Classification of Histopathology Slides with Persistence Homology Convolutions

2025-07-18

AI Summary

Convolutional neural networks (CNNs) for histopathological image classification often fail to preserve topological information due to the locality and translation-invariance constraints of standard convolutions. Method: We propose Persistent Homology Convolution (PHConv), the first convolutional operator that unifies local topological feature modeling with translation invariance. PHConv computes persistent homology–based topological summaries—e.g., Betti number curves—within pixel neighborhoods and embeds them into the kernel weight learning process, enabling joint geometric-topological representation learning. Results: Extensive experiments on multiple public histopathology benchmarks demonstrate that PHConv consistently improves classification accuracy (average +2.3%), exhibits greater robustness to hyperparameter variation, and achieves superior generalization compared to both standard CNNs and state-of-the-art global topological enhancement methods. Its core contribution lies in overcoming the limitations of global topological descriptors by introducing a differentiable, local, and learnable topological-aware convolutional paradigm.

Technology Category

• Computer Vision: Learning & Optimization for CV
• Machine Learning: Learning with Manifolds
• Search and Optimization: Non-convex Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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 Persistent Homology Convolutions. This method captures information about the locality and translation invariance 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.

Problem

• Classify histopathology slides using topological features
• Address loss of local topological information in CNNs
• Improve medical diagnostics with persistent homology convolutions

Innovation

• Uses Persistent Homology Convolutions for local topology
• Improves classification by capturing geometric features
• Outperforms traditional CNNs in histopathology analysis