Topological Data Analysis of Black Hole Images

TL;DR

This paper introduces a topological data analysis approach using persistent homology to automatically characterize high-resolution black hole images, extracting features like connected components and holes, with a new image preparation algorithm called metronization.

Contribution

The paper presents the novel application of persistent homology to black hole images and introduces the metronization algorithm for image preprocessing.

Findings

Persistent homology effectively characterizes black hole image features.

Metronization enables topological analysis of synthetic black hole images.

Topological signatures correlate with physical features in black hole images.

Abstract

Features such as photon rings, jets, or hot. spots can leave particular topological signatures in a black hole image. As such, topological data analysis can be used to characterize images resulting from high resolution observations (synthetic or real) of black holes in the electromagnetic sector. We demonstrate that persistent homology allows for this characterization to be made automatically by counting the number of connected components and one-dimensional holes. Further, persistent homology also allows for the distance between connected components or diameter of holes to be extracted from the image. In order to apply persistent homology on synthetic black hole images, we also introduce metronization, a new algorithm to prepare black hole images into a form that is suitable for topological analysis.