Statistical Inference on Grayscale Images via the Euler-Radon Transform

Understand

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.