Processing large point clouds is a challenging task. Therefore, the data is often sampled to a size that can be processed more easily. The question is how to sample the data? A popular sampling technique is Farthest Point Sampling (FPS). However, FPS is agnostic to a downstream application (classification, retrieval, etc.). The underlying assumption seems to be that minimizing the farthest point distance, as done by FPS, is a good proxy to other objective functions.We show that it is better to learn how to sample. To do that, we propose a deep network to simplify 3D point clouds. The network, termed S-NET, takes a point cloud and produces a smaller point cloud that is optimized for a particular task. The simplified point cloud is not guaranteed to be a subset of the original point cloud. Therefore, we match it to a subset of the original points in a post-processing step. We contrast our approach with FPS by experimenting on two standard data sets and show significantly better results for a variety of applications. Our code is publicly available 1

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There is a growing number of tasks that work directly on point clouds. As the size of the point cloud grows, so do the computational demands of these tasks. A possible solution is to sample the point cloud first. Classic sampling approaches, such as farthest point sampling (FPS), do not consider the downstream task. A recent work showed that learning a task-specific sampling can improve results significantly. However, the proposed technique did not deal with the non-differentiability of the sampling operation and offered a workaround instead.We introduce a novel differentiable relaxation for point cloud sampling. Our approach employs a soft projection operation that approximates sampled points as a mixture of points in the primary input cloud. The approximation is controlled by a temperature parameter and converges to regular sampling when the temperature goes to zero. During training, we use a projection loss that encourages the temperature to drop, thereby driving every sample point to be close to one of the input points.This approximation scheme leads to consistently good results on various applications such as classification, retrieval, and geometric reconstruction. We also show that the proposed sampling network can be used as a front to a point cloud registration network. This is a challenging task since sampling must be consistent across two different point clouds. In all cases, our method works better than existing non-learned and learned sampling alternatives. Our code is publicly available 1 .