Summary
The paper considers the task of surface reconstruction from point clouds without normals with INRs. They consider solving for the SDF by solving the p-Poisson equation (with manifold constraint) as p\to\infty. However as the obvious loss function form of this is difficult to optimise, they consider a variable splitting strategy. They also do this w.r.t. ensuring that their gradient solution is conservative. Finally they add a minimal surface area regularisation term.
Strengths
- Variable splitting is a nice approach to the issues with neural networks and automatic differentiation
- Model is backed strongly by theoretical intuition
- Auxilary variables sharing the network structure is nice
- Decent results
Weaknesses
- It would be nice to have some intuition as to why you propose to use the p-Poisson equation rather than other PDEs like the Eikonal equation. At first glance it seems that the reason is because it is possible to describe it as a variational problem as shown in equation 2, however that doesn't get used by your method. Another argument you posit is that without the vanishing viscosity method a normal eikonal PDE based solution may produce a non-unique weak solution, why is it clear that your method does not produce a non-unique weak solution? Is it because of the curl-free constraint being enforced?
- How important is the enforcement of the loose eikonal constraint within the curl-free constraint? It somewhat diminishes the story of trying to solve the SDF problem using a different PDE to the eikonal equation.
- It is not clear why the curl-free constraint is needed. $\nabla u$ is curl-free by design, so isn't minimising $||\nabla u - G||$ in (8) sufficient? Why is a separate auxiliary variable necessary, apart from enforcing a loose Eikonal constraint by construction? Doesn't the argument about needed to set $\lambda_1$ infinitely large to enforce the constraint apply to $\lambda_3$ as well?
- The qualitative diagrams (Figure 5-7) for the ablation study are great for intuition and understanding, however you should have quantitative results on what happens when you remove each of those components (especially for curl-free)
I like this type of approach, willing to increase the score if clarity on the necessity of both the curl-free constraint and the eikonal construction constraint as well as quantitative ablations are given.
Questions
- What is $F$? Is it kept to the example given, $1/3x$?
- I am confused why the curl-free constraint needed. By equation 10, the new curl-free constraint ensures that $G=\nabla v$ for some $v$, but why allow it to be some $v$ that is not the $u$ being outputed as the INR value, and/or instead constrain it to be similar to the current INR value $u(x)$?
- I would like more intuition on the role of the curl-free constraint. Figure 5 seems to show that it forces the model to pay attention to detail more, however I don't see why this is the case theoretically. Is it because the eikonal term is loosely being enforced within the curl-free objective by construction?
- The good results of IGR on Thingi10K seems unlikely given its bad performance on SRB, it is almost as good as your model. Is there a property of Thingi10K that causes this? Is there a reason your model and IGR would be so similar on Thingi10K?
- The performance of your model on Daratech in SRB seems a bit confusing, in the results it does really badly on $d_C$ however it looks fairly good in Figure 6?
Rating
6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.
Confidence
4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.
Limitations
Some discussion given.
No clear potential negative societal impact or broader societal impacts to discuss