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
Update: A related paper on this topic appeared at iDSC2020.
The current version is available on git.sthu.org.
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:
Then the 0-th dimensional persistence diagram looks like this:
H. Edelsbrunner and J. Harer, Computational Topology. An Introduction, 2010, ISBN 0-8218-4925-5. ↩