G-LoG Bi-filtration for Medical Image Classification

TL;DR

This paper introduces G-LoG bi-filtration, a novel topological feature extraction method for medical images, which improves classification performance over traditional single-parameter filtrations and rivals deep learning models.

Contribution

The paper proposes the G-LoG bi-filtration for medical images, demonstrating its stability and superior performance in topological data analysis compared to existing methods.

Findings

G-LoG bi-filtration outperforms single-parameter filtration in experiments.

A simple MLP on topological features matches deep learning models.

Bi-filtration provides stable features with respect to maximum norm.

Abstract

Building practical filtrations on objects to detect topological and geometric features is an important task in the field of Topological Data Analysis (TDA). In this paper, leveraging the ability of the Laplacian of Gaussian operator to enhance the boundaries of medical images, we define the G-LoG (Gaussian-Laplacian of Gaussian) bi-filtration to generate the features more suitable for multi-parameter persistence module. By modeling volumetric images as bounded functions, then we prove the interleaving distance on the persistence modules obtained from our bi-filtrations on the bounded functions is stable with respect to the maximum norm of the bounded functions. Finally, we conduct experiments on the MedMNIST dataset, comparing our bi-filtration against single-parameter filtration and the established deep learning baselines, including Google AutoML Vision, ResNet, AutoKeras and auto-sklearn. Experiments results demonstrate that our bi-filtration significantly outperforms single-parameter filtration. Notably, a simple Multi-Layer Perceptron (MLP) trained on the topological features generated by our bi-filtration achieves performance comparable to complex deep learning models trained on the original dataset.