2024/10/28 by Christophe Lohou, Lohou, Christophe
Computer Science · #Computational Geometry (cs.CG) #Computer Vision and Pattern Recognition (cs.CV) #Digital Image Processing Techniques #FOS: Computer and information sciences #Medical Image Segmentation Techniques #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2410.21588
openalex publication_date 2024/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we adapt the two topological numbers, which have been proposed to efficiently characterize simple points in specific neighborhoods for 3D binary images, to the case of 2D binary images. Unlike the 3D case, we only use a single neighborhood to define these two topological numbers for the 2D case. Then, we characterize simple points either by using the two topological numbers or by a single topological number linked to another one condition. We compare the characterization of simple points by topological numbers with two other ones based on Hilditch crossing number and Yokoi number. We also highlight the number of possible configurations corresponding to a simple point, which also represents the maximum limit of local configurations that a thinning algorithm operating by parallel deletion of simple (individual) points may delete while preserving topology (limit usually not reachable, depending on the deletion strategy).