A Topological Loss Function for Deep-Learning Based Image Segmentation Using Persistent Homology

We introduce a method for training neural networks to perform image or volume segmentation in which prior knowledge about the topology of the segmented object can be explicitly provided and then incorporated into the training process. By using the differentiable properties of persistent homology, a...

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Published in:	IEEE transactions on pattern analysis and machine intelligence Vol. 44; no. 12; pp. 8766 - 8778
Main Authors:	Clough, James R., Byrne, Nicholas, Oksuz, Ilkay, Zimmer, Veronika A., Schnabel, Julia A., King, Andrew P.
Format:	Journal Article
Language:	English
Published:	United States IEEE 01.12.2022 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	Algorithms convolutional neural networks Data analysis Deep Learning Homology Image Processing, Computer-Assisted - methods Image segmentation Labels Loss measurement Magnetic resonance imaging Magnetic Resonance Imaging - methods medical imaging Myocardium Network topologies Network topology Neural networks Neural Networks, Computer Object recognition persistent homology Segmentation Shape Topology Training
ISSN:	0162-8828, 1939-3539, 2160-9292, 1939-3539
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Abstract	We introduce a method for training neural networks to perform image or volume segmentation in which prior knowledge about the topology of the segmented object can be explicitly provided and then incorporated into the training process. By using the differentiable properties of persistent homology, a concept used in topological data analysis, we can specify the desired topology of segmented objects in terms of their Betti numbers and then drive the proposed segmentations to contain the specified topological features. Importantly this process does not require any ground-truth labels, just prior knowledge of the topology of the structure being segmented. We demonstrate our approach in four experiments: one on MNIST image denoising and digit recognition, one on left ventricular myocardium segmentation from magnetic resonance imaging data from the UK Biobank, one on the ACDC public challenge dataset and one on placenta segmentation from 3-D ultrasound. We find that embedding explicit prior knowledge in neural network segmentation tasks is most beneficial when the segmentation task is especially challenging and that it can be used in either a semi-supervised or post-processing context to extract a useful training gradient from images without pixelwise labels.
AbstractList	We introduce a method for training neural networks to perform image or volume segmentation in which prior knowledge about the topology of the segmented object can be explicitly provided and then incorporated into the training process. By using the differentiable properties of persistent homology, a concept used in topological data analysis, we can specify the desired topology of segmented objects in terms of their Betti numbers and then drive the proposed segmentations to contain the specified topological features. Importantly this process does not require any ground-truth labels, just prior knowledge of the topology of the structure being segmented. We demonstrate our approach in four experiments: one on MNIST image denoising and digit recognition, one on left ventricular myocardium segmentation from magnetic resonance imaging data from the UK Biobank, one on the ACDC public challenge dataset and one on placenta segmentation from 3-D ultrasound. We find that embedding explicit prior knowledge in neural network segmentation tasks is most beneficial when the segmentation task is especially challenging and that it can be used in either a semi-supervised or post-processing context to extract a useful training gradient from images without pixelwise labels. We introduce a method for training neural networks to perform image or volume segmentation in which prior knowledge about the topology of the segmented object can be explicitly provided and then incorporated into the training process. By using the differentiable properties of persistent homology, a concept used in topological data analysis, we can specify the desired topology of segmented objects in terms of their Betti numbers and then drive the proposed segmentations to contain the specified topological features. Importantly this process does not require any ground-truth labels, just prior knowledge of the topology of the structure being segmented. We demonstrate our approach in four experiments: one on MNIST image denoising and digit recognition, one on left ventricular myocardium segmentation from magnetic resonance imaging data from the UK Biobank, one on the ACDC public challenge dataset and one on placenta segmentation from 3-D ultrasound. We find that embedding explicit prior knowledge in neural network segmentation tasks is most beneficial when the segmentation task is especially challenging and that it can be used in either a semi-supervised or post-processing context to extract a useful training gradient from images without pixelwise labels.We introduce a method for training neural networks to perform image or volume segmentation in which prior knowledge about the topology of the segmented object can be explicitly provided and then incorporated into the training process. By using the differentiable properties of persistent homology, a concept used in topological data analysis, we can specify the desired topology of segmented objects in terms of their Betti numbers and then drive the proposed segmentations to contain the specified topological features. Importantly this process does not require any ground-truth labels, just prior knowledge of the topology of the structure being segmented. We demonstrate our approach in four experiments: one on MNIST image denoising and digit recognition, one on left ventricular myocardium segmentation from magnetic resonance imaging data from the UK Biobank, one on the ACDC public challenge dataset and one on placenta segmentation from 3-D ultrasound. We find that embedding explicit prior knowledge in neural network segmentation tasks is most beneficial when the segmentation task is especially challenging and that it can be used in either a semi-supervised or post-processing context to extract a useful training gradient from images without pixelwise labels.
Author	Oksuz, Ilkay Schnabel, Julia A. Clough, James R. Zimmer, Veronika A. Byrne, Nicholas King, Andrew P.
AuthorAffiliation	Computer Engineering Department Istanbul Technical University 34467 Sariyer/Istanbul Turkey School of Biomedical Engineering and Imaging Sciences King's College London WC2R 2LS London United Kingdom School of Biomedical Engineering and Imaging Sciences King's College London 4616 WC2R 2LS London United Kingdom
AuthorAffiliation_xml	– name: School of Biomedical Engineering and Imaging Sciences King's College London 4616 WC2R 2LS London United Kingdom – name: Computer Engineering Department Istanbul Technical University 34467 Sariyer/Istanbul Turkey – name: School of Biomedical Engineering and Imaging Sciences King's College London WC2R 2LS London United Kingdom
Author_xml	– sequence: 1 givenname: James R. orcidid: 0000-0002-9135-0545 surname: Clough fullname: Clough, James R. email: james.clough@kcl.ac.uk organization: School of Biomedical Engineering and Imaging Sciences, King's College London, London, United Kingdom – sequence: 2 givenname: Nicholas orcidid: 0000-0003-3401-9570 surname: Byrne fullname: Byrne, Nicholas email: nicholas.byrne@kcl.ac.uk organization: School of Biomedical Engineering and Imaging Sciences, King's College London, London, United Kingdom – sequence: 3 givenname: Ilkay orcidid: 0000-0001-6478-0534 surname: Oksuz fullname: Oksuz, Ilkay email: ilkay.oksuz@kcl.ac.uk organization: School of Biomedical Engineering and Imaging Sciences, King's College London, London, United Kingdom – sequence: 4 givenname: Veronika A. orcidid: 0000-0002-5093-5854 surname: Zimmer fullname: Zimmer, Veronika A. email: veronika.zimmer@kcl.ac.uk organization: School of Biomedical Engineering and Imaging Sciences, King's College London, London, United Kingdom – sequence: 5 givenname: Julia A. orcidid: 0000-0001-6107-3009 surname: Schnabel fullname: Schnabel, Julia A. email: julia.schnabel@kcl.ac.uk organization: School of Biomedical Engineering and Imaging Sciences, King's College London, London, United Kingdom – sequence: 6 givenname: Andrew P. orcidid: 0000-0002-9965-7015 surname: King fullname: King, Andrew P. email: andrew.king@kcl.ac.uk organization: School of Biomedical Engineering and Imaging Sciences, King's College London, London, United Kingdom
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SubjectTerms	Algorithms convolutional neural networks Data analysis Deep Learning Homology Image Processing, Computer-Assisted - methods Image segmentation Labels Loss measurement Magnetic resonance imaging Magnetic Resonance Imaging - methods medical imaging Myocardium Network topologies Network topology Neural networks Neural Networks, Computer Object recognition persistent homology Segmentation Shape Topology Training
Title	A Topological Loss Function for Deep-Learning Based Image Segmentation Using Persistent Homology
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