# Classification of Histopathology Slides with Persistent Homology Convolutions

arXiv: https://arxiv.org/abs/2507.14378 · HTML: https://mlsanity.com/paper/2507.14378/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 60 references that are in the map.
- First posted on arXiv 18 Jul 2025.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [The Intrinsic Dimension of Images and Its Impact on Learning](https://mlsanity.com/paper/2104.08894/) (2021)
- [Persistence Images: A Stable Vector Representation of Persistent Homology](https://mlsanity.com/paper/1507.06217/) (2015)
- [A roadmap for the computation of persistent homology](https://mlsanity.com/paper/1506.08903/) (2015)
- [PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures](https://mlsanity.com/paper/1904.09378/) (2019)
- [Machine learning methods for histopathological image analysis](https://mlsanity.com/paper/1709.00786/) (2017)
- [Fast and Accurate Tumor Segmentation of Histology Images using Persistent Homology and Deep Convolutional Features](https://mlsanity.com/paper/1805.03699/) (2018)
- [The Simplex Tree: an Efficient Data Structure for General Simplicial Complexes](https://mlsanity.com/paper/2001.02581/) (2020)
- [XNet: A convolutional neural network (CNN) implementation for medical X-Ray image segmentation suitable for small datasets](https://mlsanity.com/paper/1812.00548/) (2018)
- [Topology-Guided Multi-Class Cell Context Generation for Digital Pathology](https://mlsanity.com/paper/2304.02255/) (2023)

## Abstract (arXiv)

Convolutional neural networks (CNNs) are a standard tool for computer vision tasks such as image classification. However, typical model architectures may result in the loss of topological information. In specific domains such as histopathology, topology is an important descriptor that can be used to distinguish between disease-indicating tissue by analyzing the shape characteristics of cells. Current literature suggests that reintroducing topological information using persistent homology can improve medical diagnostics; however, previous methods utilize global topological summaries which do not contain information about the locality of topological features. To address this gap, we present a novel method that generates local persistent homology-based data using a modified version of the convolution operator called textitPersistent Homology Convolutions. This method captures information about the locality and translation equivariance of topological features. We perform a comparative study using various representations of histopathology slides and find that models trained with persistent homology convolutions outperform conventionally trained models and are less sensitive to hyperparameters. These results indicate that persistent homology convolutions extract meaningful geometric information from the histopathology slides.