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

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.

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 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.

Topology-preserving augmentation for CNN-based segmentation of congenital heart defects from 3D paediatric CMR

Patient-specific 3D printing of congenital heart anatomy demands an accurate segmentation of the thin tissue interfaces which characterise these diagnoses. Even when a label set has a high spatial overlap with the ground truth, inaccurate delineation of these interfaces can result in topological errors. These compromise the clinical utility of such models due to the anomalous appearance of defects. CNNs have achieved state-of-the-art performance in segmentation tasks. Whilst data augmentation has often played an important role, we show that conventional image resampling schemes used therein can introduce topological changes in the ground truth labelling of augmented samples. We present a novel pipeline to correct for these changes, using a fast-marching algorithm to enforce the topology of the ground truth labels within their augmented representations. In so doing, we invoke the idea of cardiac contiguous topology to describe an arbitrary combination of congenital heart defects and develop an associated, clinically meaningful metric to measure the topological correctness of segmentations. In a series of five-fold cross-validations, we demonstrate the performance gain produced by this pipeline and the relevance of topological considerations to the segmentation of congenital heart defects. We speculate as to the applicability of this approach to any segmentation task involving morphologically complex targets.