Topological peak detection in two-dimensional data

A simple Python implementation of the 0-th dimensional persistent homology for 2D images. It is basically a two-dimensional version of the method described in my blog article persistent topology for peak detection.

The implementation uses a union-find data structure instead of the more efficient implemention used for one-dimensional data. The union-find data structure implementation was taken from PADS and sligthly modified.

The related literature is Computational Topology by Herbert Edelsbrunner.1

Download

The current version is available on git.sthu.org.

Demonstration

The code has been used for answers to the following two stackoverflow questions:

An ipython notebook is included in the git repository to demonstrate the code. Assume we are given the input of the first stackoverflow question:

Input image

Then the 0-th dimensional persistence diagram looks like this:

Persistence diagram

  1. H. Edelsbrunner and J. Harer, Computational Topology. An Introduction, 2010, ISBN 0-8218-4925-5.