This chapter treats pictures as graph-theoretic objects and introduces graph-theoretic concepts that will be used throughout the book. It defines 2D and 3D adjacency graphs based on the grid point and grid cell models and on the assumption that pixels and voxels are the smallest units (“atoms ”) of a 2D or 3D grid. By specifying local circular orders, these graphs become oriented adjacency graphs; such graphs are related to 2D combinatorial maps, which provide descriptions of spatial subdivisions.
4.1 Graphs, Adjacency Structures, and Adjacency Graphs
The study of geometric properties of regions in 2D or 3D pictures requires specification of conditions under which pixels or voxels are considered to be adjacent ...