This software implements the algorithms for computing topological persistence as described in [1]. Given a 3D point cloud, the software computes the zeroth (Betti 0) and first (Betti 1) homology groups which correspond to the number of connected components and holes in the dataset, respectively. This is done by first approximating the input space using a Vietoris-Rips complex. Next, the simplicial persistence pairs for a given resolution are computed incrementally. Finally, the birth and death times of the 0- and 1-simplices are recorded to an output file.
To start a MATLAB session, invoke the run_matlab.sh script which adds the necessary paths and environment variables to the current session. You may have to customize this script for your environment.
The software takes as input a PCD file along with a maximum scale parameter. To compute the Betti numbers for the dataset run the following command:
>> ipa('in_file.pcd', 'out_file.txt', 0.003)
The birth and death times of the simplices are written to 'out_file.txt.'
[1] H. Edelsbrunner, D. Letscher, and A. Zomorodian, "Topological persistence and simplification," Discrete and Computational Geometry, pp. 511-533, 2002.
