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

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Document pages: 11 pages

Abstract: With respect to spatial overlap, CNN-based segmentation of short axiscardiovascular magnetic resonance (CMR) images has achieved a level ofperformance consistent with inter observer variation. However, conventionaltraining procedures frequently depend on pixel-wise loss functions, limitingoptimisation with respect to extended or global features. As a result, inferredsegmentations can lack spatial coherence, including spurious connectedcomponents or holes. Such results are implausible, violating the anticipatedtopology of image segments, which is frequently known a priori. Addressing thischallenge, published work has employed persistent homology, constructingtopological loss functions for the evaluation of image segments against anexplicit prior. Building a richer description of segmentation topology byconsidering all possible labels and label pairs, we extend these losses to thetask of multi-class segmentation. These topological priors allow us to resolveall topological errors in a subset of 150 examples from the ACDC short axis CMRtraining data set, without sacrificing overlap performance.

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