RGB image-based data analysis via discrete Morse theory and persistent homology
This work addresses the need for efficient topological analysis of popular RGB image data, though it is incremental as it builds on prior grayscale methods.
The paper tackles the problem of computationally demanding image analysis by extending existing grayscale topological analysis methods to RGB images, introducing novel RGB-to-grayscale transformations to extract topological information and applying this to datasets like water scarcity and crime variability.
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.