Efficient Betti Matching Enables Topology-Aware 3D Segmentation via Persistent Homology
This work addresses the problem of computationally expensive topology-aware segmentation for researchers and practitioners in medical imaging or 3D analysis, though it is incremental as it optimizes an existing method rather than introducing a new paradigm.
The authors tackled the computational challenge of using persistent homology for topology-aware 3D segmentation by developing an efficient Betti matching algorithm, achieving significant speedups over the state-of-the-art Cubical Ripser and improving topological correctness in segmentation predictions across multiple datasets.
In this work, we propose an efficient algorithm for the calculation of the Betti matching, which can be used as a loss function to train topology aware segmentation networks. Betti matching loss builds on techniques from topological data analysis, specifically persistent homology. A major challenge is the computational cost of computing persistence barcodes. In response to this challenge, we propose a new, highly optimized implementation of Betti matching, implemented in C++ together with a python interface, which achieves significant speedups compared to the state-of-the-art implementation Cubical Ripser. We use Betti matching 3D to train segmentation networks with the Betti matching loss and demonstrate improved topological correctness of predicted segmentations across several datasets. The source code is available at https://github.com/nstucki/Betti-Matching-3D.