Topologically faithful multi-class segmentation in medical images
Alexander H. Berger Nico Stucki Laurin Lux Vincent Buergin Suprosanna Shit Anna Banaszak Daniel Rueckert Ulrich Bauer Johannes C. Paetzold
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.