__ Summary and Contributions__: The authors introduce a non-rigid tracker for given RGB-D frames. Combining correspondence networks with differentiable optimization solver enables the proposed network to be trained in an end-to-end fashion. Additional module that estimates correspondence weights allow robust tracking.

__ Strengths__: 1. Integrating the ideas of state-of-the-art methods (correspondence prediction and optimization solver) in a differentiable way
2. The paper is generally well written and organized with promising results

__ Weaknesses__: 1. Originality: Given that similar ideas have appeared in the previous works (correspondence prediction [4] and differentiable optimization solver [15]), the proposed method would be considered as a combination of them with some modifications. For example, dense correspondences are estimated rather than sparse ones in [4], but this is formulated simply leveraging previous state-of-the-art optical flow technique. The used energy terms and loss functions are similarly defined to [15] except that eq. (9) is based on reconstruction of "displacements" rather than "features" in [15]. These make me hard to find new technical insights from the paper.
2. Ablation study: Under severe non-rigid motions, dense correspondences would not be always beneficial than sparse ones due to their robustness to geometric variations. Since the experiments are conducted solely on benchmark of [4] which seems to have mild variations along time axis, additional evaluation and analysis will be expected under larger geometric variations (ex. by decreasing sampling rate of keyframe).

__ Correctness__: It would be nice to highlight the differences between the proposed method and [4], [15].

__ Clarity__: The paper is generally well-written and structured clearly.

__ Relation to Prior Work__: See the Correctness section.
Authors might want to cite these as related self-supervised RGB tracking works:
- Learning Correspondence from the Cycle-consistency of Time (CVPR 2019)
- Joint-task Self-supervised Learning for Temporal Correspondence (NeurIPS 2019)
- MAST: A Memory-Augmented Self-supervised Tracker (CVPR 2020)

__ Reproducibility__: Yes

__ Additional Feedback__: Instead of learning correspondence confidences from reconstruction loss given ground-truth correspondences, It would be interesting by considering introspection to down weight ambiguous matches as proposed in [A].
[A] Supervising the New with the Old: Learning SFM from SFM (ECCV 2018)
-- After rebuttal --
After reading the authors rebuttal and seeing the comments from the other reviewers, I still think It's hard to find new technical insights from this paper.
Given that [15] learns non-rigid tracking in an end-to-end fashion through the differentiable solver, this paper combines [15] with non-rigid matches similar to [4].
Thus, as claimed in the rebuttal L5-12, the technical contributions lie on 1) estimating correspondence confidences and 2) using dense correspondence rather sparse one.
Despite of the expected good results, their formulations are straight-forward without tailored modifications for RGB-D tracking as R4 also pointed out.
Specifically, learning correspondence confidences by weighting the final matching objectives (as in Eq.(9) and (10) ) is a classical technique [a,b] to discount the effects of outlier matches.
In general, learning intermediate attentions via a weighted loss for a proxy task [c,d,e] is a well-known strategy for boosting the performance.
In terms of architecture, the proposed correspondence weighting networks just consist of sequential 7 convolutional layers (L132-135 in supp.).
Additionally, the estimation of dense correspondences is done by simply adapting previous SOTA optical flow algorithms without any changes.
[a] View Synthesis by Appearance Flow, ECCV 2016
[b] Learning Dense Correspondence via 3D-guided Cycle Consistency, CVPR 2016
[c] Spatial Transformer Networks, NeurIPS 2015
[d] Dynamic Filter Networks, NeurIPS 2016
[e] Deformable Convolutional Networks, ICCV 2017

__ Summary and Contributions__: The authors present a deep structured model for non-rigid tracking. The key idea is to combine deep learning with existing optimization methods and takes the best of both worlds. Since the optimization algorithm can be written as a neural network layer without learnable parameters, the model can be trained in an end-to-end fashion. After joint training, the network learns to re-weight the correspondences in a self-supervised fashion. The optimization solver can effectively estimate the non-rigid transform over the pre-defined graph. They achieve state-of-the-art performance while being 86 times faster.

__ Strengths__: - The authors present a good pipeline of non-rigid tracking at the instance level. The energy optimization steps ensure the deformation graph to be locally rigid and are unrolled into end-to-end learning. Although every module is not entirely novel in its own, the experiments show that combining them can achieve state-of-the-art performance. (For instance, [18] learns to predict the damping factor for LM solver; [19] unrolls GN as recurrent neural network.)
- Comparing to prior art [4], the authors significantly reduce the computational time of correspondence prediction by 85 times
- Writing and experiments are good in general. The implementations are technically sound in details. Based on the writing, the method should be reproducible from the writing.

__ Weaknesses__: - It seems to me that the warp loss is the super set of the graph loss. When p \in P_s is a node of the graph V, the warp loss reduces to the graph loss. Therefore the two loss functions can be viewed as one, with the weightings of each point cloud being different, depending on whether you are a graph node or not.
- Do the authors re-weight the term for each edge in ARAP? Theoretically, one should assign different weightings to different edges unless the edges are all more or less of the same length. Can the authors comment more on this?
- How does the graph size affect the method? How do the authors decide this? My guess is that increasing the number of nodes shall improve the performance, but it will also increase the computational cost. How do the authors balance this?
- Seems like the method relies on a decent segmentation model to build the graph. What will happen if the estimated mask is noisy? To what extent will the proposed method be affected by it.
- How does the number of optimization steps affect the performance? Will the performance degrade if you unroll more steps during inference?
- I don't think bilinear sampling the depth image is a good idea. To my knowledge, using nearest neighbor is better. Otherwise it may result in some smearing effect at the boundaries. Would be great if the authors can comment on this.
*** extra suggestions after the rebuttal ***
- I agree with other reviewers that the authors should not claim "GN solver" as their contribution as a lot of work have done very similar things before (eg [18, 19]). Rather they should focus their claim on what benefits ARAP brings them.
- I think building a working system based on previous successful architectures is totally fine. But I do agree that the authors shall conduct more study on this to validate their claim, eg, comparing the results of their correspondence network with the original PWC-net; replacing their correspondence network with PWC and compare the final error, etc. Otherwise its a bit hard to tell if the network is working as they claimed.

__ Correctness__: - I'm a bit skeptical regarding the claim in L168-170. Since the optimization process is not "feature-based" [29], the impact of the network on the solver shall not be as effective as prior work. I thus wonder to what extent can the "weights" and "correspondences" improve the convergent iterations.

__ Clarity__: - I think it will be great to mention explicitly that the camera parameters are already given a priori. Personally I'm aware of this, but I think its still good to make things clearer for the readers.

__ Relation to Prior Work__: The literature review is in general well-written. I think it will be even better if the authors be more specific that they are not the first one to leverage neural networks to predict the weight of optimization terms.

__ Reproducibility__: Yes

__ Additional Feedback__: In general this paper provides a good pipeline for non-rigid tracking. The performance is clearly state-of-the-art. Implementation details are also clearly presented. The paper will be even better if more ablations are provided (see above).
As this point, I would give this paper a poster rating.

__ Summary and Contributions__: This paper introduces a differentiable non-rigid tracking solver, which enables end-to-end learning of correspondence prediction and its weighting. The key idea is to backpropogate the gradient information from the deformation solver to the correspondence prediction network and the weighting network, making the networks output prediction that are beneficial for non-rigid tracking. Experiments show that the proposed method enables more robust tracking and reconstruction than state-of-the-art approaches.

__ Strengths__: This paper proposes a novel method that embeds the non-rigid tracking solver into neural network training and enables gradient backpropogation from deformation solver to correspondence prediction. As far as I know, this paper is the first one to do so and hence the idea is quite novel.

__ Weaknesses__: - Additional comparison: Although I understand the proposed method is a general method without relying on scene priors (such as human templates), I think it would be informative to add an additional comparison against other template-based non-rigid reconstruction methods such as DoubleFusion[31].
- Two additional questions that need to be clarified: 1) Why using an optical flow network for correspondence prediction? Since depth information is available, I think a scene flow network would be a more reasonable choice. 2) Why not defining the "graph loss" on the whole point cloud (because in this way you can regularize the node rotation)?
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I initially recommended acceptance of this paper because I like the idea of making the matching & tracking pipeline differentiable and end-to-end. But as R1 and R4 pointed out, this paper lacks sufficient technical novelty given that [15] has already proposed a differentiable optimization solver. Unfortunately, in the rebuttal the authors didn't fully clarify the novelty of their method and claimed that the "main contribution is self-supervised correspondence weighting" (LINE 37), which I found unsatisfactory. I believe this paper needs to discuss more on its novelty and how it differs from previous arts. Therefore, I would like to adjust my rating from 7 to 6 and encourage the author to further refine the paper and resubmit it to another venue.

__ Correctness__: Yes

__ Clarity__: Yes, the paper is well written and easy to follow.

__ Relation to Prior Work__: Yes. It would be better if the author can discuss in detail how the proposed neural non-rigid tracking solver differs from RegNet[11] and [A] because these papers also propose to learn to solve rigid/non-rigid alignment.
[A] Learning to Optimize Non-Rigid Tracking. arXiv, 2003.12230.

__ Reproducibility__: Yes

__ Additional Feedback__: Is it possible to provide the texture fusion results? Because the reconstruction results of objects with rich texture can better demonstrate the tracking accuracy improvements in a fine-grain scale.

__ Summary and Contributions__: This paper focuses on selecting confident correspondence from an offer-the-shelf optical flow method, and then align two rgbd images under non-rigid deformation. To this end, a differentiable solver is applied to make the pipeline differentiable, and the optical flow and weight network be learned specifically to this non-rigid rgbd alignment task.

__ Strengths__: The main strength of the paper is that it breaks the non-rigid tracking into two stages: first is the optical flow estimation and correspondence weighting, i.e. the photometric alignment, and second the deformable camera pose estimation, i.e. the geometric alignment. The network is only applied in the photometric alignment stage and the geometric alignment is a white-box minimization, which makes the learning easier and more explainable.

__ Weaknesses__: The main weakness of this paper is lacking insights and novel formulations. Since the target audiences will only be a small group of people within NeuralPS community, the novelty of this paper is limited and can not inspire broader audiences.
More specifically:
The photometric alignment directly applies an existing optical flow method, which is not customized for this problem. At least the authors should consider to include geometric features into the correlation computation of flow to fully utilize the geometric information from depth sensors.
The weighting scheme of the correspondence itself is a worth studying topic but this paper did not fully explore this part.
The minimization procedure is more like a direct and basic implementation of existing solvers. The objective function is common and easy to minimize, and the number of sampled points is relatively small and a LU decomposition is appliable.

__ Correctness__: The claims and method are correct, so is the empirical methodology.

__ Clarity__: The paper is well written and easy to follow.

__ Relation to Prior Work__: The relation with previous works is well discussed.

__ Reproducibility__: Yes

__ Additional Feedback__: It is a good pipeline in terms of performance but lacks some insights and contributions as an inspiring paper. I would recommend the authors to shift their focus on how to design a better photometric alignment model specifically for non-rigid RGBD alignment and detach the correspondence from the specific differentiable solver, i.e., the differentiable solver is only for learning good correspondence estimation and weighting during training, once they are learned we can insert the correspondence estimation and weighting into any other non-rigid tracking framework and achieve a consistent improvement.
--------------Post Rebuttal Update-----------------
I maintain my rating after reading the rebuttal and comments from other reviewers.
I keep the opinion that this paper has a solid pipeline but lacks sufficient novelty as a research paper, which is similar to another reviewer.
However, I am happy to see an improved version of this paper in the next venues.