Topologically Faithful Multi-Class Segmentation in Medical Images

MCML Authors

Laurin Lux

→ Group Daniel Rückert
 Artificial Intelligence in Healthcare and Medicine

Nico Stucki

→ Group Ulrich Bauer
 Applied Topology and Geometry

Vincent Bürgin

→ Group Stefanie Jegelka
 Foundations of Deep Neural Networks

Daniel Rückert

Prof. Dr.

Director

Artificial Intelligence in Healthcare and Medicine

Ulrich Bauer

Prof. Dr.

Principal Investigator

Applied Topology and Geometry

Abstract

Topological accuracy in medical image segmentation is a highly important property for downstream applications such as network analysis and flow modeling in vessels or cell counting. Recently, significant methodological advancements have brought well-founded concepts from algebraic topology to binary segmentation. However, these approaches have been underexplored in multi-class segmentation scenarios, where topological errors are common. We propose a general loss function for topologically faithful multi-class segmentation extending the recent Betti matching concept, which is based on induced matchings of persistence barcodes. We project the N-class segmentation problem to N single-class segmentation tasks, which allows us to use 1-parameter persistent homology, making training of neural networks computationally feasible. We validate our method on a comprehensive set of four medical datasets with highly variant topological characteristics. Our loss formulation significantly enhances topological correctness in cardiac, cell, artery-vein, and Circle of Willis segmentation.

inproceedings

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MICCAI 2024

27th International Conference on Medical Image Computing and Computer Assisted Intervention. Marrakesh, Morocco, Oct 06-10, 2024.

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Authors

A. H. Berger • L. Lux • N. Stucki • V. Bürgin • S. Shit • A. Banaszaka • D. Rückert • U. Bauer • J. C. Paetzold

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Links

DOI

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Research Areas

 A2 | Mathematical Foundations

 A3 | Computational Models

 C1 | Medicine