Generative Topology for Shape Synthesis

However, this work has several critical issues:

• Limited Novelty:
  • As mentioned in the introduction, the application of ECT on 3D point cloud analysis has been well explored in (Röell & Rieck, 2024). The formulation of ECT is directly adopted from (Röell & Rieck, 2024) without modification, and the writing and description of the formulation are also highly similar to (Röell & Rieck, 2024).
  • The main contribution, introducing an additional encoder to invert ECT representation into an explicit point cloud via a point cloud generative network, is considered trivial.
• Evaluation Performance:
  • While the authors claim that the proposed framework achieves comparable performance, several recent baselines are omitted, including:
    • [1] LION: Latent Point Diffusion Models for 3D Shape Generation. NeurIPS 2022.
    • [2] Autoregressive 3D Shape Generation via Canonical Mapping. ECCV 2022.
    • [3] Shape Generation and Completion Through Point-Voxel Diffusion. ICCV 2021.
    • [4] Diffusion Probabilistic Models for 3D Point Cloud Generation. CVPR 2021.
  • The authors argue that existing processing networks, such as Point-Voxel networks, are unsuitable for point cloud representation but provide no comparison. Notably, [1] and [4] adopt PVCNN for point cloud generation, and a comparison should be provided to support this claim.
  • Moreover, [2] and [3] learn a latent representation that can faithfully reconstruct point clouds. Before claiming the proposed representation's superiority, reconstruction performance and efficiency must be compared with these works.
• Non-equivariant Network:
  • Despite showing some effectiveness (Table 4), the current network (ECT-MLP) is not inherently equivariant, which weakens the discussion on learning equivariant representations.

Justification of Rating: This work explores the use of ECT for point cloud generation tasks. However, its technical contribution is limited, primarily based on a direct adoption of the formulation in (Röell & Rieck, 2024) without significant modifications. The comparisons with existing methods lack several important baselines to support its claims. Despite being an interesting direction, the manuscript requires substantial revision to reconsider its formulation and include additional experiments. Therefore, I recommend rejecting the paper and encouraging the authors to resubmit after addressing these issues.

I am a bit confused by the proposal by the authors. While the ECT seems like a powerful approach, its application to point clouds is a bit confounding, considering point clouds do not hold any topological information beyond that of a set, and the Euler Characteristic reduces to a trivial formula for them. Indeed, the attempt to discuss point clouds as simplicial complexes seems somewhat forced, albeit mathematically correct. As far as I understand, without having an actual underlying topology implied the the simplicial complex structure, the power of ECT is significantly reduced, and as far as I understand, the method reduces to classifying points based on their "depth" with respect to selected "view directions" - this does not strike me as extremely novel nor powerful. The results do not seem to show significant improvement over the quite saturated SotA. I additionally note that in several places, the authors are not mathematically rigorous, e.g., "A key feature of these invariants is that they are an intrinsic property meaning that they do not depend on a specific choice of coordinate", followed by "To extend the expressivity of this invariant, we need to provide it with geometrical and topological information about the input data" in which the authors proceed the embed the SC in 3D coordinates and exactly violate the notion of an intrinsic property they focus on before.

1. While the model is efficient, it has a comparatively large number of parameters, which could be a drawback in some applications. Further optimization to reduce the number of parameters without compromising performance could be beneficial.
2. The paper notes that the ECT is susceptible to scale differences in the input dataset. Addressing this issue to make the model more robust would be an improvement.
3. More experiments on diverse datasets could further demonstrate the generalization capabilities of the model, not only on three categories (chair, airplane, car). More complex shape with various topologies should be evaluated to demonstrate the core idea of the proposed method.
4. While the model performs well, providing more insight into how the ECT encodes and decodes shape information could help readers better understand the underlying mechanisms. Figure 1 is to transfer the coarse idea to readers.
5. The performance does not achieve the best from the quantitative evaluations; some point cloud generation on diffusion model should be considered as the baseline to compare. [1] Lion: Latent point diffusion models for 3d shape generation
6. The limitations and failure cases should be demonstrated in the paper.

• Over-generalization. The paper attempts to stay general about the dimension of the point clouds, but he writing is not always consistent. For example, in the paragraph starting at L138, "spherical coordinate", "voxel grid", and "scale cubically" are only appropriate for 3D scenario. However, what comes after implies arbitrary dimensions. This creates confusions. It might be a good idea to stay consistent and put 3D-specific and general contents to different sections / paragraphs.
• There needs major improvement on the writing. For example, there are factual errors such as L161 "We realise both of these steps using an MLP", which is not the case as the encoding process is done with ECT algorithm. There are also inconsistencies such as the purpose of the "encoder" in Figure 1 not matching the text in L161, and broken sentences such as L178 "Next to the improved ECT calculations, we thus...".
• L146-147 Cubic scaling of memory and compute w.r.t. the resolution of polar coordinate ECT: This is likely not true. The compute and memory will scale linearly with the number of angles used in the ECT, regardless of the dimension. Could you elaborate how you have arrived at the conclusion?
• The performance of the proposed method is not very good, lagging behind the previous works in almost all the settings.
• The rotation augmentation experiment (Figure 4) does not add any value, as any method can acquire equivariancy through data augmentation, and there lacks any comparisons with other methods.
• Reproducibility: The resolution of the ECT map is not known. This also creates a confusion on the expected input shape of ECT-MLP.
• The permutation invariant property of ECT is not fully taken advantage of. The decoder MLP converting the ECT to points is not permutation equivariant, possibly hindering the quality.