  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.
