G-LoG Bi-filtration for Medical Image Classification

Qingsong Wang; Jiaxing He; Bingzhe Hou; Tieru Wu; Yang Cao; Cailing Yao

cs.CVFeb 20, 2026

G-LoG Bi-filtration for Medical Image Classification

Authors: Qingsong Wang, Jiaxing He, Bingzhe Hou, Tieru Wu, Yang Cao, Cailing Yao

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.

Figures & tables

Figure 1. Bi-parameter persistence modules $H_{0}$ and $H_{1}$ generated by G-LoG bi-filtration from a medical tissue image.

Figure 2. Bi-parameter persistence modules $H_{0}$ , $H_{1}$ and $H_{2}$ generated by G-LoG bi-filtration from a 3D medical organ volume.

Figure 3. The preimages of the purple and green regions correspond to the manifolds $\mathcal{M}$ and $\mathcal{N}$ , respectively.

Panel of Figure 4 — Figure 4. Classification pipeline using G-LoG bi-filtration

Method	PathMNIST		ChestMNIST		DermaMNIST		OCTMNIST		PneumoniaMNIST		RetinaMNIST
	AUC	ACC	AUC	ACC	AUC	ACC	AUC	ACC	AUC	ACC	AUC	ACC
ResNet-18 (28)	0.983	0.907	0.768	0.947	0.917	0.735	0.943	0.743	0.944	0.854	0.717	0.524
ResNet-18 (224)	0.989	0.909	0.773	0.947	0.920	0.754	0.958	0.763	0.956	0.864	0.710	0.493
ResNet-50 (28)	0.990	0.911	0.769	0.947	0.913	0.735	0.952	0.762	0.948	0.854	0.726	0.528
ResNet-50 (224)	0.989	0.892	0.773	0.948	0.912	0.731	0.958	0.776	0.962	0.884	0.716	0.511
auto-sklearn	0.934	0.716	0.649	0.779	0.902	0.719	0.887	0.601	0.942	0.855	0.690	0.515

Table 1. Comparison of seven deep learning baselines, single-parameter and our G-LoG bi-filtration on MedMNIST2D (I).

Method	BreastMNIST		BloodMNIST		TissueMNIST		OrganAMNIST		OrganCMNIST		OrganSMNIST
	AUC	ACC	AUC	ACC	AUC	ACC	AUC	ACC	AUC	ACC	AUC	ACC
ResNet-18 (28)	0.901	0.863	0.998	0.958	0.930	0.676	0.997	0.935	0.992	0.900	0.972	0.782
ResNet-18 (224)	0.891	0.833	0.998	0.963	0.933	0.681	0.998	0.951	0.994	0.920	0.974	0.778
ResNet-50 (28)	0.857	0.812	0.997	0.956	0.931	0.680	0.997	0.935	0.992	0.905	0.972	0.770
ResNet-50 (224)	0.866	0.842	0.997	0.956	0.931	0.680	0.998	0.947	0.993	0.911	0.975	0.785
auto-sklearn	0.836	0.803	0.984	0.878	0.828	0.532	0.963	0.762	0.976	0.829	0.945	0.672

Table 2. Comparison of seven deep learning baselines, single-parameter and our G-LoG bi-filtration on MedMNIST2D (II).

Method	OrganMNIST3D		NoduleMNIST3D		FractureMNIST3D		AdrenalMNIST3D		VesselMNIST3D		SynapseMNIST3D
	AUC	ACC	AUC	ACC	AUC	ACC	AUC	ACC	AUC	ACC	AUC	ACC
ResNet-18+2.5D	0.977	0.788	0.838	0.835	0.587	0.451	0.718	0.772	0.748	0.846	0.634	0.696
ResNet-18+3D	0.996	0.907	0.863	0.844	0.712	0.508	0.827	0.721	0.874	0.877	0.820	0.745
ResNet-18+ACS	0.994	0.900	0.873	0.847	0.714	0.497	0.839	0.754	0.930	0.928	0.705	0.722
ResNet-50+2.5D	0.974	0.769	0.835	0.848	0.552	0.397	0.732	0.763	0.751	0.877	0.669	0.735
ResNet-50+3D	0.994	0.883	0.875	0.847	0.725	0.494	0.828	0.745	0.907	0.918	0.851	0.795

Table 3. Comparison of eight deep learning baselines, single-parameter and our G-LoG bi-filtration on MedMNIST3D (I).

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Topological data analysis (TDA), particularly persistent homology (PH), captures geometric structural properties in medical images (e.g., connected components, loops, shape characteristics), which conventional pixel-level deep learning approaches often neglect. While many topological descriptors are known for converting persistence diagrams (PDs) or raw images into topological feature vectors, existing methods mostly default to a single fixed descriptor (e.g., persistence images), leaving the diversity of topological representations largely unexplored. To the best of our knowledge, there is no known large language model (LLM)-based agentic framework that can automatically determine the most suitable topological descriptors for a given image dataset and produce the corresponding topological feature vectors for downstream tasks. To fill this gap, we propose TopoAgent, an LLM-based agentic framework that automates topology learning for medical image analysis.TopoAgent operates through a Perception--Reasoning--Action--Reflection loop supported by 21 domain-specific tools and dual memory that accumulates experience across runs. Its skill set is distilled from systematic evaluation of 15 topological descriptors across 26 datasets with six classifiers. TopoAgent analyzes input images and their topological characteristics, reasons about which topological descriptors best suit the input, and determines the optimal descriptor and its configuration, all without task-specific training.

Abstract

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