A Multi-parameter Persistence Framework for Mathematical Morphology
Computational Geometry
2021-03-25 v1 Computer Vision and Pattern Recognition
Algebraic Topology
Abstract
The field of mathematical morphology offers well-studied techniques for image processing. In this work, we view morphological operations through the lens of persistent homology, a tool at the heart of the field of topological data analysis. We demonstrate that morphological operations naturally form a multiparameter filtration and that persistent homology can then be used to extract information about both topology and geometry in the images as well as to automate methods for optimizing the study and rendering of structure in images. For illustration, we apply this framework to analyze noisy binary, grayscale, and color images.
Cite
@article{arxiv.2103.13013,
title = {A Multi-parameter Persistence Framework for Mathematical Morphology},
author = {Yu-Min Chung and Sarah Day and Chuan-Shen Hu},
journal= {arXiv preprint arXiv:2103.13013},
year = {2021}
}