2025/04/17 by Daniel Gonzalez-Alvarado, Gonzalez-Alvarado, Daniel, Fabio Schlindwein +9
Computer Science · #Computational Geometry and Mesh Generation #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #Medical Image Segmentation Techniques #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2504.13024
openalex publication_date 2025/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
This paper introduces patch assignment flows for metric data labeling on graphs. Labelings are determined by regularizing initial local labelings through the dynamic interaction of both labels and label assignments across the graph, entirely encoded by a dictionary of competing labeled patches and mediated by patch assignment variables. Maximal consistency of patch assignments is achieved by geometric numerical integration of a Riemannian ascent flow, as critical point of a Lagrangian action functional. Experiments illustrate properties of the approach, including uncertainty quantification of label assignments.