<i>HPRO</i>: Direct Visibility of Point Clouds for Optimization

Abstract Given a point cloud, which is assumed to be a sampling of a continuous surface, and a viewpoint, which points are visible from that viewpoint? Since points do not occlude each other, the real question is which points would be visible if the surface they were sampled from were known. While an existing approximation method addresses this problem, it is unsuitable for use in optimization processes or learning models due to its lack of differentiability. To overcome this limitation, the paper introduces a novel differentiable approximation method. It is based on identifying the extreme points of a point set in a differentiable manner. This approach can be effectively integrated into optimization algorithms or used as a layer in neural networks, allowing for the computation and utilization of visible points in various tasks, such as optimal viewpoint selection. The paper also provides theoretical proofs of the operator's correctness in the limit, further validating its effectiveness. The code is available at https://github.com/sagikatz/HPRO