Topologically Faithful Multi-class Segmentation in Medical Images
This work addresses the need for topologically accurate segmentation in medical imaging for applications like vessel analysis and cell counting, representing an incremental advancement by extending binary methods to multi-class scenarios.
The paper tackles the problem of topological errors in multi-class medical image segmentation by proposing a general loss function based on Betti matching, which significantly enhances topological correctness across four diverse medical datasets.
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.