MultiPull: Detailing Signed Distance Functions by Pulling Multi-Level Queries at Multi-Step

Reconstructing a continuous surface from a raw 3D point cloud is a challenging task. Recent methods usually train neural networks to overfit on single point clouds to infer signed distance functions (SDFs). However, neural networks tend to smooth local details due to the lack of ground truth signed distances or normals, which limits the performance of overfitting-based methods in reconstruction tasks. To resolve this issue, we propose a novel method, named MultiPull, to learn multi-scale implicit fields from raw point clouds by optimizing accurate SDFs from coarse to fine. We achieve this by mapping 3D query points into a set of frequency features, which makes it possible to leverage multi-level features during optimization. Meanwhile, we introduce optimization constraints from the perspective of spatial distance and normal consistency, which play a key role in point cloud reconstruction based on multi-scale optimization strategies. Our experiments on widely used object and scene benchmarks demonstrate that our method outperforms the state-of-the-art methods in surface reconstruction.

Paper

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Peer review

Reviewer VUUa5/10 · confidence 4/52024-07-10

Summary

The authors propose a method to reconstruct neural multi-scale SDFs from point clouds using an optimization-based approach. The multi-scale SDF is represented with a network architecture based on previous work [11] and optimized using a new iterative pulling approach, where the SDF for each scale is optimized to pull a query point to the 0-level-set (using the gradient and value of the SDF at the query), starting with a relatively distant query point for the coarsest SDF, and using the updated query position from the result of the previous scale in the next-finer SDF. Losses based on GridPull [20], but adapted to the multi-scale setting are used as objective for the optimization. The authors show that this approach performs better than several exisiting surface reconstruction methods on several synthetic and real-world datasets.

Strengths

- The iterative multi-scale pulling approach seems novel as far as I can tell, and does make sense to me (apart from some details). It effectively optimizes coarser SDFs to describe regions more distant from the surface but to miss details close to the surface, and more detailed SDFs to describe regions close to the surface with more details. - The evaluation is quite comprehensive, including several datasets and a good ablation study (although some relevant recent methods are not included), and shows a good improvement over existing work.

Weaknesses

- The evaluation is missing some relevant recent methods for optimization-based surface reconstruction. (See details below) - Some relevant related work is not cited. (See details below) - The exposition is missing motivation for some design choices and is hard to understand in some parts. (See details below) Overall, even though the authors missed some related work, results look quite promising and I think the idea is novel and interesting enough to make me lean towards acceptance. The exposition can probably be improved somewhat in the final version. Details: - The field of surface reconstruction from point clouds is quite vast, so the authors missed several works, for example (see also related work within these papers to get more missing work): -Training-free methods: - Neural-Singular-Hessian: Implicit Neural Representation of Unoriented Point Clouds by Enforcing Singular Hessian, Wang et al., TOG 2023 - Iterative Poisson Surface Reconstruction (iPSR) for Unoriented Points, Hou et al., TOG 2022 - Learning-based methods: - 3DShape2Vecset: A 3D Shape Representation for Neural Fields and Generative Diffusion Models, Zhang et al., TOG 2023 - Geoudf: Surface reconstruction from 3d point clouds via geometry-guided distance representation, Ren et al., TOG 2023 - Given good normals, surface reconstruction becomes much easier - the normal computation could be followed by Poisson reconstruction based on the normals for example. Therefore papers to compute oriented normals are relevant, such as: - Orienting Point Clouds with Dipole Propagation, Metzer et al., TOG 2021 - Globally Consistent Normal Orientation for Point Clouds by Regularizing the Winding-Number Field, Xu et al., TOG 2023 - SHS-Net: Learning Signed Hyper Surfaces for Oriented Normal Estimation of Point Clouds, Li et al., CVPR 2023 - Several design choices are not motivated well enough: - It is unclear to me why the SDF evaluated at Q_1 uses a feature y_1 as input that was computed from a query position Q_0, rather than a feature computed at query position Q_1. This is an interesting design choice that could use more discussion. An ablation would also be interesting: how would the method perform when re-evaluating h_0, ..., h_i at Q_i instead of Q_0 when computing y_i for f(Q_i, y_i) (in that case inputting Q_i a second time to the LSNN might also not be necessary)? - In Eq. 6, the design choice of only scaling D_1 and D_2 with the error-based factor, but not D_3 needs to be motivated. Also, as Section 3.2 was written for a general number of layers N_L, it would be good to continue this generality in Section 3.3, if possible. How would Eq. 6 look for a general N_L., for example? - In Eq. 7, the design choice for using the minimum over the three levels. - The exposition is hard to understand in some parts and could be improved: - Several passages are currently hard to understand and could use clarification. For example: "The is because Q_i locate at different scales in space,, making it difficult to simultaneously account for the optimization step sizes at different scales with the inconsistent gradient directions caused by continuous movement." Its possible to get a good guess at what the authors mean here, but it requires re-reading a few times and is not 100% clear even then. Partially this seems to be due to bad grammar, partially due to a somewhat convoluted formulation. Generally the paper text could use more passes to avoid these issues. - In Section 3.1, it should be mentioned early on that the FFT module is based on (or at least very similar to) MFN [11]. Also, the exact differences between the proposed approach in Section 3.1 and the approach of MFN [11] should be discussed and clarified. - In Section 3.3, it would be good to mention that the loss functions are based on GridPull [20]. Also, it would be good to discuss the exact differences to GridPull (I assume the adpation to the multi-scale setting is the main difference). - The architecture of the Linear Sequence Neural Network (LSNN) is never described. If it is taken from existing work, this work should be cited, otherwise it needs to be described, at least in Appendix A. - In the paragraph starting at line 112 and Eq. 4, it is unclear which weights are initialized according to this strategy (the omega_i in Eq. 1? The W_i in Eq. 3? The offset theta_i and b_i?), and which parameters are plotted in Figure 3 (the L_i are not defined clearly). - In Eq. 4, \eta is not defined. - Near line 138, the query point update should probably use Q_{i-1} everywhere on the right-hand-side (instead of Q_i, which is not known yet). Or alternatively, Q_{i+1} on the left-hand side. - In Eq. 1, I don't follow why the predicted signed distance f(Q_1, y_1) is in the loss. Why should that be optimized to be 0? This should be clarified. - in Eq. 1, ", i \in [1,I]" can be removed, since it is redundant with the subscript in the sum - In the section starting at line 160, how is the target surface point q determined? This is described in the appendix, but should be shortly mentioned in the main paper as well. - In Eq. 7, argmin should probably be min instead. Also, the "1 - ..." in both lines seems odd, should it only be in one of the lines (otherwise the loss would be *higher* the more similar the gradient directions are, instead of lower). - Near Eq. 8, the authors mention that L_surf encourages the SDF at the *final* query point to be close to 0, but Eq. 8 does not show an index for Q. Is L_surf applied to Q_{N_L} only or to all Q_i? This should be clarified. - Near line 202: Fig. 4.1 should probably be Fig. 5 - In Table 7, Step 5 should probably have CD_L2 of 0.0357 (not 0.357) - SAL [15] is in the bibliography, but not referenced from Section 2. - Citations [45] and [59] are duplicates. - An inference time comparison between methods should be included.

Questions

A clarification of the design choices could help, as well as a discussion of the differences and advantages/disadvantages compared to the missing related work.

Rating

5

Confidence

4

Soundness

2

Presentation

2

Contribution

3

Limitations

Limitations in the long computation time are discussed. I don't foresee any particular negative societal impacts.

Reviewer ZVf15/10 · confidence 2/52024-07-11

Summary

This paper presents a model for reconstructing SDF from point clouds. The proposed approach introduces components, including Frequency Feature Transformation and Multi-Step Pulling, to iteratively refine the reconstructed SDF. The experiments demonstrate that this method performs well across multiple 3D object and scene datasets.

Strengths

The use of multiple levels of features and query is a valid and well-founded idea. The experiments are through and the visualization of the results looks good.

Weaknesses

1. Some intuitions behind the methodology are not clearly explained. Specifically, the rationale for using frequency features to represent query points needs further clarification. While the use of multiple levels of query points is understandable, the choice of LSNN at each level and how query points are used in this model require more detailed explanation. 2. Some of the notations are inconsistent. S is used for both raw point cloud in L91 and SDF surface on L99. D is used for both feature dimensions and distance. 3. Minor: The number reported on the last row of Table 7 appears to be wrong.

Questions

1. What’s the intuition for using frequency features and why using LSNN in MSP? 2. From the visualization, the proposed method seems to produce results with fewer holes and smoother surfaces. Is this due to the model learning better features, or is there a specific loss design different from prior work? 3. Could you compare the MSP using the same features from prior work to demonstrate its performance even without the proposed feature? This would help to convincingly show its effectiveness.

Rating

5

Confidence

2

Soundness

3

Presentation

2

Contribution

2

Limitations

No negative social impacts have been identified. See weakness.

Reviewer NaoM7/10 · confidence 4/52024-07-12

Summary

This paper proposes MultiPull, a method for reconstructing a surface model by SDF from a 3D point cloud containing only the coordinates of each point. The paper proposes a method for estimating the SDF using the Fourier transform of the surface model predicted from the point cloud only at multi-scale. It also introduces gradient consistency and distance awareness for multi-scale consistency. The key idea is to use multi-scale frequency features, for which we introduce an FFT module corresponding to an encoder and an MSP module corresponding to an implicit decoder. The proposed method shows high reconstruction performance compared to existing methods and is effective on different datasets.

Strengths

- The problem of reconstructing a surface from only 3D point clouds, accessible in a real environment by a 3D sensor, is a common but important problem and an important technology for real-world applications of 3D data. However, the reconstruction performance of existing methods is limited, and a better method is needed. The proposed method aims to fill this gap, and the significance of the research is highly appreciated. - The paper is well written, especially in its straightforward and accurate description of the difficulties in setting up the problem. The detailed description of the proposed method also makes the paper easy to understand. - The insight into the initialization of MFN is an interesting point, which I consider to be one of the contributions of the paper. - Experimental results on various datasets are presented, showing the effectiveness of the proposed method.

Weaknesses

- l.138: "\cdot" is better than "\times" to avoid confusion with the cross product. - My understanding is that there seems to be no guarantee that the scale of the displacement of the query point at each frequency varies with the frequency of interest. Is this understanding correct? Is there some possible constraint on the magnitude of the slope that would be consistent with the frequency of interest? (Or is it that this concern does not exist, since the experimental separation by frequency has been verified?) - l.166: For the purpose of consistency, would it not be appropriate to use the average or correlation rather than argmin to select only one of Q1, Q2, or Q3? If you have any additional explanation, I would appreciate it. - In the introduction, it would be desirable to specify whether the proposed method is a test-only optimization (i.e., does not require prior training, such as NeuralPull or SALD) or a method that requires prior training (e.g., DeepSDF). Figure 3 in [*1] clearly shows the position of the proposed method in relation to related research. My understanding is that the paper plots to the same point as NGLOD, and it is preferable to explicitly state that only test time is considered. (If my understanding is incorrect, please correct me.) - l.243: After considering both performance metrics and time efficiency, we have set Step=3 by default.", can the authors discuss this trade-off? Given the nature of the LOD and the trade-off with the 3D geometry compression ratio, there may be future applications related to mesh compression. [*1] Francis Williams, Zan Gojcic, Sameh Khamis, Denis Zorin, Joan Bruna, Sanja Fidler, Or Litany. Neural Fields As Learnable Kernels for 3D Reconstruction. CVPR2022.

Questions

- l.77: "However, inferring implicit functions without 3D supervision requires a very long convergence process, which limits the performance of unsupervised methods in large-scale point cloud data." I agree with this point from my experiments, but can the author provide a specific reference in the paper? - l.99: "To this end, we constrain query points to be as close to their nearest neighbor on S." I understood sampling from the nearest neighbor, but did not understand how Q is constructed. Are non-nearest points just ignored?

Rating

7

Confidence

4

Soundness

3

Presentation

3

Contribution

3

Limitations

- I agree with the limitations described in the paper. This is a promising direction for future work. - If there are areas of future work that you would like to see described in Weaknesses and Questions, these may be limitations.

Reviewer uTM53/10 · confidence 5/52024-07-17

Summary

This paper proposes to learn multi-scale implicit fields from 3D point clouds for accurate optimization of SDFs in a coarse-to-fine manner. The spatial query points are first mapped to frequency features through the FFT module. Then the MSP module is designed to exploit the multi-level frequency features to progressively pull the query points towards to target surface. Various experiments and ablation studies demonstrate the effectiveness of the proposed learning approach.

Strengths

1. The adopted frequency-domain learning paradigm and the pulling-based SDF learning paradigm are effective and advantageous. 2. The experimental comparison shows the performance superiority of the constructed learning pipeline.

Weaknesses

The major weakness of this work is its limited novelty. In general, I think the proposed techniques are just an incremental combination of the pulling-based SDF learning approach [18] (Neural-Pull) and the multiplicative fourier learning approach [14] (MFLOD), although with some marginal modifications in order to combine them. The authors seem to have intentionally overlooked the introduction and detailed discussion of these two types of highly related works. Hence, reviewers that are not very familiar with the two lines of works may overestimate the value and technical novelty of the proposed method. Note that I am not saying that combining some existing techniques is not meaningful. What I mean is that, for this paper, the contribution cannot reach the bar of NeurIPS.

Questions

In lines 82-83, the authors wrote “The creation of 3D shapes LOD usually depends on mesh decimation, which has difficulty in blending between LODs.” I notice that this particular sentence is directly copied from the paper of MFLOD [14]. Explanations are needed.

Rating

3

Confidence

5

Soundness

3

Presentation

3

Contribution

2

Limitations

The presented limitations are vague and less constructive.

Authorsrebuttal2024-08-08

We are happy to take any questions

Dear reviewers, We appreciate your comments and expertise. Please let us know if there is anything we can clarify further. We would be happy to take this opportunity to discuss with you. Thanks, The authors

Authorsrebuttal2024-08-11

Dear reviewers, As the reviewer-author discussion period is about to end, we are looking forward to your feedback on our rebuttal. Please let us know if our responses address your concerns. We would be glad to make any further explanation and clarification. Thanks, The authors

Reviewer NaoM2024-08-12

I appreciate the polite point-by-point responses from the authors. In particular, I believe that the validity of the paper has been increased by additional results for (2) and (4). I have no further questions at this time.

Reviewer VUUa2024-08-12

Thanks for the detailed replies and the new set of evaluations! The added comparison to Neural-Singular-Hessian looks promising. This addresses my concern to some extent (although a more complete comparison would obviously be better). About the frequency features, I understand the author's point of view that choosing the same query point for all features ensures their consistency, but on the other hand, it also requires these features to make predictions about distant more positions, i.e. about query positions Q1, Q2, ..., as well as needing to take the trajectory caused by previous levels into account (i.e. where did Q1 end up given the prediction of the previous level?), which seems like a more difficult non-local task to me. A more in-depth discussion/analysis would be interesting here, but I would consider this to be optional. The author's response addresses most of my concerns.

Authorsrebuttal2024-08-12

Thanks for the comments. Actually, we were using multi-step pulling procedure, that is the end point of previous pulling will be the start point of the next pulling. This is like recursively calling the SDF iteration by iteration, which does not bring too much burden. Moreover, only the first pulling is observed the large movement, while all the following pulling is just like little adjustment. This is because the first pulling will pull most of queries to somewhere by the zero-level set, then the following pulling will not have too much room to move the queries, or the queries will get pulled far away from the zero-level set in another direction. Thus, pulling in the last several steps is still happening in a pretty local area. Moreover, it did slow down the feature query process if we use pulled queries like Q1 or Q2 to query features. Currently, using Q0 can help us obtain all features needed in the following pretty fast. We will make sure to include these as a discussion in our revision. Best, The authors

Authorsrebuttal2024-08-13

Dear reviewer uTM5, As the reviewer-author discussion period is about to end, can you please let us know if our rebuttal addressed your concerns? If it is not the case, we are looking forward to taking the last minute to make further explanation and clarification. Thanks, The authors

Program Chairsdecision2024-09-25

Decision

Accept (poster)

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