Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

TL;DR

This work proposes 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 and significantly enhances topological correctness in cardiac, cell, artery-vein, and Circle of Willis segmentation.

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.

Topologically Faithful Multi-class Segmentation in Medical Images

TL;DR

This work proposes 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 and significantly enhances topological correctness in cardiac, cell, artery-vein, and Circle of Willis segmentation.

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.
Paper Structure (21 sections, 7 equations, 5 figures, 5 tables)

This paper contains 21 sections, 7 equations, 5 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Related works
  3. Method
  4. Overview of persistent homology for image segmentation.
  5. Single-class loss functions for multi-class segmentations.
  6. Weighting.
  7. Data and Experimentation
  8. Datasets.
  9. Baselines.
  10. Metrics
  11. Training and model selection
  12. Results
  13. ACDC.
  14. Platelet.
  15. OCTA-500.
  16. ...and 6 more sections

Figures (5)

  • Figure 1: Top: image, ground truth, and exemplary segmentation of the cardiac dataset. Bottom: ground truth (left) next to the segmentation (right), pairwise for every class. With our multi-class Betti-matching formulation, we match connected components (dim-0) and cycles (dim-1) in each individual class. Matched features in dim-0 and dim-1 are colored in a checkerboard pattern and have colored feature cycles, respectively. All classes' matched and unmatched features guide our loss function for multi-class topology-preserving segmentation.
  • Figure 2: Qualitative results on ACDC (a), Platelet (b), OCTA-500 (c), and TopCoW (d) dataset. Our method improves topological correctness in all multi-class segmentation tasks. We indicate some topological errors with black arrows.
  • Figure 3: Betti Matching error (left) and Dice score (right) with varying $\gamma^{\text{m}}$
  • Figure 4: Additional ablation on the introduced weighting term with the ACDC dataset. We find a different trend compared to Fig. 3, showcasing that the weight parameter must be tuned according to the dataset.
  • Figure 5: Additional qualitative results on ACDC (a), Platelet (b), OCTA-500 (c), and TopCoW (d) dataset.