Chapter 2 - Grids and Digitization

Abstract

This chapter discusses the 2D and 3D grid point and grid cell adjacency models and the grid (cell) incidence model, which combines cells of different dimensionalities. It reviews the connectedness and the algorithms for “labeling” the connected components. The digitization models, including the classic Gauss, Jordan, and grid intersection models, and definition of a “domain” model that generalizes all of them, are also reviewed. The measurements made on digital pictures can approximate the measurements that are made ideally on real objects or real pictures. The digital geometry deals with the computation of geometric measurements or properties from the digital pictures and with the study of how well these measurements approximate the corresponding ideal measurements on the real objects or pictures. The grid constant θ is the distance between the neighboring grid lines. Grid resolution is the inverse of the grid constant. It refers to the number of grid elements per unit of distance without specifying the physical size of the unit. The parameters h and θ are useful for discussing the possible effects of improvements in the geometric or picture resolution. They are relevant in the theoretic studies of convergence behavior of the algorithms under refinement of grid resolution i.e. decrease of the grid constant.