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

Yanfan Zhu, Yash Singh, Khaled Younis, Shunxing Bao, Yuankai Huo

TL;DR

The paper addresses 3D medical image analysis with topology-based features, highlighting limitations of prior 2D approaches. It proposes a 3D TDA pipeline that converts entire 3D images into a superpixel-based point cloud and computes Persistence Images using an optimized Gaussian smoothing within the GUDHI alpha-complex framework. The approach shows competitive performance on MedMNist3D datasets, notably achieving top results on Organ3D, Adrenal3D, and Fracture3D, with 2D-homology-based PI providing especially strong signals. Public code is provided, and the work discusses practical considerations and avenues for future improvements including dataset-specific behavior and potential hybrids with other methods.

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.

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

TL;DR

The paper addresses 3D medical image analysis with topology-based features, highlighting limitations of prior 2D approaches. It proposes a 3D TDA pipeline that converts entire 3D images into a superpixel-based point cloud and computes Persistence Images using an optimized Gaussian smoothing within the GUDHI alpha-complex framework. The approach shows competitive performance on MedMNist3D datasets, notably achieving top results on Organ3D, Adrenal3D, and Fracture3D, with 2D-homology-based PI providing especially strong signals. Public code is provided, and the work discusses practical considerations and avenues for future improvements including dataset-specific behavior and potential hybrids with other methods.

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.
Paper Structure (9 sections, 4 equations, 3 figures, 1 table)

This paper contains 9 sections, 4 equations, 3 figures, 1 table.

Table of Contents

  1. INTRODUCTION
  2. METHOD
  3. Point Cloud Converter Based on Superpixels
  4. Optimized Gaussian Coefficient
  5. DATA AND EXPERIMENTAL DESIGN
  6. Data
  7. Experimental Design
  8. RESULTS
  9. DISCUSSION

Figures (3)

  • Figure 1: Compare Our Method to 2D TDA Method. Note that only one parameter is needed for the entire dataset to generate the Persistence Image, rather than a set of parameters, and our method results in less information loss.
  • Figure 2: Persistent Homology Filtration Process. Each row in the barcode represents the birth and death of a new topological feature at a certain filtration value. Red indicates the 0-dimensional homology group, which represents connected components, while blue represents the 1-dimensional homology group, which captures loops or cycles within the data.
  • Figure 3: The dataset preprocessing workflow transforms a single 3D medical image into a PI.

Theorems & Definitions (1)

  • Definition 2.1