Persistent Homology with Improved Locality Information for more Effective Delineation
This work addresses the need for more effective delineation of curvilinear structures in domains like medical imaging and road network analysis, representing an incremental improvement over prior methods.
The paper tackles the problem of persistent homology methods being too global and ignoring feature locations by introducing a new filtration function that combines thresholding-based and height function filtrations. The result is that deep networks trained with their PH-based loss function produce reconstructions of road networks and neuronal processes that better reflect ground-truth connectivity compared to existing PH-based loss functions.
Persistent Homology (PH) has been successfully used to train networks to detect curvilinear structures and to improve the topological quality of their results. However, existing methods are very global and ignore the location of topological features. In this paper, we remedy this by introducing a new filtration function that fuses two earlier approaches: thresholding-based filtration, previously used to train deep networks to segment medical images, and filtration with height functions, typically used to compare 2D and 3D shapes. We experimentally demonstrate that deep networks trained using our PH-based loss function yield reconstructions of road networks and neuronal processes that reflect ground-truth connectivity better than networks trained with existing loss functions based on PH. Code is available at https://github.com/doruk-oner/PH-TopoLoss.