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

arXiv: https://arxiv.org/abs/2512.07190 · HTML: https://mlsanity.com/paper/2512.07190/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 39 references that are in the map.
- First posted on arXiv 8 Dec 2025.

## Builds on (most cited first, 24 of 24)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Spatial Transformer Networks](https://mlsanity.com/paper/1506.02025/) (2015)
- [Skin Lesion Analysis Toward Melanoma Detection 2018: A Challenge Hosted by the International Skin Imaging Collaboration (ISIC)](https://mlsanity.com/paper/1902.03368/) (2019)
- [Persistence Images: A Stable Vector Representation of Persistent Homology](https://mlsanity.com/paper/1507.06217/) (2015)
- [PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures](https://mlsanity.com/paper/1904.09378/) (2019)
- [Deep Learning with Topological Signatures](https://mlsanity.com/paper/1707.04041/) (2017)
- [MedMamba: Vision Mamba for Medical Image Classification](https://mlsanity.com/paper/2403.03849/) (2024)
- [Graph Filtration Learning](https://mlsanity.com/paper/1905.10996/) (2019)
- [Topologically faithful image segmentation via induced matching of persistence barcodes](https://mlsanity.com/paper/2211.15272/) (2022)
- [Cubical Ripser: Software for computing persistent homology of image and volume data](https://mlsanity.com/paper/2005.12692/) (2020)
- [PHG-Net: Persistent Homology Guided Medical Image Classification](https://mlsanity.com/paper/2311.17243/) (2023)
- [Boosting Medical Image Classification with Segmentation Foundation Model](https://mlsanity.com/paper/2406.11026/) (2024)
- [Self Pre-training with Topology- and Spatiality-aware Masked Autoencoders for 3D Medical Image Segmentation](https://mlsanity.com/paper/2406.10519/) (2024)
- [Topo-VM-UNetV2: Encoding Topology into Vision Mamba UNet for Polyp Segmentation](https://mlsanity.com/paper/2505.06210/) (2025)
- [TopoTxR: A topology-guided deep convolutional network for breast parenchyma learning on DCE-MRIs](https://mlsanity.com/paper/2411.03464/) (2024)
- [TopoImages: Incorporating Local Topology Encoding into Deep Learning Models for Medical Image Classification](https://mlsanity.com/paper/2508.01574/) (2025)
- [CuMPerLay: Learning Cubical Multiparameter Persistence Vectorizations](https://mlsanity.com/paper/2510.12795/) (2025)

## Built on by (most cited first, 2 of 2)

- [TopoCL: Topological Contrastive Learning for Medical Imaging](https://mlsanity.com/paper/2603.14647/) (2026)
- [TopoAgent: An Agentic Framework for Automated Topology Learning in Medical Imaging](https://mlsanity.com/paper/2606.29763/) (2026)

## Abstract (arXiv)

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.