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 .
N. Byrne—Funded by a National Institute for Health Research (NIHR), Doctoral Research Fellowship for this research project. This report presents independent research funded by the NIHR. The views expressed are those of the author(s) and not necessarily those of the NHS, the NIHR or the Department of Health and Social Care. The authors have no conflicts of interest to disclose.
G. Montana and A.P. King—Joint last authors..
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Notes
- 1.
- 2.
In \(B^{ij}_{d}\) we divide indices between sub and super scripts to make clear the difference between class labels (i, j) and topological dimension (d), without further significance.
- 3.
We use the union operator (\(\cup \)) to combine individual classes of a multi-class segmentation. When applied to a binary segmentation, \(Y_{i \cup j}\) is the pixel-wise Boolean union of classes i and j. When applied to a probabilistic segmentation, \(\hat{Y}_{i \cup j}\) is the pixel-wise probability of class i or j. We consider the union of a class with itself to be the segmentation of the single class: \(Y_{i \cup j=i} = Y_{i}\) and \(\hat{Y}_{i \cup j=i} = \hat{Y}_{i}\).
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Byrne, N., Clough, J.R., Montana, G., King, A.P. (2021). A Persistent Homology-Based Topological Loss Function for Multi-class CNN Segmentation of Cardiac MRI. In: Puyol Anton, E., et al. Statistical Atlases and Computational Models of the Heart. M&Ms and EMIDEC Challenges. STACOM 2020. Lecture Notes in Computer Science(), vol 12592. Springer, Cham. https://doi.org/10.1007/978-3-030-68107-4_1
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