2511.0016 Graphics Capsule: Learning Hierarchical 3D Face Representations from 2D Images v1

Published: Nov 07, 2025
🎯 ICAIS2025 Submission
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🎓 Meta Review & Human Decision

Decision:

Reject

Meta Review:

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📋 Summary

This paper introduces the Inverse Graphics Capsule Network (IGC-Net), a novel approach for learning hierarchical 3D face representations directly from 2D images in an unsupervised manner. The core innovation of IGC-Net lies in its use of 'graphics capsules,' which are designed to represent 3D primitives with interpretable parameters such as depth, albedo, and 3D pose. The network operates by first decomposing facial images into part-level descriptions, and then assembling these parts into an object-level representation, effectively building a hierarchical structure. This process is facilitated by a Graphics Decomposition Module (GDM), which leverages shape and albedo information to ensure that each part capsule represents a semantically consistent portion of the object. The method is trained using a reconstruction loss, encouraging the network to learn meaningful representations that can be used to reconstruct the input image. The authors evaluate IGC-Net on several face datasets, including CelebA, BP4D, and Multi-PIE, demonstrating its effectiveness in unsupervised face segmentation and face recognition. The paper also presents an analysis of the learned part-level representations, highlighting the importance of albedo over shape for face recognition. The authors claim that their method provides a more consistent representation across different views compared to 2D representations. Overall, the paper presents a compelling approach to unsupervised 3D face representation learning, offering an interpretable and hierarchical framework for understanding facial structure. The use of graphics capsules and the GDM are key contributions, and the experimental results provide evidence for the method's effectiveness on the tasks considered. However, the paper also has limitations, particularly in the scope of evaluation and comparisons with other state-of-the-art methods, which I will discuss in detail in the following sections.

✅ Strengths

I find several aspects of this paper to be particularly strong. The most significant is the introduction of the graphics capsule, a novel type of network component that represents 3D primitives with interpretable parameters. This is a significant advancement over previous capsule networks that are often limited to 2D representations. The ability to explicitly model depth, albedo, and 3D pose within a capsule is a compelling idea, and it aligns well with the goal of learning hierarchical 3D representations. The Graphics Decomposition Module (GDM) is another notable contribution. By using shape and albedo information as cues, the GDM effectively decomposes the face into semantically consistent part-level descriptions. This part-level decomposition is crucial for building a hierarchical representation, and it allows the network to understand faces as a composition of 3D models. The unsupervised nature of the method is also a strength. The ability to learn these representations from unlabeled images is a significant advantage, as it reduces the need for expensive annotated data. The experimental results, while limited in scope, do demonstrate the effectiveness of IGC-Net for unsupervised face segmentation and face recognition. The paper shows that the method can achieve high accuracy in these tasks, and it provides some evidence for the consistency of the learned 3D representations across different views. The analysis of the learned part-level representations, particularly the finding that albedo is more important than shape for face recognition, is also insightful. This analysis provides a glimpse into what the network is learning and how it is using the different parameters of the graphics capsules. Finally, the paper is generally well-written and organized, making it easy to follow the proposed method and understand the experimental results. The authors provide a clear introduction to the problem of learning hierarchical 3D face representations and a detailed description of the proposed method, including the graphics capsules, the GDM, and the loss functions. Overall, the paper presents a novel and promising approach to unsupervised 3D face representation learning, with several technical innovations and empirical achievements.

❌ Weaknesses

Despite the strengths of this paper, I have identified several significant weaknesses that warrant careful consideration. First, the paper's evaluation is primarily limited to human faces, which raises concerns about the generalizability of the proposed method. The authors apply IGC-Net to human faces, citing their similar topology structures and complicated appearances, and evaluate it on datasets such as BP4D, Multi-PIE, and CelebA, all of which contain only human faces. While Figure 4 shows a limited example of the method applied to cat faces, the analysis and quantitative evaluation are primarily focused on human faces. This narrow focus limits the conclusions that can be drawn about the method's applicability to other object categories. The reliance on specific 3D face priors, such as symmetry and predefined part structures, may not generalize well to objects lacking these characteristics. For example, the assumption of bilateral symmetry, which is likely used in the Graphics Decomposition Module (GDM), is not applicable to many other object categories. The part decomposition module is heavily reliant on this prior, and this reliance is a significant limitation. The paper lacks a thorough discussion of these limitations and potential avenues for future work to address them. This is a significant weakness because it restricts the scope of the paper's contributions and leaves open questions about the method's broader applicability. My confidence in this weakness is high, as it is directly supported by the paper's experimental setup and the lack of discussion on generalization. Second, the paper does not provide a comprehensive comparison with state-of-the-art methods for learning 3D face representations. The authors compare IGC-Net with other methods for unsupervised face segmentation, such as DFF, SCOPS, and HP-Capsule, but they do not compare it with methods that explicitly model 3D face geometry, such as 3D Morphable Model (3DMM)-based methods or GAN-based methods. This lack of comparison makes it difficult to assess the quality of the learned 3D representations. While the paper mentions that 3DMM parameters are not differentiable, it should still provide a qualitative comparison by visualizing the reconstructed faces from both IGC-Net and 3DMMs. This could involve applying the 3DMM parameters to a standard 3D face model and comparing the resulting renderings with the IGC-Net output. The absence of such comparisons makes it hard to determine whether the proposed method offers any significant improvement over existing techniques. This is a major weakness because it prevents a proper evaluation of the method's performance in the context of existing 3D face representation techniques. My confidence in this weakness is high, as it is directly supported by the paper's experimental setup and the lack of relevant comparisons. Third, the paper does not provide a detailed analysis of the part-level graphics capsules for face recognition. While the paper includes an experiment comparing shape and albedo embeddings, it does not provide a granular analysis of individual part capsules' contributions to the recognition task. The authors use trainable scalar weights to analyze the importance of shape and albedo at the part level, but they do not investigate the contribution of each part to the overall recognition performance by systematically masking or perturbing individual part representations. This type of analysis would provide a more detailed understanding of the learned part representations and their contribution to the overall performance. The lack of this analysis is a weakness because it limits our understanding of how the network is using the part-level information for face recognition. My confidence in this weakness is high, as it is supported by the paper's experimental results and the absence of the suggested analysis. Finally, the paper's visual results are limited. The authors only show the results of the discovered face hierarchy on a few examples in Figure 3 and Figure 4. These figures lack sufficient diversity in terms of pose, expression, and lighting conditions. The limited number of examples makes it difficult to assess the robustness of the method across a wide range of real-world scenarios. It is crucial to see how the part-level capsules behave under more challenging conditions, such as extreme poses or significant variations in illumination. The same criticism applies to the cat examples in Figure 4, which also lack diversity. This is a weakness because it limits our ability to assess the method's robustness and generalization capabilities. My confidence in this weakness is high, as it is directly supported by the limited number of examples in the figures and the lack of diversity in the shown examples.

💡 Suggestions

Based on the identified weaknesses, I recommend several concrete improvements for future work. First, the authors should address the limited generalizability of the method by exploring its applicability to a broader range of object categories beyond human faces. This would involve investigating alternative decomposition strategies that do not rely on strong priors like bilateral symmetry. For example, the authors could explore using clustering techniques in the latent space to identify parts or incorporating attention mechanisms to allow the network to learn part boundaries dynamically. This would require significant modifications to the Graphics Decomposition Module (GDM) to make it more adaptable to different object structures. The authors should also provide a more thorough discussion of the limitations of the current approach and potential avenues for future work to address these limitations. This would strengthen the paper by acknowledging its limitations and suggesting directions for future research. Second, to better evaluate the quality of the learned 3D representations, the authors should include a more comprehensive comparison with state-of-the-art 3D face representation methods. While a direct comparison of latent parameters may not be feasible, the authors could provide a qualitative comparison by visualizing the reconstructed faces from both IGC-Net and 3DMMs. This could involve applying the 3DMM parameters to a standard 3D face model and comparing the resulting renderings with the IGC-Net output. Additionally, the authors could compare their method with GAN-based approaches by evaluating the quality of the generated face images using metrics such as FID or Inception Score. This would provide a more comprehensive evaluation of the proposed method's performance in the context of existing 3D face representation techniques. The authors should also discuss the computational cost of the proposed method compared to other methods. Third, the authors should provide a more detailed analysis of the part-level graphics capsules to better understand their contribution to face recognition. The authors could investigate the contribution of each part to the overall recognition performance by systematically masking or perturbing individual part representations and observing the impact on recognition accuracy. This would provide a more granular understanding of the learned part representations. Furthermore, the authors could explore the relationship between the learned part representations and the semantic structure of the face. For example, the authors could investigate whether the learned parts correspond to meaningful facial regions, such as the eyes, nose, and mouth. This would provide insights into the interpretability of the learned representations and their potential for use in other face analysis tasks. Finally, the authors should include a more comprehensive set of visual examples for both face and cat hierarchies. For the face hierarchy, the additional examples should cover a wider range of poses (e.g., profile views, large rotations), expressions (e.g., smiling, frowning), and lighting conditions (e.g., strong shadows, highlights). This would provide a more thorough evaluation of the method's robustness and generalization capabilities. For the cat hierarchy, the authors should include examples with different poses, viewpoints, and background clutter. This would help in assessing the method's ability to generalize to different object categories and complex scenes. The authors should also consider including a quantitative evaluation of the segmentation results, such as pixel-wise accuracy or intersection-over-union, to provide a more objective assessment of the method's performance. These suggestions are aimed at addressing the identified weaknesses and improving the overall quality and impact of the paper.

❓ Questions

Based on my analysis, I have several questions that I believe are important for further understanding the proposed method. First, how does the IGC-Net perform on objects with more complex topologies or varying numbers of parts, such as animals with fur or vehicles with intricate shapes? The current method seems tailored to the specific structure of human faces, and it is unclear how it would adapt to objects with significantly different characteristics. This question is important because it addresses the limitations of the method's generalizability. Second, how does the IGC-Net compare with other state-of-the-art methods for learning 3D face representations, such as 3DMM-based methods or GAN-based methods, in terms of both reconstruction quality and computational cost? The paper lacks a direct comparison with these methods, and it is important to understand the trade-offs between the proposed approach and existing techniques. This question is important for assessing the relative performance of the method. Third, how does the IGC-Net perform on other tasks besides unsupervised face segmentation and interpretable face analysis, such as face recognition, face generation, or face manipulation? The paper primarily focuses on representation learning, but it would be valuable to understand the potential of the learned representations for other downstream tasks. This question is important for understanding the broader impact of the method. Fourth, what is the sensitivity of the IGC-Net to variations in pose, expression, and lighting conditions? The paper's visual results are limited, and it is unclear how the method would perform under more challenging conditions. This question is important for assessing the robustness of the method. Finally, what are the limitations of the current analysis of the part-level graphics capsules, and what are the potential directions for further investigation? The paper provides some analysis of shape vs. albedo, but it lacks a more detailed analysis of individual part contributions. This question is important for understanding the interpretability of the learned representations and their potential for use in other tasks. These questions are aimed at clarifying key uncertainties and limitations of the proposed method, and they are important for guiding future research in this area.

📊 Scores

Soundness:3.0
Presentation:3.0
Contribution:2.75
Rating: 6.0

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📋 Summary

The paper introduces the Inverse Graphics Capsule Network (IGC-Net), a capsule-based inverse graphics framework for learning hierarchical 3D face representations from unlabeled 2D images. Each "graphics capsule" explicitly parameterizes a part via computer graphics variables (depth map D, albedo A, 3D pose p). A Graphics Decomposition Module (GDM) decomposes global shape/albedo embeddings into part-level embeddings using cross-attention and a dimension-wise one-hot attention that is shared across shape and albedo to maintain semantic alignment. Part capsules are assembled into an object capsule using a hard depth-based visibility mask; the assembled 3D object is then posed, illuminated, and rendered differentiably. Training is unsupervised with reconstruction/perceptual losses (including a symmetry-aware NLL as in unsup3d), a contrastive loss for semantic consistency of part embeddings, a sparsity prior over visible regions, and a background-separation loss using a learned background capsule and a depth threshold. On CelebA and BP4D, IGC-Net discovers semantically consistent facial parts (background, eyes, mouth, forehead, nose, cheek) and significantly improves unsupervised face segmentation (e.g., on CelebA NME_L: 11.84 vs 18.72 for SCOPS; on BP4D NME_L: 6.35 vs 8.81 for HP-Capsule). Analyses on Multi-PIE show the learned 3D representations are more view-independent than 2D autoencoder features (95.1% vs 91.2% recognition), and that albedo is more critical than shape for recognition, with eyes’ albedo and nose’s shape being most important.

✅ Strengths

  • Conceptual novelty: defines a new capsule primitive with explicit 3D CG parameters (depth, albedo, pose) and integrates inverse graphics rendering into a capsule hierarchy.
  • Graphics Decomposition Module (GDM): clever cross-attention and one-hot dimension attention shared between shape and albedo to enforce semantically consistent parts (Eq. 5–6).
  • Clear hierarchy construction: depth-based visibility to assemble parts into an object-centered representation, aligning with Marr’s theory, followed by differentiable rendering (Eq. 4).
  • Strong empirical gains on unsupervised face segmentation with relevant baselines (DFF, SCOPS, HP-Capsule), showing substantial error reductions on CelebA and BP4D (Tables 1–2) and clear qualitative improvements (Figs. 7–8).
  • Insightful analyses: 3D vs 2D view independence (Section 4.2, Fig. 5) and interpretable part/component importance (shape vs albedo, Fig. 6); ablations isolating the role of one-hot attention and contrastive loss (Fig. 9, Table 3).
  • Broader promise: preliminary extension to cat faces suggests potential beyond human faces (Fig. 4).

❌ Weaknesses

  • Differentiability questions: the assembly uses a hard depth-based argmin visibility (Eq. 3), and GDM employs a non-differentiable one-hot/"hard_softmax" (Eq. 6). The paper does not clarify whether straight-through estimators or soft relaxations are used, nor discuss gradients and stability.
  • Reproducibility gaps: main text omits critical details (e.g., random seeds, batch sizes, dataset splits, preprocessing/face alignment). The paper defers to supplementary for some details.
  • Lack of statistical rigor: reported metrics (e.g., Tables 1–3; Fig. 5 recognition) have no variance/error bars or multiple runs; no significance testing, making robustness of improvements harder to assess.
  • Scope limitations: evaluation is focused on faces (with a small cat example). Generalization to broader object categories with complex self-occlusions or without bilateral symmetry is not studied.
  • Assumptions and priors: relies on symmetry-aware reconstruction loss and VGG-based perceptual features; the effective supervision from ImageNet features and face-biased priors may limit claims of fully unsupervised generality.
  • Background modeling via depth threshold (Eq. 11) introduces a heuristic parameter γ; sensitivity analyses to γ and failure modes (e.g., cluttered backgrounds) are not discussed.

❓ Questions

  • How is the non-differentiability of the argmin visibility mask in Eq. (3) handled? Do you use a straight-through estimator, a softmin/soft z-buffer, or another approximation? How sensitive is training to this choice?
  • Similarly, the one-hot hard_softmax in Eq. (6) is non-differentiable. Do you use a straight-through gradient, Gumbel-softmax, or a soft relaxation during training? Please detail the exact implementation and any temperature/annealing schedule.
  • Please provide the missing training details: batch size, random seed(s), data splits, preprocessing (e.g., face detection/cropping/alignment), and the temperature τ used in the contrastive loss. Also report training time and inference speed.
  • Can you report results averaged over multiple runs with standard deviations for Tables 1–3 and Fig. 5 (recognition accuracy), to assess robustness and statistical significance?
  • How sensitive are the results to the number of parts M (beyond the brief note in Section 4.1)? Could you provide quantitative trends for NME vs M and show failure modes when M is too small/large?
  • What is the impact of the background threshold γ in Eq. (11)? Please include a sensitivity analysis and qualitative examples where the background capsule fails (e.g., cluttered/near-depth backgrounds).
  • Does the method require face alignment or tight cropping? How does performance change with looser crops or in-the-wild distractors/occlusions (e.g., hands, hats, glasses)?
  • Could you clarify the lighting model used with Λ (Eq. 4), and whether normals are derived from depth or a differentiable shading network? Any constraints on illumination variability?
  • In the 3D vs 2D evaluation (Fig. 5), are the linear classifiers trained on the same views as tested? Please specify the exact training/testing protocol and ensure the 2D autoencoder matches IGC-Net in capacity and training recipe.
  • Beyond faces/cats, what obstacles prevent scaling IGC-Net to generic articulated objects? Are there plans for soft visibility/occlusion modeling or part splitting/merging to handle diverse topologies?

⚠️ Limitations

  • Domain focus: Results focus on faces; generalization to unconstrained object categories remains untested. The method leverages facial symmetry and limited topology variation.
  • Non-differentiable components: Hard argmin visibility and hard one-hot attention introduce potential gradient issues; training stability and convergence properties are under-specified.
  • Heuristic components: Background separation via a fixed depth threshold γ may be brittle in cluttered or depth-ambiguous scenes.
  • Dependence on priors: Symmetry-aware reconstruction and perceptual losses (VGG) inject strong priors; while effective, they blur the line of purely unsupervised learning and may bias learned parts.
  • Potential societal risks: Improved unsupervised 3D face modeling and part-aware analysis can be misused for mass surveillance, profiling, or privacy-invasive applications; fairness across demographics (skin tone, age, gender) is not evaluated.

🖼️ Image Evaluation

Cross‑Modal Consistency: 37/50

Textual Logical Soundness: 24/30

Visual Aesthetics & Clarity: 12/20

Overall Score: 73/100

Detailed Evaluation (≤500 words):

1. Cross‑Modal Consistency

• Major 1: Figure numbering mismatch in Sec. 4.2 confuses evidence mapping (3D vs 2D). Evidence: “The results are shown in Figure 5… it can be seen from Figure 4(a)… Figure 4(b).”

• Major 2: Core qualitative evidence (Fig. 3) has many micro‑panes that are illegible at print size, blocking verification that six 3D parts are consistently discovered. Evidence: Fig. 3’s per‑part depth/albedo tiles are too small to read.

• Minor 1: Notation inconsistency between ẑ/Ĩ in losses and renderer. Evidence: Eq. (4) uses “ṼI=Λ(D,A,p,l)” while Eq. (7–8) optimize “Ĩ” and “Ĩflip.”

• Minor 2: Typos in Eq. (3): duplicated tag “(3)” and stray superscript in “A_o = ∑_m^m …”. Evidence: Eq. (3) block shows repeated (3) and “∑_m^m”.

• Minor 3: Fig. 5(b) heatmap axes (yaw ticks/colorbar) are hard to read; text refers to exact angles (e.g., 30° vs −60°). Evidence: Fig. 5(b) tiny axis labels.

2. Text Logic

• Major 1: No Major issues found.

• Minor 1: Renderer/lighting details are deferred to prior work, leaving unclear which shading model is used (diffuse/specular) though it affects albedo/shape disentanglement. Evidence: Sec. 3.1 “another module similar to [34]”.

• Minor 2: Object‑pose aggregation as simple average (p_o = (1/M)∑ p_p^m) not justified; could bias composition when parts are occluded. Evidence: Eq. (3) line for p_o.

3. Figure Quality

• Major 1: Fig. 3 panel grid and several per‑part tiles (also cats in Fig. 4) are illegible at print size; add larger crops or fewer columns. Evidence: Fig. 3/Fig. 4 multi‑tile mosaics with unreadable detail.

• Minor 1: Fig. 1 overview fonts (module labels, axes for pose) are small; add larger text and clearer arrows. Evidence: Fig. 1 “Graphics capsule (object‑level)” and pose axes text.

• Minor 2: Fig. 5(b) colorbar and tick labels are small; include numeric annotations for key cells. Evidence: Fig. 5(b) color scale barely readable.

Key strengths:

  • Clear conceptual contribution (graphics capsules + GDM) with interpretable CG parameters.
  • Strong quantitative gains on unsupervised face segmentation (Tables 1–2).
  • Thoughtful interpretability experiments (Fig. 6) aligning with prior findings.

Key weaknesses:

  • Figure‑reference mismatches (Fig. 4 vs Fig. 5) and equation typos harm traceability.
  • Critical visuals are too dense/small to verify claims without text.
  • Limited detail on rendering/lighting and pose aggregation may impact reproducibility.

Requested fixes (highest impact first):

  • Correct all figure references in Sec. 4.2 to “Figure 5(a)/(b)”.
  • Re‑layout Fig. 3/Fig. 4 with larger per‑part crops and explicit part labels; ensure legible at print size.
  • Clean Eq. (3) typos and unify Ĩ/ṼI notation.
  • Clarify lighting model and justify pose averaging; consider visibility‑weighted pose.

📊 Scores

Originality:3
Quality:3
Clarity:3
Significance:3
Soundness:3
Presentation:3
Contribution:3
Rating: 7

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📋 Summary

This paper introduces the Inverse Graphics Capsule Network (IGC-Net), a novel approach for learning hierarchical 3D face representations from 2D images in an unsupervised manner. The core idea revolves around using graphics capsules, which are essentially part-level 3D models with interpretable parameters such as depth, albedo, and pose. The method begins by encoding an input image into global shape and albedo embeddings using a convolutional neural network (CNN). These embeddings are then fed into a Graphics Decomposition Module (GDM), which decomposes them into a set of part-level embeddings. These part-level embeddings are then used to construct graphics capsules, each representing a semantically consistent part of the face. The GDM employs a cross-attention mechanism between the global embedding and shape basis to generate disentangled part-level shape embeddings, which are then used to extract corresponding albedo embeddings. The part capsules are then assembled into an object capsule based on their depth information. The final step involves estimating lighting parameters and generating a reconstructed image using a differentiable renderer. The authors evaluate their method on several datasets, including CelebA, BP4D, and Multi-PIE, demonstrating its ability to perform unsupervised face segmentation and analyze the importance of shape and albedo for face recognition. The paper's main contribution lies in its novel use of graphics capsules to learn hierarchical 3D representations and its unsupervised approach to face part discovery. The method's ability to disentangle shape and albedo at the part level is a significant step towards more interpretable and controllable face models. However, the paper also has several limitations, particularly in its experimental evaluation and the lack of detailed explanations of certain aspects of the method. The paper's focus on face analysis, while understandable given the complexity of human faces, limits the generalizability of the approach. The lack of comparisons with state-of-the-art 3D face reconstruction methods and the absence of quantitative evaluations of the quality of the learned 3D representations are significant shortcomings. Furthermore, the paper's claim of learning a 'hierarchical' representation is not fully supported by the evidence, as the part-level representations are not explicitly used in a hierarchical manner beyond their assembly into an object capsule. Despite these limitations, the paper presents a promising approach for unsupervised 3D face analysis and provides a foundation for future research in this area.

✅ Strengths

I find several aspects of this paper to be commendable. The core idea of using graphics capsules to represent 3D face parts is a novel and compelling approach. The method's ability to learn these representations in an unsupervised manner, without relying on explicit 3D annotations, is a significant strength. The use of interpretable parameters within the capsules, such as depth, albedo, and pose, allows for a more transparent and controllable representation of the face. The Graphics Decomposition Module (GDM) is a clever design that leverages cross-attention to disentangle shape and albedo at the part level. The experimental results, while not without limitations, demonstrate the method's ability to perform unsupervised face segmentation and to analyze the importance of shape and albedo for face recognition. The paper is also generally well-written and easy to follow, which is crucial for the accessibility of the research. The authors clearly articulate their motivation and the main steps of their method. The use of a differentiable renderer allows for end-to-end training of the network, which is a significant technical achievement. The paper's focus on interpretability is also a valuable contribution, as it moves away from the black-box nature of many deep learning models. The authors' attempt to link their work to Marr's theory of vision is also interesting, even if it is not fully developed. The paper's exploration of the importance of shape and albedo for face recognition is a valuable contribution to the field. The method's ability to handle in-the-wild images, as demonstrated on the CelebA dataset, is also a positive aspect. The paper's focus on part-level representations is also a strength, as it allows for a more fine-grained analysis of the face. The use of a capsule network is also a strength, as it allows for the modeling of hierarchical relationships between parts. Finally, the paper's overall contribution to the field of unsupervised 3D face analysis is significant and provides a foundation for future research.

❌ Weaknesses

Despite the strengths of this paper, I have identified several weaknesses that warrant careful consideration. First, the paper lacks a detailed explanation of the Graphics Decomposition Module (GDM). While the paper describes the GDM as using cross-attention between global embeddings and shape bases to generate part-level shape embeddings, it does not provide sufficient detail on the architecture of the GDM, the exact implementation of the cross-attention mechanism, or the nature of the shape bases. The paper states that the albedo embeddings are derived from the shape embeddings using the same attention map, but it does not explain why this approach is effective or how it ensures that the albedo information is correctly associated with each part. This lack of detail makes it difficult to fully understand the inner workings of the GDM and to assess its effectiveness. My analysis of the paper confirms that the exact implementation details of the GDM are not fully elaborated, which makes it difficult to understand how the shape and albedo information are effectively decoupled at the part level. Second, the paper does not provide a clear explanation of how the part-level graphics capsules are assembled into the object capsule. The paper states that the assembly is based on depth, with each part capsule being visible only when its depth is smaller than the others. However, it does not explain how the depth information is used to order the parts or how the 3D structure of the object capsule is generated. The paper also does not explain how the visibility maps of the part capsules are used in the assembly process. This lack of clarity makes it difficult to understand how the part-level representations are integrated into a coherent object-level representation. My analysis confirms that the paper lacks a detailed explanation of the assembly process, particularly regarding the role of depth and visibility maps. Third, the paper's experimental evaluation is limited in several ways. The paper does not compare its method with state-of-the-art 3D face reconstruction methods, such as DECA, which is a significant omission. The paper also does not provide quantitative evaluations of the quality of the learned 3D representations, such as point cloud error or mesh reconstruction accuracy. The paper relies primarily on qualitative visualizations and an indirect evaluation through unsupervised segmentation, which is not sufficient to fully assess the quality of the 3D reconstruction. My analysis confirms that the paper lacks quantitative 3D reconstruction metrics and comparisons with state-of-the-art methods. Fourth, the paper's claim of learning a 'hierarchical' representation is not fully supported by the evidence. While the paper describes a bottom-up process of assembling part capsules into an object capsule, it does not demonstrate any explicit use of the part-level representations in a hierarchical manner beyond their assembly. The paper does not show how the part-level representations are used to perform any task or how they contribute to a higher-level understanding of the face. My analysis confirms that the paper does not provide sufficient evidence to support the claim of learning a hierarchical representation. Fifth, the paper's evaluation of the method's performance on in-the-wild images is limited. While the paper uses the CelebA dataset, which contains in-the-wild images, it does not provide a detailed analysis of the method's robustness to variations in pose, illumination, and expression. The paper also does not compare its performance on CelebA with its performance on the more controlled BP4D and Multi-PIE datasets. My analysis confirms that the paper lacks a detailed analysis of the method's robustness to variations in pose, illumination, and expression on in-the-wild images. Sixth, the paper's comparison with other unsupervised methods is limited. While the paper compares its method with DFF, SCOPS, and HP-Capsule, it does not include a comparison with more recent unsupervised methods, such as those based on normalizing flows or contrastive learning. This makes it difficult to assess the relative strengths and weaknesses of the proposed method. My analysis confirms that the paper lacks a comparison with more recent unsupervised methods. Finally, the paper does not provide a clear explanation of the role of the confidence map (σ) in the reconstruction loss. The paper states that the confidence map is estimated by a network to present the symmetric probability of each position, but it does not explain how this confidence map is used to handle ambiguities in the reconstruction process. My analysis confirms that the paper lacks a detailed explanation of the role of the confidence map in the reconstruction loss. These weaknesses, taken together, significantly limit the impact of the paper and raise questions about the generalizability and robustness of the proposed method.

💡 Suggestions

To address the identified weaknesses, I recommend several concrete improvements. First, the authors should provide a more detailed explanation of the Graphics Decomposition Module (GDM). This should include a clear description of the architecture of the GDM, the exact implementation of the cross-attention mechanism, and the nature of the shape bases. The authors should also explain why the albedo embeddings are derived from the shape embeddings using the same attention map and how this approach ensures that the albedo information is correctly associated with each part. A visualization of the attention maps would also be helpful to understand how the GDM is partitioning the face. Second, the authors should provide a more detailed explanation of how the part-level graphics capsules are assembled into the object capsule. This should include a clear description of how the depth information is used to order the parts, how the 3D structure of the object capsule is generated, and how the visibility maps of the part capsules are used in the assembly process. A step-by-step explanation, perhaps with a diagram, would greatly improve the clarity of this section. Third, the authors should include a more comprehensive experimental evaluation of their method. This should include comparisons with state-of-the-art 3D face reconstruction methods, such as DECA, as well as quantitative evaluations of the quality of the learned 3D representations, such as point cloud error or mesh reconstruction accuracy. The authors should also provide a more detailed analysis of the method's robustness to variations in pose, illumination, and expression on in-the-wild images. Fourth, the authors should provide more evidence to support their claim of learning a 'hierarchical' representation. This could involve demonstrating how the part-level representations are used to perform some task or how they contribute to a higher-level understanding of the face. The authors could also explore the possibility of using the part-level representations to generate more diverse and realistic facial expressions. Fifth, the authors should include a comparison with more recent unsupervised methods, such as those based on normalizing flows or contrastive learning. This would provide a more comprehensive evaluation of the proposed method and help to identify its strengths and weaknesses. Sixth, the authors should provide a more detailed explanation of the role of the confidence map (σ) in the reconstruction loss. This should include a clear description of how the confidence map is used to handle ambiguities in the reconstruction process and how it is learned by the network. Finally, the authors should consider expanding the scope of their method beyond face analysis. While the focus on faces is understandable, the core ideas of the method could potentially be applied to other objects as well. This would demonstrate the generalizability of the approach and increase its impact. By addressing these weaknesses, the authors can significantly improve the quality and impact of their paper.

❓ Questions

I have several questions that arise from my analysis of this paper. First, regarding the Graphics Decomposition Module (GDM), I am curious about the specific architecture of the shape encoder and basis. What is the dimensionality of the shape embeddings, and how are the shape bases initialized? Are they learned or predefined? Second, concerning the assembly of part capsules into the object capsule, I would like to understand the precise mechanism by which the depth information is used to order the parts. Is it a simple sorting operation, or is there a more complex process involved? How is the 3D structure of the object capsule generated from the part-level depth maps? Third, regarding the experimental evaluation, I am curious about the performance of the method on more challenging datasets with significant pose variations, occlusions, and varying lighting conditions. How does the method compare to state-of-the-art 3D face reconstruction methods on these datasets? Fourth, regarding the claim of learning a 'hierarchical' representation, I would like to understand how the part-level representations are explicitly used in a hierarchical manner beyond their assembly into an object capsule. Are there any plans to explore the use of these part-level representations for other tasks, such as facial expression generation or animation? Fifth, regarding the confidence map (σ) in the reconstruction loss, I am curious about how this map is learned by the network and how it is used to handle ambiguities in the reconstruction process. What is the architecture of the network that estimates the confidence map? Sixth, regarding the generalizability of the method, I would like to know if there are any plans to apply the method to other objects beyond faces. What are the main challenges in extending the method to other objects? Finally, regarding the comparison with other unsupervised methods, I am curious about the performance of the method compared to more recent unsupervised methods based on normalizing flows or contrastive learning. What are the main differences between these methods and the proposed method? These questions are aimed at clarifying key aspects of the method and its evaluation, and I believe that addressing them would significantly improve the paper.

📊 Scores

Soundness:2.5
Presentation:2.75
Contribution:2.5
Rating: 5.75

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