NeurIPS 2020

### Review 1

Summary and Contributions: In this paper, the authors present PIE-Net, a neural network based approach to edge detection in point cloud. This end-to-end approach is a three module detector: a edge/corner detector at point level, a curve proposal network and curve proposal selector. Three type of curves (the most common in the dataset) are handled by the approach: segment, circles and B-splines. The method is evaluated on the ABC dataset for edge detection and outperforms the state of the art.

Strengths: - Edge/Corner detection and curve parametrization is a well known problem if surface reconstruction / shape abstraction. - The end-to-end detection and estimation process is an apealing idea. The three-step process is sounded. - PIE-Net is the first deep method that directly estimates the parametric curves. - PIE-NET outperforms the state of the art by a large margin on the ABC dataset for edge detection.

Weaknesses: - The paper is not self-contained. Lines 133/144: the paper shuld be self contained and no explicit reference to the supplementary material shall be find in the text. The author have used the supplementary material for section 6 and 7 which describes essential components of the method: loss function, curve proposals, curve selection. - My main concern is the relevance for the NeuRIPS community which is usually more focused on machine learning than computer graphics / computational geometry. The interest for the geometry commmunity is strong. However the machine learning side seems not to be the objective of the paper: close curve loss is described in the supplementary material. The parameter $\tau_c$ and $\tau_e$ are not really discussed.

Correctness: .

Clarity: The paper is well written and easy to understand (except for missing parts added to the supplementary material). Figures are relevant and illustrate well the text.

Relation to Prior Work: The edge estimation in point cloud with deep learning is a fairly new topic. The related work concerning other feature estimation like normals or curvature could be more developped but that is not critical.

Reproducibility: Yes

Additional Feedback: ### Typos - line 154: L should be a cursive font ### Other comments - Ablation study: Sphere radius: wouldn't it someting like $R'=(1+\epsilon)R$ be good radius for the circle? when noise points of the edge could fall outside the sphere? - Ablation study: $\tau_c$ and $\tau_e$: In classification one would expect the threshold be 0.5, not hand crafted. What is the cause of this "overlearning"? Should the NMS be sufficient to compensate the innacuracies? - Number of sampled points: 8096 points. How does it perform with less points / random number of points / non uniform sampling ? - The use of the nearest neighbor assigment for ground truth generation make it dependent on the number of sampled points: less point generates larger edges. How would you circumvent this ? ### Recommendation Despite the strong benchmark results, I rate the paper to "marginally below acceptance threshold" (cf weaknesses). To me the paper should include part of (if not all) the supplementary material. Moreover, even though the task / approach to the task is new, the novelty on the machine learning side is limited. ### Update after rebuttal Response are convincing, the quality of the paper is good. I rate the paper to 6.

### Review 2

Summary and Contributions: The paper proposes a new interesting method to detect edges in point clouds. The edges are output as parametric curves (lines/b-splines/circles). The method works in three steps: 1. point classification (edge x corner x none) 2. curve proposal generation 3. proposal selection The method heavily builds upon PointNet++, which is used for multiple purposes.

Strengths: The proposed method is new, its exposition sound, and would be relevant for the NeurIPS community. The method clearly outperforms alternative methods, including EC-Net. Also the provided evaluation of the method is thorough enough (e.g., using a large CAD models dataset) and well executed (e.g., random edge-detection results shown) showing promising results of the method.

Weaknesses: The only important thing I am really missing in the paper is an evaluation of the runtime of the method. Especially given that all pairs of detected corners are considered for the generation of open curve proposals. A clear limitation, pointed out by the authors, is that the presented version of the method uses a limited set of geometric primitives, e.g., ellipses are not included. However, the reasons for this are explained and reasonable. It would be useful if authors could add a sentence or two about how this could be patched and if they would expect some difficulties. Another downside is the method involves relatively many ad-hoc/heuristic bits. Specific points: - I find it unfortunate that important parts of the paper are in the supplementary. The closed curve proposal generation is at least referred to from the main text, however, the proposal selection is just omitted without mention. There should be at least a sentence pointing to the supplement. - An explanation of the clustering (L129) could be improved, as of now I would reimplement it using Euclidean distance and a maximum linkage threshold of \delta. Please check this is the intended way and explain better otherwise.

Correctness: The claims in the paper as well as the methodology used for evaluating the method seem sound to me. In Sec. 4.3, please check the noise perturbation, I would guess the range should be [1 - X, 1 + X], not [-1 - X, 1 + X].

Clarity: The writing is clear and the method is well explained. It was a pleasure to read. Minor comments: - L174: corners -> corner - Section 4.1 "Ablation studies" is more of an "Selection of parameter values", the current heading is slightly misleading - L250: learning-base -> learning-based

Relation to Prior Work: Yes, the differences to the state-of-the-art method, EC-Net, are discussed. The proposed method is also benchmarked against EC-Net.

Reproducibility: Yes

Additional Feedback: I would like to thank the authors for the additional information and clarification.

### Review 3

Summary and Contributions: The authors propose an end-to-end learnable technique to robustly identify feature edges in 3D point cloud data. The edges are represented as a collection of parametric curves. Experimental results show that the proposed method is significantly better than the state-of-the-art and generalizes well to novel shape categories.

Strengths: 1. The idea of treating parametric edge inference as a region proposal task is interesting. 2. The model uses a deep network to detect edges, corners and performs curve proposal generation.

Weaknesses: 1. The novelty of the paper is limited. To my knowledge, this paper is just a combination of several existing approaches, such as PointNet, non-maximal suppression, etc. 2. The application of this method is also limited. The authors only evaluate on one dataset, which limits the application of the PIE-NET.

Correctness: Yes

Clarity: Yes. The writing is clear.

Relation to Prior Work: Yes

Reproducibility: Yes

### Review 4

Summary and Contributions: This paper introduces the novel (for deep learning) problem of edge and corner detection on 3D point clouds, which has clear motivation in terms of future application and relation to 2D vision. The paper approaches this problem by first classifying whether each point belongs to a corner or edge. Each pair of corners is then considered to propose a edge, which is given by a segmentation mask of which points belong to it, what type of edge it is (e.g. line or curve), and its closed-form parameterization. This framework surpasses previous state-of-the-art non-learning based methods.

Strengths: The novelty of the task and its potential usage in downstream tasks such as scene understanding are apparent. The method is simple and straightforward, which I consider a strength given that the goal of the paper is to essentially build a edge-detection module that can be plugged into a variety of downstream tasks. The experiments are convincing in showing that a learned edge detector is superior to previous non-learning based geometric methods. Moreover, generalization to new object categories, which is commonly a disadvantage of learning-based methods compared to non-learning methods, is not a big issue for this method. Code and data are available and easy to read.

Weaknesses: Based on the code, it seems that the point segmentation and edge proposal module are trained separately. Please make this clear in the main text. As pointed out by other reviewers, the central contribution of this paper would be of use towards the graphics/vision commuity rather than the machine learning community. However, I still believe that the paper is worthy of acceptance at Neurips.

Correctness: Experiments are thorough and convincing.

Clarity: Yes

Relation to Prior Work: Yes

Reproducibility: Yes

Additional Feedback: Is there a reason an end-to-end method wasn't used (i.e. one stage of training)? After reading the rebuttal and discusion with reviewers, I maintain that the topic of this paper is suitable for publication at Neurips and the quality is well above the publication threshold.