  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/
