# G-LoG Bi-filtration for Medical Image Classification

arXiv: https://arxiv.org/abs/2602.18329 · HTML: https://mlsanity.com/paper/2602.18329/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 38 references that are in the map.
- First posted on arXiv 20 Feb 2026.

## Builds on (most cited first, 20 of 20)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [MedMNIST v2 -- A large-scale lightweight benchmark for 2D and 3D biomedical image classification](https://mlsanity.com/paper/2110.14795/) (2021)
- [Persistence Images: A Stable Vector Representation of Persistent Homology](https://mlsanity.com/paper/1507.06217/) (2015)
- [MedMNIST Classification Decathlon: A Lightweight AutoML Benchmark for Medical Image Analysis](https://mlsanity.com/paper/2010.14925/) (2020)
- [Auto-Sklearn 2.0: Hands-free AutoML via Meta-Learning](https://mlsanity.com/paper/2007.04074/) (2020)
- [Auto-Keras: An Efficient Neural Architecture Search System](https://mlsanity.com/paper/1806.10282/) (2018)
- [MedViT: A Robust Vision Transformer for Generalized Medical Image Classification](https://mlsanity.com/paper/2302.09462/) (2023)
- [A Stable Multi-Scale Kernel for Topological Machine Learning](https://mlsanity.com/paper/1412.6821/) (2014)
- [Topology-Aware Segmentation Using Discrete Morse Theory](https://mlsanity.com/paper/2103.09992/) (2021)
- [Persistence Curves: A canonical framework for summarizing persistence diagrams](https://mlsanity.com/paper/1904.07768/) (2019)
- [Towards a topological-geometrical theory of group equivariant non-expansive operators for data analysis and machine learning](https://mlsanity.com/paper/1812.11832/) (2018)
- [Complex Mixer for MedMNIST Classification Decathlon](https://mlsanity.com/paper/2304.10054/) (2023)
- [Stability of 2-Parameter Persistent Homology](https://mlsanity.com/paper/2010.09628/) (2020)
- [Computing the Multicover Bifiltration](https://mlsanity.com/paper/2103.07823/) (2021)
- [Multi-parameter Module Approximation: an efficient and interpretable invariant for multi-parameter persistence modules with guarantees](https://mlsanity.com/paper/2206.02026/) (2022)
- [Delaunay Bifiltrations of Functions on Point Clouds](https://mlsanity.com/paper/2310.15902/) (2023)
- [Persistence B-Spline Grids: Stable Vector Representation of Persistence Diagrams Based on Data Fitting](https://mlsanity.com/paper/1909.08417/) (2019)
- [Topological Machine Learning for Mixed Numeric and Categorical Data](https://mlsanity.com/paper/2003.04584/) (2020)
- [Mix-GENEO: A Flexible Filtration for Multiparameter Persistent Homology Detects Digital Images](https://mlsanity.com/paper/2401.04332/) (2024)
- [Nerve Models of Subdivision Bifiltrations](https://mlsanity.com/paper/2406.07679/) (2024)

## Abstract (arXiv)

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.