Venue: NeurIPS 2022 Conference

Reviews:

final_score: rating: 5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.
review_content: summary: The paper proposes a new method for representing surfaces on grids using prior-based losses: viscosity loss and Coarea loss. They have shown better results than neural network SDFs in reconstructing surfaces on the Surface Reconstruction Benchmark.
strengths_and_weaknesses: Pro:

1. Instead of using a neural network as a bridge to build implicit surface representation, the authors propose to go back to using the grid-based method. It is easier to train than a neural network and is easier to find the zero surface.

2. The authors bring two new priors to the domain, viscosity and Coarea loss, to replace Eikonal loss and control the surface's area. They use the finite difference to compute the gradient or the Laplacian.

Con:

1. It does not directly compare how Viscosity loss and Coarea loss would perform with the neural network. The comparison with other works seems not fair.
questions: For the comparison, each sample is "optimized"/ "learned" on a separate grid? Does it downgrade to only solving a PDE, not a learning problem? It seems not so fair to compare with the neural network-based method, which can extend to "arbitrarily" resolution, while the grid is fixed.
limitations: The limitation mainly comes from the grid-based representation. It seems can only represent one model after optimization, unlike other network-based can use a latent code as an additional condition.
review_title: null

final_score: rating: 4: Borderline reject: Technically solid paper where reasons to reject, e.g., limited evaluation, outweigh reasons to accept, e.g., good evaluation. Please use sparingly.
review_content: summary: This submission proposes 2 new geometric prior terms for fitting regular grids of SDFs to point clouds. The 2 priors are simulating the viscosity of the field to smooth it, and minimizing the area of the 0 level set.
strengths_and_weaknesses: Strengths:
- technical soundness
- nice presentation with clear figures
- great ablation of the 2 added priors and their respective effects.

Weaknesses:
MAJOR - experiments are only conducted on 5 shapes only, no precise information is given about the optimization strategy (grid resolution, gradient descent steps...), and no normal consistency is provided.
MINOR - the introduction, the too short related work section, and the general scoping of the paper wrongly confuses 3D shape reconstruction from a point cloud with 3D shape representation with neural networks. Both are orthogonal research topics.
MINOR - the paper claims that using a grid of SDF has "clear benefits", but what are they? And the proposed 2 loss terms could be used on implciit networks as well..
questions: - How are gradients computed from the grid in eq. (3)?
- Why is Fig(2) showing a problem? the 0-isosurface is the same...
- In Tab. 2, why is Daratesh better without any additional loss term?
- 4.2 ablates different weights for the viscosity term. How hard is it to tune in practice?
limitations: A limitation not mentioned by the authors is that it is not possible to learn a shape prior with this formulation: only single shape fitting is possible.
review_title: null

final_score: rating: 6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
review_content: summary: The paper proposes a method for SDF based surface reconstruction from point clouds using grid based functions, rather than the recently popular INR approaches. They use standard INR losses along with a new prior loss that has two components, a viscosity prior (for smoothness in the SDF) and a coarea prior (for minimal surface area). They show quantitative results on the SRB dataset, which are comparative to SoTA, and qualitative results on the Stanford 3D scanning repository.
strengths_and_weaknesses: Strengths
- Agree that general direct priors are still important for surface reconstruction given how important the task is and how various the shapes can be, and the paper gives two interesting priors
- Mathematical explanation, intuition and visualisations of the two components of the prior all show their value
- Results with normals are comparative to SoTA
- Good ablations of the components
- Paper is well written

Weaknesses
- Limited quantitative results (5 shapes). While SRB is a well established baseline, having this as the only quantitative results is not great.
- Given that the method is not using a neural network and is grid based, a major strength of the method should be lower optimisation time, with the weakness being storage of the learned INR. A discussion of both is missing, with no comparison of optimisation time or learned storage to other methods.
- The use of minimising the Laplacian as a prior has been explored in INR work, such as DiGS [* 1] and NSP [32], and has connections to PHASE [18]. This is not discussed at all (and should be in the related work), and DiGS is not even cited.
- Poor results without normals, especially given the contribution is meant to be a good prior for SDFs and thus should give results comparable to PHASE [18] or DiGS [* 1].

[* 1] https://arxiv.org/abs/2106.10811
questions: PHASE [18] is quite similar (a method with a direct prior based on smoothness and minimal area) and gets better (or similar) performance. Why is this the case? Is it just because of it using a neural network vs this work being network free, or could it possibily be better direct priors?

The following work might be of interest to you: https://arxiv.org/abs/2206.03087v1, it is a concurrent work (accepted to CVPR2022) with similar priors (they have them as regularizations): a Hessian regularization for smoothness and a minimal surface regularization.
limitations: Yes, limitations in conclusion, and social impact in subsection in conclusion.
review_title: null

final_score: rating: 4: Borderline reject: Technically solid paper where reasons to reject, e.g., limited evaluation, outweigh reasons to accept, e.g., good evaluation. Please use sparingly.
review_content: summary: The proposed method tries to improve the surface reconstruction quality by introducing two losses.
The viscosity loss tries to imporve the smoothness of the surface part without points.
The coarea loss tries to approximate the area of the zero level set.
The experiments show the proposed method can get better surface reconstruction results, especially with sparse point inputs.
strengths_and_weaknesses: Strengths
1. The paper is generally well written. All the figures and equations are clear.
2. The authors clearly explain why the viscosity loss should be introduced.
3. The experiments results on sparse point inputs are improved.

Weaknesses
1. The main contribution of the paper is the introduction of two losses. There is no neural network sturctue contribution.
2. The motivation of coarea loss is not explained clearly. We can only know its effectness by the ablation study.
3. The quantitive results on benchmarks and of the ablation study are not improved significantly. On several data of the benchmark, the top results are not generated by the proposed method. In the ablation study, the baseline method cannot beat other settings.
4. The experiments are performed on point clouds without many noises. 
questions: 1. Could the authors explain why the coarea loss is introduced more clearly?
2. Could the authors do some experiments on point clouds by MVS, which have more noises than the data used in the paper?
limitations: The authors discuss the limitation in the conclusion briefly. The work does not have potential negative societal impact.
review_title: null

Meta-review: metareview: The paper originally received mixed scores, with two reviewers recommending acceptance and two rejection. While the reviewers acknowledged the soundness of the approach, the clarity of the explanations, and the good ablations of the method's components, they expressed concerns regarding the limited scope of the experiments, the lack of runtime analysis, and the fairness of the comparison to baselines. The authors' feedback convincingly addressed these concerns; in the discussion, tYGS agreed to raise their score to Weak Accept, and ubX9 to borderline accept. This led to a consensus for acceptance. We nonetheless strongly encourage the authors to incorporate elements of their feedback in the camera-ready version of their paper.
confidence: Certain
Decision: Accept