2016/04/25 by Martin Brooks, Brooks, Martin · 3 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Advanced Fluorescence Microscopy Techniques #Artificial intelligence #Cartography #Cell Image Analysis Techniques #Computational Geometry (cs.CG) #Computer Vision and Pattern Recognition (cs.CV) #Computer graphics (images) #Computer science #Computer vision #FOS: Computer and information sciences #FOS: Mathematics #Fractal #Fractal analysis #Fractal dimension #General Topology (math.GN) #Geography #Geology #Image (mathematics) #Image processing #Mathematical analysis #Mathematics #Parallel computing #Persistence (discontinuity) #Scale (ratio) #Scale space #Segmentation #Space (punctuation) #Topological and Geometric Data Analysis #Vectorization (mathematics) #cs.CG #cs.CV #math.GN
paper · pdf · doi:10.48550/arxiv.1604.07361
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2016/04/25 · arxiv created 2016/06/21 · arxiv updated 2016/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A persistence lens is a hierarchy of disjoint upper and lower level sets of a continuous luminance image's Reeb graph. The boundary components of a persistence lens's interior components are Jordan curves that serve as a hierarchical segmentation of the image, and may be rendered as vector graphics. A persistence lens determines a varilet basis for the luminance image, in which image simplification is a realized by subspace projection. Image scale space, and image fractal analysis, result from applying a scale measure to each basis function.