The Weighted Euler Characteristic Transform for Image Shape Classification
Computational Geometry
2023-07-27 v1 Algebraic Topology
Abstract
The weighted Euler characteristic transform (WECT) is a new tool for extracting shape information from data equipped with a weight function. Image data may benefit from the WECT where the intensity of the pixels are used to define the weight function. In this work, an empirical assessment of the WECT's ability to distinguish shapes on images with different pixel intensity distributions is considered, along with visualization techniques to improve the intuition and understanding of what is captured by the WECT. Additionally, the expected weighted Euler characteristic and the expected WECT are derived.
Cite
@article{arxiv.2307.13940,
title = {The Weighted Euler Characteristic Transform for Image Shape Classification},
author = {Jessi Cisewski-Kehe and Brittany Terese Fasy and Dhanush Giriyan and Eli Quist},
journal= {arXiv preprint arXiv:2307.13940},
year = {2023}
}
Comments
25 pages, 13 figures