Learning Probabilistic Topological Representations Using Discrete Morse Theory
This addresses the challenge of maintaining topological accuracy in segmentation for applications like medical imaging or annotation, though it appears incremental as it builds on existing topological methods.
The paper tackles the problem of accurate delineation of fine-scale structures by proposing a deep learning method that learns probabilistic topological representations using discrete Morse theory and persistent homology, generating true structures instead of pixel-maps to improve topological integrity in segmentation tasks.
Accurate delineation of fine-scale structures is a very important yet challenging problem. Existing methods use topological information as an additional training loss, but are ultimately making pixel-wise predictions. In this paper, we propose the first deep learning based method to learn topological/structural representations. We use discrete Morse theory and persistent homology to construct an one-parameter family of structures as the topological/structural representation space. Furthermore, we learn a probabilistic model that can perform inference tasks in such a topological/structural representation space. Our method generates true structures rather than pixel-maps, leading to better topological integrity in automatic segmentation tasks. It also facilitates semi-automatic interactive annotation/proofreading via the sampling of structures and structure-aware uncertainty.