Persistence Image from 3D Medical Image: Superpixel and Optimized Gaussian Coefficient

Abstract: Topological data analysis (TDA) uncovers crucial properties of objects in medical imaging. Methods based on persistent homology have demonstrated their advantages in capturing topological features that traditional deep learning methods cannot detect in both radiology and pathology. However, previous research primarily focused on 2D image analysis, neglecting the comprehensive 3D context. In this paper, we propose an innovative 3D TDA approach that incorporates the concept of superpixels to transform 3D medical image features into point cloud data. By Utilizing Optimized Gaussian Coefficient, the proposed 3D TDA method, for the first time, efficiently generate holistic Persistence Images for 3D volumetric data. Our 3D TDA method exhibits superior performance on the MedMNist3D dataset when compared to other traditional methods, showcasing its potential effectiveness in modeling 3D persistent homology-based topological analysis when it comes to classification tasks. The source code is publicly available at https://github.com/hrlblab/TopologicalDataAnalysis3D.