Image recognition via Vietoris-Rips complex

TL;DR

This paper introduces a novel image feature extraction method using algebraic topology, specifically Vietoris-Rips complexes, which captures image complexity and is robust to noise.

Contribution

The paper presents a new approach to image feature extraction by constructing Vietoris-Rips complexes from weighted graphs derived from images, enhancing robustness and informational capture.

Findings

Features effectively capture image characteristics.

Method demonstrates robustness to noise.

Detects high-information sub-images.

Abstract

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.