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Learning Probabilistic Topological Representations Using Discrete Morse Theory
Xiaoling Hu · Dimitris Samaras · Chao Chen

@
in Medical Imaging meets NeurIPS »

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 abstract, 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.

Author Information

Xiaoling Hu (Stony Brook University)
Dimitris Samaras (Stony Brook University)
Chao Chen (Stony Brook University)

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