We propose Concavity-induced Distance (CID) as a novel way to measure the dissimilarity between a pair of points in an unoriented point cloud. CID indicates the likelihood of two points or two sets of points belonging to different convex parts of an underlying shape represented as a point cloud. After analyzing its properties, we demonstrate how CID can benefit point cloud analysis without the need for meshing or normal estimation, which is beneficial for robotics applications when dealing with raw point cloud observations. By randomly selecting very few points for manual labeling, a CID-based point cloud instance segmentation via label propagation achieves comparable average precision as recent supervised deep learning approaches, on S3DIS and ScanNet datasets. Moreover, CID can be used to group points into approximately convex parts whose convex hulls can be used as compact scene representations in robotics, and it outperforms the baseline method in terms of grouping quality. Our project website is available at: https://ai4ce.github.io/CID/

翻译：我们提出凸度诱导距离（CID）作为一种新颖的方法，用于测量无向点云中两点之间的不相似性。CID 指示两点或两组点属于以点云表示的基础形状的不同凸部分的似然性。在分析其性质后，我们展示了CID如何在无需网格化或法线估计的情况下惠及点云分析，这对处理原始点云观测的机器人应用具有优势。通过随机选取极少量点进行手动标注，基于CID的标签传播点云实例分割在S3DIS和ScanNet数据集上达到了与近期监督深度学习方法相当的平均精度。此外，CID可用于将点分组为近似凸的部分，其凸包可作为机器人中紧凑的场景表示，且在分组质量上优于基线方法。我们的项目网站可访问：https://ai4ce.github.io/CID/