A persistent homology-based topological loss function for multi-class CNN segmentation of cardiac MRI

With respect to spatial overlap, CNN-based segmentation of short axis\ncardiovascular magnetic resonance (CMR) images has achieved a level of\nperformance consistent with inter observer variation. However, conventional\ntraining procedures frequently depend on pixel-wise loss functions, limiting\noptimisation with respect to extended or global features. As a result, inferred\nsegmentations can lack spatial coherence, including spurious connected\ncomponents or holes. Such results are implausible, violating the anticipated\ntopology of image segments, which is frequently known a priori. Addressing this\nchallenge, published work has employed persistent homology, constructing\ntopological loss functions for the evaluation of image segments against an\nexplicit prior. Building a richer description of segmentation topology by\nconsidering all possible labels and label pairs, we extend these losses to the\ntask of multi-class segmentation. These topological priors allow us to resolve\nall topological errors in a subset of 150 examples from the ACDC short axis CMR\ntraining data set, without sacrificing overlap performance.\n