Integrating Multi-scale and Multi-filtration Topological Features for Medical Image Classification

TL;DR

The paper addresses the underutilization of topological information in medical image classification by introducing a topology-guided framework that extracts stable multi-scale, multi-filtration persistent diagrams. It consolidates these diagrams with a vineyard algorithm, encodes them via a cross-attention-based PD encoder, and fuses the topology embeddings into CNN/Transformer backbones in an end-to-end pipeline. Across ISIC 2018, Kvasir, and CBIS-DDSM, the approach yields consistent improvements over strong baselines and SOTA methods, with ablations validating the contributions of scale stabilization and multi-filtration fusion. This topology-centric augmentation enhances robustness and interpretability in medical image classification while remaining model-agnostic for integration with various vision architectures.

Abstract

Modern deep neural networks have shown remarkable performance in medical image classification. However, such networks either emphasize pixel-intensity features instead of fundamental anatomical structures (e.g., those encoded by topological invariants), or they capture only simple topological features via single-parameter persistence. In this paper, we propose a new topology-guided classification framework that extracts multi-scale and multi-filtration persistent topological features and integrates them into vision classification backbones. For an input image, we first compute cubical persistence diagrams (PDs) across multiple image resolutions/scales. We then develop a ``vineyard'' algorithm that consolidates these PDs into a single, stable diagram capturing signatures at varying granularities, from global anatomy to subtle local irregularities that may indicate early-stage disease. To further exploit richer topological representations produced by multiple filtrations, we design a cross-attention-based neural network that directly processes the consolidated final PDs. The resulting topological embeddings are fused with feature maps from CNNs or Transformers. By integrating multi-scale and multi-filtration topologies into an end-to-end architecture, our approach enhances the model's capacity to recognize complex anatomical structures. Evaluations on three public datasets show consistent, considerable improvements over strong baselines and state-of-the-art methods, demonstrating the value of our comprehensive topological perspective for robust and interpretable medical image classification.

Figures (3)

• Figure 1: (a) Illustrating the pipeline of our proposed approach. (b) Illustrating the generation of a stable persistence diagram from the multi-scale persistence diagrams using the "vineyard" tracking Algorithm \ref{['alg:vineyard']} (using a single filtration function as an example). (c) The architecture of the proposed persistence diagrams (PDs) encoder. VisionLoss and TopoLoss represent the vision loss and topological loss, respectively. We use an image from the ISIC 2018 dataset and a CNN backbone for illustration. For simplicity, the batch normalization and rectified linear unit that follow each 1D convolution layer are omitted.
• Figure 2: Examples of persistence diagrams in an image from the ISIC 2018 dataset under different filtrations. (a) An original image; (b) image with intensity values and its corresponding persistence diagram; (c) image with gradient magnitude values and its corresponding persistence diagram. In the PDs, red circles denote 0-D persistent homology (H0), and blue squares denote 1-D persistent homology (H1).
• Figure 3: Examples of stable persistence diagrams generated from multi-scale persistence diagrams in images of the Kvasir dataset. Here, scale 1 corresponds to $224 \times 224$, scale 2 to $112 \times 112$, and scale 3 to $56 \times 56$.