4、Shape Complexes and Skeletons in Computational Geometry and Topology

Shape Complexes and Skeletons in Computational Geometry and Topology

1. Introduction to Shape Complexes

In the realm of computational geometry and topology, shape complexes play a pivotal role in understanding and analyzing the structure of shapes within digital images. A shape complex is a mathematical construct used to approximate and tile shapes. It consists of vertices, edges, and filled triangles that collectively cover an image and facilitate the detection, comparison, analysis, and classification of shapes.

Key Components of Shape Complexes

• Vertices : Points in the shape complex that serve as seed points for constructing edges and triangles.
• Edges : Lines connecting pairs of ve