# Image recognition via Vietoris-Rips complex

arXiv: https://arxiv.org/abs/2109.02231 · HTML: https://mlsanity.com/paper/2109.02231/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 37 references that are in the map.
- First posted on arXiv 6 Sep 2021.

## Builds on (most cited first, 15 of 15)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [A Survey on Deep Learning in Medical Image Analysis](https://mlsanity.com/paper/1702.05747/) (2017)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Dynamic Routing Between Capsules](https://mlsanity.com/paper/1710.09829/) (2017)
- [Image Segmentation Using Deep Learning: A Survey](https://mlsanity.com/paper/2001.05566/) (2020)
- [Object Detection in 20 Years: A Survey](https://mlsanity.com/paper/1905.05055/) (2019)
- [A Survey on Neural Network Interpretability](https://mlsanity.com/paper/2012.14261/) (2020)
- [Opportunities and Challenges in Explainable Artificial Intelligence (XAI): A Survey](https://mlsanity.com/paper/2006.11371/) (2020)
- [A Survey of the Recent Architectures of Deep Convolutional Neural Networks](https://mlsanity.com/paper/1901.06032/) (2019)
- [Stacked Capsule Autoencoders](https://mlsanity.com/paper/1906.06818/) (2019)
- [Fashion Meets Computer Vision: A Survey](https://mlsanity.com/paper/2003.13988/) (2020)
- [A Topological "Reading" Lesson: Classification of MNIST using TDA](https://mlsanity.com/paper/1910.08345/) (2019)
- [Persistent homology machine learning for fingerprint classification](https://mlsanity.com/paper/1711.09158/) (2017)
- [Effective persistent homology of digital images](https://mlsanity.com/paper/1412.6154/) (2014)

## Abstract (arXiv)

Extracting informative features from images has been of capital importance in computer vision. In this paper, we propose a way to extract such features from images by a method based on algebraic topology. To that end, we construct a weighted graph from an image, which extracts local information of an image. By considering this weighted graph as a pseudo-metric space, we construct a Vietoris-Rips complex with a parameter varepsilon by a well-known process of algebraic topology. We can extract information of complexity of the image and can detect a sub-image with a relatively high concentration of information from this Vietoris-Rips complex. The parameter varepsilon of the Vietoris-Rips complex produces robustness to noise. We empirically show that the extracted feature captures well images' characteristics.