# Rethinking Persistent Homology for Visual Recognition

arXiv: https://arxiv.org/abs/2207.04220 · HTML: https://mlsanity.com/paper/2207.04220/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 26 references that are in the map.
- First posted on arXiv 9 Jul 2022.

## Builds on (most cited first, 13 of 13)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Persistence Images: A Stable Vector Representation of Persistent Homology](https://mlsanity.com/paper/1507.06217/) (2015)
- [Topology-Preserving Deep Image Segmentation](https://mlsanity.com/paper/1906.05404/) (2019)
- [A Topological Loss Function for Deep-Learning based Image Segmentation using Persistent Homology](https://mlsanity.com/paper/1910.01877/) (2019)
- [Topological Autoencoders](https://mlsanity.com/paper/1906.00722/) (2019)
- [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)
- [A Topology Layer for Machine Learning](https://mlsanity.com/paper/1905.12200/) (2019)
- [Learning metrics for persistence-based summaries and applications for graph classification](https://mlsanity.com/paper/1904.12189/) (2019)
- [Stochastic Convergence of Persistence Landscapes and Silhouettes](https://mlsanity.com/paper/1312.0308/) (2013)
- [Fast and Accurate Tumor Segmentation of Histology Images using Persistent Homology and Deep Convolutional Features](https://mlsanity.com/paper/1805.03699/) (2018)
- [A persistent homology-based topological loss function for multi-class CNN segmentation of cardiac MRI](https://mlsanity.com/paper/2008.09585/) (2020)
- [PLLay: Efficient Topological Layer based on Persistence Landscapes](https://mlsanity.com/paper/2002.02778/) (2020)

## Built on by (most cited first, 4 of 4)

- [TopoFR: A Closer Look at Topology Alignment on Face Recognition](https://mlsanity.com/paper/2410.10587/) (2024)
- [Topology-Aware Loss for Aorta and Great Vessel Segmentation in Computed Tomography Images](https://mlsanity.com/paper/2307.03137/) (2023)
- [Convolutional Persistence Transforms](https://mlsanity.com/paper/2208.02107/) (2022)
- [PI-Att: Topology Attention for Segmentation Networks through Adaptive Persistence Image Representation](https://mlsanity.com/paper/2408.08038/) (2024)

## Abstract (arXiv)

Persistent topological properties of an image serve as an additional descriptor providing an insight that might not be discovered by traditional neural networks. The existing research in this area focuses primarily on efficiently integrating topological properties of the data in the learning process in order to enhance the performance. However, there is no existing study to demonstrate all possible scenarios where introducing topological properties can boost or harm the performance. This paper performs a detailed analysis of the effectiveness of topological properties for image classification in various training scenarios, defined by: the number of training samples, the complexity of the training data and the complexity of the backbone network. We identify the scenarios that benefit the most from topological features, e.g., training simple networks on small datasets. Additionally, we discuss the problem of topological consistency of the datasets which is one of the major bottlenecks for using topological features for classification. We further demonstrate how the topological inconsistency can harm the performance for certain scenarios.