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

TL;DR

This paper introduces a topological loss function based on persistent homology to improve multi-class CNN segmentation of cardiac MRI by enforcing plausible topology, reducing errors like holes and spurious components.

Contribution

It extends persistent homology-based topological loss functions to multi-class segmentation, enhancing spatial coherence without compromising overlap accuracy.

Findings

Resolved all topological errors in 150 test examples

Maintained high overlap performance in segmentation

Improved spatial coherence of CNN outputs

Abstract

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