Explicit topological priors for deep-learning based image segmentation using persistent homology

TL;DR

This paper introduces a novel deep learning segmentation method that explicitly incorporates topological priors using persistent homology, improving topological correctness in cardiac MRI segmentation.

Contribution

It is the first to integrate topological prior knowledge into deep learning segmentation using persistent homology, enhancing topological accuracy.

Findings

Improves topological correctness of segmentation results.

Maintains pixelwise accuracy while enforcing topological constraints.

Demonstrates effectiveness on cardiac MRI data from UK Biobank.

Abstract

We present a novel method to explicitly incorporate topological prior knowledge into deep learning based segmentation, which is, to our knowledge, the first work to do so. Our method uses the concept of persistent homology, a tool from topological data analysis, to capture high-level topological characteristics of segmentation results in a way which is differentiable with respect to the pixelwise probability of being assigned to a given class. The topological prior knowledge consists of the sequence of desired Betti numbers of the segmentation. As a proof-of-concept we demonstrate our approach by applying it to the problem of left-ventricle segmentation of cardiac MR images of 500 subjects from the UK Biobank dataset, where we show that it improves segmentation performance in terms of topological correctness without sacrificing pixelwise accuracy.