The Weighted Euler Characteristic Transform for Image Shape Classification

TL;DR

This paper introduces the weighted Euler characteristic transform (WECT), a novel shape descriptor for image data that incorporates pixel intensities, and evaluates its effectiveness in distinguishing shapes.

Contribution

The paper presents the WECT as a new shape analysis tool, derives its expected values, and assesses its performance on images with varying pixel intensities.

Findings

WECT effectively distinguishes shapes based on pixel intensity distributions.

Visualization techniques enhance understanding of WECT features.

Expected values of WECT are analytically derived.

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.