Topological Methods for 3D Point Cloud Processing


Contrary to other data modalities, processing 3D point clouds poses several significant challenges. Point cloud data generated by inexpensive sensors suffers from the presence of artifacts, non-uniform noise, and variation in density. Established 2D image processing techniques are not directly applicable to 3D point clouds. The main reasons for this are the following: (i) difference in data representation - an image is organized as a matrix while a 3D point cloud is an unorganized and irregularly distributed set of points; (ii) difference in information presentation - an image contains ambiguous spatial information and abundant spectral information, while a 3D point cloud contains explicit spatial information and possibly no spectral information; (iii) difference in spatial neighborhood - an image is arranged in a grid-like pattern thus allowing the neighborhood of a pixel to be easily determined, conversely the neighborhood of 3D point cloud must be determined by a nearest neighbors search.


  • We created a new global shape descriptor based on computing the topological persistence of the zeroth and first homology groups of a 3D point cloud
  • We developed a novel topology-based information gain metric for directing the next best view of a noisy 3D sensor


  1. W.J. Beksi and N. Papanikolopoulos, "A Topology-Based Descriptor for 3D Point Cloud Modeling: Theory and Experiments," Image and Vision Computing, 2019.
    Paper  •   Citation
  2. C. Collander, W.J. Beksi, and M. Huber, "Learning the Next Best View for 3D Point Clouds via Topological Features," International Conference on Robotics and Automation (ICRA), 2021.
    Paper  •   Preprint  •   Source Code  •   Citation