# Concavity-Induced Distance for Unoriented Point Cloud Decomposition

arXiv: https://arxiv.org/abs/2306.11051 · HTML: https://mlsanity.com/paper/2306.11051/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 34 references that are in the map.
- First posted on arXiv 19 Jun 2023.

## Builds on (most cited first, 12 of 12)

- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [ScanNet: Richly-annotated 3D Reconstructions of Indoor Scenes](https://mlsanity.com/paper/1702.04405/) (2017)
- [Open3D: A Modern Library for 3D Data Processing](https://mlsanity.com/paper/1801.09847/) (2018)
- [Joint 2D-3D-Semantic Data for Indoor Scene Understanding](https://mlsanity.com/paper/1702.01105/) (2017)
- [PointGroup: Dual-Set Point Grouping for 3D Instance Segmentation](https://mlsanity.com/paper/2004.01658/) (2020)
- [Learning Shape Abstractions by Assembling Volumetric Primitives](https://mlsanity.com/paper/1612.00404/) (2016)
- [CvxNet: Learnable Convex Decomposition](https://mlsanity.com/paper/1909.05736/) (2019)
- [SGPN: Similarity Group Proposal Network for 3D Point Cloud Instance Segmentation](https://mlsanity.com/paper/1711.08588/) (2017)
- [GSPN: Generative Shape Proposal Network for 3D Instance Segmentation in Point Cloud](https://mlsanity.com/paper/1812.03320/) (2018)
- [3D-PRNN: Generating Shape Primitives with Recurrent Neural Networks](https://mlsanity.com/paper/1708.01648/) (2017)
- [Label-Efficient Learning on Point Clouds using Approximate Convex Decompositions](https://mlsanity.com/paper/2003.13834/) (2020)
- [LRGNet: Learnable Region Growing for Class-Agnostic Point Cloud Segmentation](https://mlsanity.com/paper/2103.09160/) (2021)

## Abstract (arXiv)

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/