2021/09/06 by Yasuhiko Asao, Asao, Yasuhiko, Jumpei Nagase +5
Computer Science · Mathematics · #Advanced Image and Video Retrieval Techniques #Algebraic number #Artificial intelligence #Combinatorics #Computer Vision and Pattern Recognition (cs.CV) #Computer science #Construct (python library) #FOS: Computer and information sciences #Feature vector #Graph #Image (mathematics) #Image Retrieval and Classification Techniques #Mathematics #Metric (unit) #Pattern recognition (psychology) #Robustness (evolution) #Topological and Geometric Data Analysis #Topology (electrical circuits) #cs.CV
paper · pdf · doi:10.48550/arxiv.2109.02231
published in arXiv (Cornell University) (Cornell University) · 10 pages
arxiv created 2021/09/06 · openalex publication_date 2021/09/06 · arxiv updated 2021/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ε 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 ε of the Vietoris-Rips complex produces robustness to noise. We empirically show that the extracted feature captures well images' characteristics.