imbalanced data solver based on MCC to address data imbalance that has contributed effectively to increasing the quality of linking object ontology to raw data without adjusting network architecture and data augmentation.

We review some typical works based on object ontology, deep multitask neural networks, and imbalanced data solvers to highlight our contributions.

Most of the works only present the set of attributes in the form of item lists or item groups. A few works used the terminology "ontology", but to the best of our knowledge, there are not works that present the object ontology in full meaning of regions, categories, and attributes.

In [8], FashionNet handles the challenges as deformation and occlusions by explicitly predicting clothing landmarks and pooling features over the estimated landmarks, resulting in more discriminative cloth representation. The authors do not use the terminology "ontology", but the DeepFashion dataset is organized based on a hierarchical tree; it is only deployed according to fashion, and it includes a two-level tree: the first level consisted of 50 categories and the second level consisted of 5 attribute groups (texture, fabric, shape, part, and style) (it does not have color attribute). The coarse-grained groups (at the category level) or fine-grained groups (at the attribute level) have the same role in deep neural networks, and the imbalanced data solver has not been considered yet.

Our idea is to improve the performance of deep neural networks based on object ontology and imbalanced data solvers with inspiration from Gödel’s incompleteness theory. This theory shows the limitation of any consistent formal system as well as the limitation of specific methods in solving problems. When the deep network configuration method is not able to create such a large effect as in the early days it took place, it is necessary to integrate object ontology and imbalanced data solvers into deep learning. Based on appropriate interventions in inputs and outputs, we introduce a new method that can help improve the performance of the object retrieval system.

The main contributions of this paper are as follows.

• Our proposed unified model consisted of object ontology, a local MDNN, and an imbalanced data solver to improve the performance of the large-scale object retrieval system from the coarse-grained level (categories) to the fine-grained level (attributes).

• Our proposed object ontology is a hierarchical semantic tree consisting of three main levels: region, category, and attribute levels. It can support the optimal learning strategy and minimize the effect of semantic gap. It is useful to improve the performance of category classification, attribute classification, and conducting training flow and retrieval flow to save computational costs in the training stage and retrieval stage on large-scale datasets, respectively.

• Our proposed local MDNN is inspired by multitask neural networks. It is based on NASNet, ResNet exploiting the local multitask neural network architecture, to improve the performance of category classification and attribute classification and for flexible system updates. The local MDNN supports linking object ontology to raw data and takes advantage of inner-group correlations of categories and attributes. If the inner-group correlations (or intergroup correlations) are exploited, the performance of classification will be improved because the elements of fine-grained categories or the fine-grained attribute group share similar learning features, the slope of their error surface becomes more uniform, and our deep local multitask learning algorithm can easily reach the global optimum effectively.

Data imbalances often occur for large-scale datasets. Data augmentation is almost impossible because each object can have multiple attributes. The solution based on the loss functions, as in [6], may be possible, but it cannot exploit transfer learning. Our proposed imbalanced data solver is inherited from MCC without adjusting network architecture and data augmentation. It is integrated into the local MDNN to improve the performance of category classification and attribute classification, but it can still exploit transfer learning to reduce computational costs in the training stage on large-scale datasets.

Our proposed query format is based on object ontology with semantic information such as regions, categories, and attributes extracted automatically from the query image. Therefore, we can express semantic information from the image to the retrieval process that the traditional methods have not implemented yet.

#2. Object Retrieval System

Fine-grained object retrieval is supposed to search for similar images that include specific object attributes. It declares a transition model from image retrieval to object attribute retrieval. Specifically, unlike traditional image retrieval systems where queries and results are often coarse (e.g., texts or images), fine-grained image retrieval aims to retrieve semantic information such as categories and attributes. In the fashion field, taking advantages of semantic information, an object retrieval method based on the combination of the global feature with fine-grained attribute information was introduced [8]. Inspired by previous works, we would like to propose a coarse-to-fine object retrieval system which not only takes advantage of the combination of the global feature with fine-grained attribute information but also optimizes the learning strategy based on ontology and resolves the imbalanced data problem by interfering with the output.

In addition to meeting the semantic retrieval results, the object retrieval system must handle large-scale problems to run in real time. However, most solutions did not take advantage of the power of GPUs for parallel processing which can significantly reduce feature-matching time and retrieval time. To leverage the support of GPUs, we inherited the search algorithm introduced by Johnson et al. (billion-scale similarity search with GPUs) which is a nonexhaustive similarity search. The search method perfectly suited the proposed CFOR system which further decreased searching time by creating multi-index files based on built-in object ontology.

#3. Attribute Learning

Attribute learning is a backbone of CFOR, and it has strong effects on performance of fine-grained object retrieval. Therefore, attribute learning is considered one of the important parts of the learning strategy.

#Attribute Learning.

This method is used for object recognition systems at the fine-grained level. Unlike learning methods that are used for the high-level concept, attribute learning supports a solution for midlevel semantic concepts or visual concepts which are known to have (more or less) correlations to each other. There are two main different learning methods: single-task learning and multitask learning.Single-task attribute learning: in this type, attributes have their own learning model. Therefore, it leads to the number of models equal to the number of attributes. Moreover, each attribute is treated separately, for which the inner-group correlations are not yet exploited. Many works are known in the fashion field by using single-task learning for fashion attributes. At that time, there were many challenges in multitask learning. A shared CNN is defined to pave a way in the final format of the multitask multilabel predictions. Therefore, multitask learning becomes possible.Multitask attribute learning: to apply this technique to attributes, samples will be collected by merging given datasets into one with one-hot binary vector demonstration. Like single-task learning, the input will be the image. Despite the output of single-task learning which is a value that describes the existence (or not) of an attribute in an image, the output of multitask learning will be a one-hot binary vector which describes the existence (or not) of a group of attributes. Rudd has shown that joint optimization over all attributes outperforms training a single independent network with the same architecture for each attribute, in which the feature space is optimized along with the classifier on a per-attribute basis, both in terms of accuracy and storage, processing efficiency. This result shows that the multitask approach is much more effective in exploiting latent correlations than independent classifiers used to learn them. Although multitask learning can yield better performance compared to single-task learning, its critical weakness is that the model cannot be reused when there is any attribute change. A retraining or additional model will be applied when a new attribute is added. Lack of reuse is the reason that multitask learning methods are not flexible for attributes that change frequently. To address these challenges, we propose that local multitask attribute learning be considered a grouping method based on object ontology to improve its reuse.

#Next

In the next post, we will mention Imbalanced Data Problem and our proposal in details.

In previous part, we have discovered the qualitative and quantitative expriments. In this part, let investigate ablation studies and user studies.

Our code can be found at: https://github.com/aioz-ai/GCD

#1. Ablation Analysis

Loss Terms. The contribution of the geometric loss $\mathcal{L}_{\rm geo}$ and contrastive loss $\mathcal{L}_{\rm nce}$ in GCD is thoroughly analyzed and presented in Table 1. The results demonstrate that both losses play a crucial role in enhancing the overall performance across all four evaluation protocols. In particular, it can be seen that the effect of $\mathcal{L}_{\rm geo}$ on realism metrics (FID, GMR, and PFC) is significant. This observation can be attributed to the fact that this loss improves the physical plausibility and naturalness of the dance motions, empirically mitigating common artifacts such as jittery motion or foot skating. By enforcing the geometric constraints, GCD can generate faithful motions that are on par with real dances. Moreover, the contrastive loss $\mathcal{L}_{\rm nce}$ contributes positively to the favorable results in the synchrony measures (GMR and GMC). This loss term encourages the model to synchronize the movements of multiple dancers within a group, thus improving the harmonious coordination and cohesion of the generated choreographies. In general, the results of $\mathcal{L}_{\rm geo}$ and $\mathcal{L}_{\rm nce}$ validate their importance across various evaluation metrics.

Group Global Attention. Results presented in first two lines of Table 1 demonstrate substantial improvements obtained by incorporating Group Global Attention into GCD. It clearly shows that without the Group Global Attention, the performance on the group dance metrics (GMR and GMC) is significantly degraded. We also observe that the removal of this block resulted in inconsistent movements across dancers, where they seem to dance in freestyle without any group choreographic rules and collide with each other in many cases, although they may still follow the rhythm of the music. Results suggest the vital importance of ensuring coherency and regulating collisions for visually appealing group dance animations.

#2. User Study

Qualitative user studies are important for evaluating generative models as the perception of users tends to be the most relevant metric for many downstream applications. Therefore, we conduct user studies to evaluate our approach in terms of group choreography generation. We organized two separate studies and enlisted roughly 50 individuals with diverse backgrounds to participate in our experiment. Each participant should have some relevant experience in music and dance (at least 1 month of studying or working in dance-related professions). The age of participants varied between 20 and 50, with approximately 55\% female and 45\% male.

In the initial study, we requested the participants to evaluate the dancing animations based on three criteria: the naturalness of the dancing motions (Realism), how well the movements match the music (Music-Motion Correspondence), and how well the dancers interact or synchronize with each other (Synchronization between Dancers). Participants were asked to rate scores from 0 to 10 for each criterion, ranging from 0-very poor, 5-acceptable, to 10-very good. The collected scores were then normalized to range $[0,1]$.

This user study encompassed a total of $189 * 3$ samples with songs that are not present in the train set, including those generated from GDanceR, real dance clips from the dataset, and generated results from our proposed method in neutral mode. Figure.1 shows average scores for all mentioned targets across three experiments. Notably, the ratings of our method are significantly higher than GDanceR across all three criteria. We also perform Tukey honest significance tests to determine the significant differences among the three methods. For the first two criteria (Realism and Music-Motion Correspondence), we observe that the mean scores of all methods are significantly different with $p < 0.05$. For synchronization critera, the differences are significant except for the scores between our method and real dances ($p\approx0.07$). This highlights that our method can even achieve comparable scores with real dances, especially in the synchronization evaluation. This can be attributed to the proposed contrastive diffusion strategy, which can effectively maintain a balance between the consistency of the movements and the group/audio context, as well as diversity in generated dances.

In the second study, we aim to assess the diversity and consistency of the generated dance outputs and determine if they met the expectations of the users. Specifically, participants were asked to assign scores ranging from 0 to 10 to evaluate the consistency and diversity of each dance clip, i.e., how synchronized or how distinctive movements between dancers does the group dance present. A lower score indicated higher consistency, while a higher score indicated greater diversity. These scores were subsequently normalized to $[-1,1]$ to align with the studying range of the control parameter employed in our proposed method.

Figure 2 depicts a scatter plot illustrating the relationship between the scores provided by the participants and the $\gamma$ parameter that was used to generate the dance samples. The parameter values were randomly drawn from a uniform distribution with range $[-1,1]$ to create the animations along with randomly sampled musical pieces. The survey shows a strong correlation between the user scores and the control parameter, in which we calculated the correlation coefficient to be approximately 0.88. The results indicate that the diversity and consistency level of the generated group choreography samples is mostly in agreement with the user evaluation, as indicated by the scores obtained.

#3. DISCUSSION AND CONCLUSION

While controlling consistency and diversity in group dance generation by using our proposed GCD has numerous advantages and potentials, there are certain limitations. Firstly, it requires tuning the parameters and a complex system that is not trivial to train, to ensure that the generated dance motions can produce the desired level of similarity among dancers while still presenting enough variation to avoid repetitive or monotonous movements. This may involve long inference processes and may require significant computational resources in both the training and testing phases.

Secondly, over-controlling consistency and diversity may introduce constraints on the creative freedom of generated dances. While enforcing consistency can lead to synchronized and harmonious group movements, it may limit the possibility of exploring unconventional or new experimental dance styles. On the other hand, promoting diversity results in unique and innovative dance sequences, but it may sacrifice coherence and coordination among dancers.

{Although our model can synthesize semantically faithful group dance animation with effective coordination among dancers, it does not capture clear physical contact between dancers such as hand touching. This is because the data we used in training does not contain such detailed hand motion information. We think that exploring group dance with realistic physical hand interactions is a promising area for future work. Additionally, while our method offers a trade-off between diversity and consistency, achieving perfect alignment between high-diversity movements and music remains a challenging task. The diversity level among dancers and the alignment with music are also heavily influenced by the training data. We believe further efforts are required to reach this.}

Lastly, the subjective nature of evaluating consistency and diversity poses a challenge. Metrics for measuring these aspects may not be best fitted. We believe it is essential to consider diverse perspectives and demand domain experts to validate the effectiveness and quality of the generated dance motions.

To conclude, we have introduced GCD, a new method for audio-driven group dance generation that effectively controls the consistency and diversity of generated choreographies. By using contrastive diffusion along with the guidance technique, our approach enables the generation of a flexible number of dancers and long-term group dances without compromising fidelity. Through our experiments, we have demonstrated the capability of GCD to produce visually appealing and synchronized group dance motions. The results of our evaluation, including comparisons with existing methods, highlight the superior performance of our method across various metrics including realism and synchronization. By enabling control over the desired levels of consistency and diversity while preserving fidelity, our work has the potential for applications in entertainment, virtual performances, and artistic expression, advancing the effectiveness of deep learning in generative choreography.

In previous part, we have discovered the experimental setups and quality analysis. In this part, let investigate consistency and diversity factors in dance generation.

Our code can be found at: https://github.com/aioz-ai/GCD

#1. Diversity and Consistency Analysis

Table.1 presents an in-depth analysis of our method's performance across seven evaluation metrics by adjusting the parameter $\gamma$ to control the consistency and diversity of the generated group choreographies. The findings reveal that our GCD with high consistency setting ($\gamma = 1$), performs better than other settings in terms of MMC, GMC, and TIR metrics, whereas the high diversity setting ($\gamma=-1$) achieves better results in the GenDiv metric. Meanwhile, the default model shows the best performance in both realism metrics (FID and GMR). {It can also be seen that the model is relatively robust to the physical plausibility score (PFC) as there are no noticeable differences among the metric in the three settings. This implies that our model is able to create group animation with different consistency or diversity levels without compromising the plausibility of the movements too much.} More interestingly, we found that there are indeed positive correlations between the two measures MMC, GMR, and the trade-off parameter. It is clear that these metrics are better when the consistency level increases. This is reasonable as we expect higher correspondence between the motion and the music (MMC) or higher correlation of the group motions (GMR) when the consistency level grows, which also agrees with the definition of these metrics.

Consistency setups in GCD lead to more similar movements between dancers. As a result, this similarity contributes to high scores in MMC, GMR, and TIR metrics. In contrast, the diversity setups can synthesize more complex motions with greater variation between dancers as measured by the GenDiv metric, but this also makes it more challenging to reach high values of FID, MMC, and TIR, compared with other setups. In addition, Figure 1 shows an example of correlations between motion beats and music beats under high consistency and diversity settings. The music beats are extracted using the beat tracking algorithm from the Librosa library. Notably, the velocity curves in high consistency setting display relatively similar shapes, whereas in the high diversity scenario, the curves are clearly distinguished among dancers.

Despite the greater variations in high diversity setting, we can observe that the generated motions are matched with the music as the music beats are mostly located near the extrema of the motion curves in both settings. The experiment indicates that our model can faithfully capture different aspects of group choreography with different settings, including diversity and synchrony of the motions. This demonstrates the potential of our method towards various dance applications such as dance training or composing. Furthermore, our method can also produce distinctively different animation sequences under the same setting while adhering to the input music.
It is also important to note that all three setups of GCD significantly outperform other baseline models. This verifies the effectiveness of our proposed approach and shows that it can create high-fidelity group dance animations in any setting. For a more detailed visualization of the results, please refer to Figure 2.

#2. Number of Dancers Analysis

Table 2 provides insights into results obtained when generating arbitrarily different numbers of dancers using our proposed GCD in the neutral setting. In general, FID, GMR, and GMC metrics do not exhibit a clearly strong correlation with the number of generated dancers but display diverse and varied results. The MMC metric consistently shows its stability across all setups.

As the number of generated dancers increases, the generation diversity (GenDiv) decreases while the trajectory intersection frequency (TIF) increases. However, it is worth noting that the differences observed in these metrics are relatively minor compared to those produced by GDanceR. This implies that our method can effectively control consistency and diversity, significantly reducing the chances of collisions between dancers and maintaining the overall quality of generated group dance motions.

For a detailed visualization of results, please refer to Figure 3. These results underscore the robustness and flexibility of our method in generating group dance motions across varying numbers of dancers while ensuring consistency, diversity, and avoiding collisions between performers.

#3. Long-term Analysis

To evaluate the efficacy of the guidance signal in GCD for creating long-term group dance sequences, we conducted a comparative analysis between GCD and the baseline model GDanceR. The experiment involved musical pieces of different durations: 15 seconds, 30 seconds and 60 seconds. We show the results with the guidance parameter $\gamma = 0.5$ to enforce consistency with the music over a long duration. For more detailed information, please refer to Figure 5 and our supplementary video.