Paper:
PointCNN: Convolution On X -Transformed Points
We present a simple and general framework for feature learning from point clouds. The key to the success of CNNs is the convolution operator that is capable of leveraging spatially-local correlation in data represented densely in grids (e.g. images). However, point clouds are irregular and unordered, thus directly convolving kernels against features associated with the points will result in desertion of shape information and variance to point ordering. To address these problems, we propose to learn an X -transformation from the input points to simultaneously promote two causes: the first is the weighting of the input features associated with the points, and the second is the permutation of the points into a latent and potentially canonical order. Element-wise product and sum operations of the typical convolution operator are subsequently applied on the X -transformed features. The proposed method is a generalization of typical CNNs to feature learning from point clouds, thus we call it PointCNN. Experiments show that PointCNN achieves on par or better performance than state-of-the-art methods on multiple challenging benchmark datasets and tasks.

Review:
Paper summary: - This work proposes a new neural network layer to perform convolution-like operations on unordered point cloud data. The main crux of the technique is the transformation of given unordered points into a canonical representation using a learned matrix multiplication and then a standard convolution is applied on those canonically represented points. Wide range of experiments on classification and segmentation tasks validate the use of the proposed technique in comparison to existing techniques.   Strengths: - Simple yet generic technique for processing point cloud data with unordered points. - Applications on both classification and segmentation on a wide range of datasets. - Very good performance compared to existing state-of-the-art techniques.   Weaknesses: - A main weakness of this work is its technical novelty with respect to spatial transformer networks (STN) and also the missing comparison to the same. The proposed X-transformation seems quite similar to STN, but applied locally in a neighborhood. There are also existing works that propose to apply STN in a local pixel neighborhood. Also, PointNet uses a variant of STN in their network architecture. In this regard, the technical novelty seems limited in this work. Also, there are no empirical or conceptual comparisons to STN in this work, which is important. - There are no ablation studies on network architectures and also no ablation experiments on how the representative points are selected. - The runtime of the proposed network seems slow compared to several recent techniques. Even for just 1K-2K points, the network seem to be taking 0.2-0.3 seconds. How does the runtime scales with more points (say 100K to 1M points)? It would be good if authors also report relative runtime comparisons with existing techniques.   Minor corrections: - Line 88: "lose" -> "loss". - line 135: "where K" -> "and K".   Minor suggestions: - "PointCNN" is a very short non-informative title. It would be good to have a more informative title that represents the proposed technique. - In several places: "firstly" -> "first". - "D" is used to represent both dimensionality of points and dilation factor. Better to use different notation to avoid confusion.   Review summary: - The proposed technique is sensible and the performance on different benchmarks is impressive. Missing comparisons to established STN technique (with both local and global transformations) makes this short of being a very good paper.   After rebuttal and reviewer discussion: - I have the following minor concerns and reviewers only partially addressed them.  1. Explicit comparison with STN: Authors didn't explicitly compare their technique with STN. They compared with PointNet which uses STN. 2. No ablation studies on network architecture. 3. Runtimes are only reported for small point clouds (1024 points) but with bigger batch sizes. How does runtime scale with bigger point clouds?  Authors did not provide new experiments to address the above concerns. They promised that a more comprehensive runtime comparison will be provided in the revision. Overall, the author response is not that satisfactory, but the positive aspects of this work make me recommend acceptance assuming that authors would update the paper with the changes promised in the rebuttal. Authors also agreed to change the tile to better reflect this work.