Year: 2023
Type: preprint
Abstract: Tools from topological data analysis have been widely used to represent binary images in many scientific applications. Methods that aim to represent grayscale images (i.e., where pixel intensities instead take on continuous values) have been relatively underdeveloped. In this paper, we introduce the Euler-Radon transform, which generalizes the Euler characteristic transform to grayscale images by using o-minimal structures and Euler integration over definable functions. Coupling the Karhunen-Loeve expansion with our proposed topological representation, we offer hypothesis-testing algorithms based on the chi-squared distribution for detecting significant differences between two groups of grayscale images. We illustrate our framework via extensive numerical experiments and simulations.
Source: arXiv (Cornell University)
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: National Institutes of Health
OpenAlex ID: W4386272748