RGB image-based data analysis via discrete Morse theory and persistent homology

TL;DR

This paper extends topological data analysis techniques to RGB images, enabling efficient extraction of topological features directly from color images for applications like water scarcity and crime data analysis.

Contribution

It introduces novel methods and software for analyzing RGB images using discrete Morse theory and persistent homology, expanding beyond grayscale analysis.

Findings

Effective extraction of topological features from RGB images

Application to real-world data on water scarcity and crime

Software enabling prediction of future image properties

Abstract

Understanding and comparing images for the purposes of data analysis is currently a very computationally demanding task. A group at Australian National University (ANU) recently developed open-source code that can detect fundamental topological features of a grayscale image in a computationally feasible manner. This is made possible by the fact that computers store grayscale images as cubical cellular complexes. These complexes can be studied using the techniques of discrete Morse theory. We expand the functionality of the ANU code by introducing methods and software for analyzing images encoded in red, green, and blue (RGB), because this image encoding is very popular for publicly available data. Our methods allow the extraction of key topological information from RGB images via informative persistence diagrams by introducing novel methods for transforming RGB-to-grayscale. This paradigm allows us to perform data analysis directly on RGB images representing water scarcity variability as well as crime variability. We introduce software enabling a a user to predict future image properties, towards the eventual aim of more rapid image-based data behavior prediction.