Image recognition via Vietoris-Rips complex
This addresses feature extraction in computer vision, but it appears incremental as it applies an existing topological method to images.
The paper tackles the problem of extracting informative features from images by proposing a method based on algebraic topology, specifically using Vietoris-Rips complexes, and empirically shows that the extracted features capture image characteristics well.
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.