Persistent Homology With Improved Locality Information for More Effective Delineation.

Area of Science:

• Computational Topology
• Machine Learning
• Medical Image Analysis

Background:

• Persistent Homology (PH) is utilized in training networks for detecting curvilinear structures and enhancing topological quality.
• Current PH methods are global, neglecting the precise location of topological features, which limits their application in tasks like medical image segmentation.

Purpose of the Study:

• To develop a novel filtration function for Persistent Homology (PH) that incorporates local feature information.
• To improve the accuracy of deep network reconstructions for curvilinear structures, such as road networks and neuronal processes.

Main Methods:

• Introduced a new filtration function combining thresholding-based filtration and height function filtration.
• Trained deep networks using the proposed PH-based loss function for reconstructing road networks and neuronal processes.
• Compared the performance against existing PH-based loss functions.

Main Results:

• Deep networks trained with the new PH-based loss function demonstrated superior reconstructions of road networks and neuronal processes.
• The proposed method significantly improved the reflection of ground-truth connectivity compared to existing loss functions.

Conclusions:

• The novel filtration function enhances deep network training by incorporating local topological information.
• This approach offers a more accurate method for analyzing and reconstructing complex structures in various scientific domains.