A persistent homology-based topological loss for CNN-based multi-class segmentation of CMR

TL;DR

This paper introduces a novel topological loss function based on persistent homology for CNN-based multi-class segmentation of cardiac MRI images, improving anatomical coherence and topology in segmentation results.

Contribution

It extends persistent homology-based loss functions to multi-class segmentation, providing a more comprehensive topological regularization for CNNs in medical imaging.

Findings

Significant improvements in segmentation topology accuracy.

Efficient implementation enables high-resolution 3D data processing.

Enhanced anatomical plausibility in multi-class CMR segmentation.

Abstract

Multi-class segmentation of cardiac magnetic resonance (CMR) images seeks a separation of data into anatomical components with known structure and configuration. The most popular CNN-based methods are optimised using pixel wise loss functions, ignorant of the spatially extended features that characterise anatomy. Therefore, whilst sharing a high spatial overlap with the ground truth, inferred CNN-based segmentations can lack coherence, including spurious connected components, holes and voids. Such results are implausible, violating anticipated anatomical topology. In response, (single-class) persistent homology-based loss functions have been proposed to capture global anatomical features. Our work extends these approaches to the task of multi-class segmentation. Building an enriched topological description of all class labels and class label pairs, our loss functions make predictable and statistically significant improvements in segmentation topology using a CNN-based post-processing framework. We also present (and make available) a highly efficient implementation based on cubical complexes and parallel execution, enabling practical application within high resolution 3D data for the first time. We demonstrate our approach on 2D short axis and 3D whole heart CMR segmentation, advancing a detailed and faithful analysis of performance on two publicly available datasets.