Topologically Faithful Image Segmentation via Induced Matching of Persistence Barcodes

Nico Stucki, Johannes C. Paetzold, Suprosanna Shit, Bjoern Menze, Ulrich Bauer
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:32698-32727, 2023.

Abstract

Segmentation models predominantly optimize pixel-overlap-based loss, an objective that is actually inadequate for many segmentation tasks. In recent years, their limitations fueled a growing interest in topology-aware methods, which aim to recover the topology of the segmented structures. However, so far, existing methods only consider global topological properties, ignoring the need to preserve topological features spatially, which is crucial for accurate segmentation. We introduce the concept of induced matchings from persistent homology to achieve a spatially correct matching between persistence barcodes in a segmentation setting. Based on this concept, we define the Betti matching error as an interpretable, topologically and feature-wise accurate metric for image segmentations, which resolves the limitations of the Betti number error. Our Betti matching error is differentiable and efficient to use as a loss function. We demonstrate that it improves the topological performance of segmentation networks significantly across six diverse datasets while preserving the performance with respect to traditional scores. Our code is publicly available (https://github.com/nstucki/Betti-matching/).

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-stucki23a, title = {Topologically Faithful Image Segmentation via Induced Matching of Persistence Barcodes}, author = {Stucki, Nico and Paetzold, Johannes C. and Shit, Suprosanna and Menze, Bjoern and Bauer, Ulrich}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {32698--32727}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/stucki23a/stucki23a.pdf}, url = {https://proceedings.mlr.press/v202/stucki23a.html}, abstract = {Segmentation models predominantly optimize pixel-overlap-based loss, an objective that is actually inadequate for many segmentation tasks. In recent years, their limitations fueled a growing interest in topology-aware methods, which aim to recover the topology of the segmented structures. However, so far, existing methods only consider global topological properties, ignoring the need to preserve topological features spatially, which is crucial for accurate segmentation. We introduce the concept of induced matchings from persistent homology to achieve a spatially correct matching between persistence barcodes in a segmentation setting. Based on this concept, we define the Betti matching error as an interpretable, topologically and feature-wise accurate metric for image segmentations, which resolves the limitations of the Betti number error. Our Betti matching error is differentiable and efficient to use as a loss function. We demonstrate that it improves the topological performance of segmentation networks significantly across six diverse datasets while preserving the performance with respect to traditional scores. Our code is publicly available (https://github.com/nstucki/Betti-matching/).} }
Endnote
%0 Conference Paper %T Topologically Faithful Image Segmentation via Induced Matching of Persistence Barcodes %A Nico Stucki %A Johannes C. Paetzold %A Suprosanna Shit %A Bjoern Menze %A Ulrich Bauer %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-stucki23a %I PMLR %P 32698--32727 %U https://proceedings.mlr.press/v202/stucki23a.html %V 202 %X Segmentation models predominantly optimize pixel-overlap-based loss, an objective that is actually inadequate for many segmentation tasks. In recent years, their limitations fueled a growing interest in topology-aware methods, which aim to recover the topology of the segmented structures. However, so far, existing methods only consider global topological properties, ignoring the need to preserve topological features spatially, which is crucial for accurate segmentation. We introduce the concept of induced matchings from persistent homology to achieve a spatially correct matching between persistence barcodes in a segmentation setting. Based on this concept, we define the Betti matching error as an interpretable, topologically and feature-wise accurate metric for image segmentations, which resolves the limitations of the Betti number error. Our Betti matching error is differentiable and efficient to use as a loss function. We demonstrate that it improves the topological performance of segmentation networks significantly across six diverse datasets while preserving the performance with respect to traditional scores. Our code is publicly available (https://github.com/nstucki/Betti-matching/).
APA
Stucki, N., Paetzold, J.C., Shit, S., Menze, B. & Bauer, U.. (2023). Topologically Faithful Image Segmentation via Induced Matching of Persistence Barcodes. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:32698-32727 Available from https://proceedings.mlr.press/v202/stucki23a.html.

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