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: This paper presents a learning-based algorithm that establishes reliable correspondences for registering a pair of point clouds.
Point cloud registration has been a long studied problem in robotics and computer vision, and there exist many papers that propose learning-based methods to perform feature learning and establish correspondences.
In my view, there are two unique ideas about this paper that differ it from previous papers:
- The proposed pipeline predicts an "anchor" point for each point cloud (in the paper this is called "one inlier") and uses the "anchor" point to "normalize" the rest of the point cloud (in the paper, the normalization is basically subtracting the anchor point from each other point in the cloud). After normalization, an additional feature learning step is performed to augment the coarse features (learned by KPConv).
- The proposed pipeline does correspondence learning and transformation estimation in an iterative manner, similar to the classical ICP algorithm. In the classical ICP, correspondences are established via nearest neighbor search. But in this paper, correspondences are established from learning, using the features learned from the "anchoring" idea mentioned above.

This paper then tests the proposed pipeline in the 3DMatch and 3DLoMatch dataset, and demonstrates the proposed pipeline delivers similar or better performance compared to several previous learned features for point cloud registration.
strengths_and_weaknesses: Strengths:
+ The paper is overall well written and easy to understand.
+ The idea of predicting or voting an "anchor" point and using it to normalize the point cloud seems to be relatively new (though I feel this idea is similar to Hough voting).
+ Experiments are well conducted and convincing.

Weaknesses:
- I feel the paper is a little bit out of fashion/date, given that the community has designed many **supervised** learned point cloud feature descriptors and moved to studying **unsupervised** or "self-supervised" feature descriptors. The proposed descriptor, though outperforming others, is still supervised and requires mining ground-truth correspondences for supervision. [Ref1] and others, for example, have already shown the possibility to learn features in a self-supervised way. Therefore, I think the paper is making an incremental contribution rather than a major contribution.
- The title of this paper, to me, is deceiving and jargoning. One inlier correspondence is NOT enough to register a pair of point clouds, and at least THREE inlier correspondences (with noncollinear points) are required to define a unique rigid transformation (see [Ref2]). What the paper really means is to predict a "anchor" point (sort of like the centroid of the point cloud) and use the anchor point to subtract all other points. I think the name of the paper needs to be better worded.


[Ref1] Yang H, Dong W, Carlone L, Koltun V. Self-supervised geometric perception. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition 2021 (pp. 14350-14361).
[Ref2] Horn BK. Closed-form solution of absolute orientation using unit quaternions. Josa a. 1987 Apr 1;4(4):629-42.
questions: Since you know the groundtruth pose, could you add into the loss function a pose error and see how it affects the performance?
limitations: Limitations not mentioned.
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: This paper proposes a position encoding method by using optimal transport and use it to normalize each point. The benefit is that the  optimal transport based position encoding can mitigate the feature ambiguity. Then, an iterative optimization process is introduced to establish the correspondence and transformation matrix. 
strengths_and_weaknesses: Strength:
1. The idea is reasonable and the overall performance is good.
2. The presentation is easy to understand.

Weakness:
1. I am a bit worried about the robustness of the proposed algorithm since the inlier ratio is significantly dropped.


questions: Why the inlier ratio is relatively low?
limitations: NO
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: This paper proposes a progressive point cloud registration method that estimates an initial transformation between two point clouds before registration estimation. The authors claim that one inlier is enough to estimate a good enough initial transformation between two point clouds, which boosts the downstream point cloud registration process, including positional encoding and progressive alignment. The main contributions of this paper are a) the one inlier finding process which is light-weight, b) the process can be jointly optimized with other steps, and c) the progressive alignment approach reduces the dependency on initialization.
strengths_and_weaknesses: ### Strengths:
#### S1. Core Idea.
The idea is novel and outperforms other methods in two public benchmarks.
#### S2. Impact on Applications.
The method is lightweight and can potentially be applied in many other pipelines / with other methods, which benefits the community.
#### S3. The paper is well written and easy to follow.

### Weaknesses:
#### W1. Limited theoretical / technical Novelty
Although the paper is novel regarding the idea, the theoretical and technical novelty is limited.
#### W2. Inaccurate Claims
This paper has made some claims with some cited papers that are inaccurate or unrelated (details below).
#### W3. Missing Justification
Some claims are made without proper proof (see details below).
#### W4. Minor Typos / Writing
* line 134: "C is ..." -> "where C is ..."
* Eq 5: "..., M," -> "..., M."
questions: #### Q1 (ad W2): Inaccurate or Unrelated Citations
line 32: "... the straightforward position encoding is not a good idea [23]."  
In [23] it shows up to 3.8% improvement on 4DLoMatch and 1.5% higher RR on 3DMatch and 2.3% on 3DLoMatch.
This does not imply straightforward position encoding is not a good idea.
To make this statement true, one should show the comparison with/without direct position encoding, which is not provided in the paper.

line 51: "This shows that only one inlier is enough to preserve the spatial consistency [2, 7] ..."  
I am not sure why those two papers are cited here. Do they mention anything related to this statement?

#### Q2 (ad W3): Claims Without Proof:
line 286: " This is because ... both consider the position information ..."  
To justify this statement, one should provide an ablation study on a model with only the difference with and without positional encoding. However, this is not provided in the evaluation section.

line 342: "our method is scene-agnostic and maintains good registration accuracy in strongly differing scenarios."  
Without a description of how the network was trained in those experiments, it is impossible to know whether the written sentence is true. 

#### Q3: Additional questions
- In Figure 3, the inlier ratio for 3DLoMatch. Why does the 0.0 percentage increase after optimization?
limitations: The authors do not mention limitations in the main paper. No text in the main paper indicates a limitation section in the supplementary material.
review_title: null

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: This paper studies correspondence-based rigid point cloud registration problem and proposes a new position encoding method for point clouds to establish better correspondences. A virtual corresponding point pair, which is regarded as the one inlier, is first constructed from a set of real correspondences, and then the two point clouds are normalized by using the two points in the correspondence as reference and the position embedding is extracted from the normalized point clouds. Point features and position embedding are added together for establishing correspondences. Based on the above method of establishing correspondences, an iterative strategy is adopted to align two point clouds gradually. Experiments are conducted on 3DMatch, 3DLoMatch and KITTI, and sota registration recall are achieved on these datasets.
strengths_and_weaknesses: Strengths:
1.The proposed one-inlier based position encoding method is novel. The method is straightforward and effective. 
2.Experiments are conducted on three typical datasets and comparison are done to latest methods. High performance is achieved.

Weakness:
1. A good position encoding should be helpful to find more and better correspondences and a better registration is only a by-product of better correspondences, but the experimental results show that the IR and FMR of the proposed method are far lower than that of GeoTrans. Analysis are needed about this issue.
2. The last two contributions are not significant. Especially, iterative optimization is widely used in recent learning-based registration methods, such as PRNet, RPM-Net.
3. The proposed position-encoding idea is not fully analyzed. See question No.1. 

Minor issue:
1. The part “one-inlier is enough” in title is a little misleading.  
2. In Fig.2, it should be the Matched Correspondences instead of {R, t}, that are transferred from the Inlier Learning module to the Progressive Alignment module.

questions: 1. In section 4.1, especially for the experiments on 3DLoMatch, the proposed method consistently has higher RR but lower FMR and IR. I agree that FMR and IR are not total positively-correlated to RR, but more analysis is needed to show why the proposed method has higher RR with a far lower IR, and how this is related to the proposed position encoding strategy. 
2. For the “Progressive alignment”, how many iterations are performed?
3. For Fig. 3, the inlier ratio of every iteration should be given, instead of only the initialization and the final optimized one.  
4. In Table 2, what constitutes the “Pose” Time? Is it the runtime of the RANSAC 50k? If so, why is the proposed method much faster than GeoTransformer with lower IR?
5. What’s the number of sample correspondences in the runtime experiment in Table 2?
6. The quality of the “one-inlier” for position encoding  should be given in each iteration.
7. RRE and RTE should be reported for the experiments on 3DMatch and 3DLoMatch since the objective of this paper is registration. 

limitations: The authors talk about the limitation of the proposed method in supplementary material. I suggest address the issue about if the proposed method is applicable to registration of objects, such as models in ModelNet40.
review_title: null

Meta-review: metareview: Thanks in large part to the rebuttal conversation, the reviewers converged to accept this paper.  The reviewers recognize the interest and value of the approach and careful empirical results, bolstered by additional results introduced during the discussion.

In preparing the camera-ready, the authors of this paper are encouraged to revisit the comments from reviewer 2PZE suggesting to verify whether the two anchor points are truly ‘inlier’ correspondence; this can be easily done by calculating the distance between the two anchor points under ground-truth transformation.  Also, please make the title change and any other edits promised in the rebuttal, especially discussion of drawbacks and avenues for future research.
confidence: Certain
Decision: Accept