Combinatorial Image Analysis by Reneta P. Barneva Bhargab B. Bhattacharya & Valentin E. Brimkov

Author:Reneta P. Barneva, Bhargab B. Bhattacharya & Valentin E. Brimkov
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

2 Definitions and Preliminaries

This section contains some definitions required to understand the paper. In Sects. 2.1 and 2.2, the construction of outer and inner isothetic covers are discussed in brief which are given in details in [2, 3].

Definition 1

(k-connectedness). Two points p and q are said to be k-connected (k = 4 or 8) in a set S if and only if there exists a sequence such that for . The 4-neighborhood of a point (x, y) is given by and its 8-neighborhood by .

Definition 2

(Digital grid). A digital grid is given by , where and represent the respective sets of (equi-spaced) horizontal grid lines and vertical grid lines. A grid size, g is defined as the distance between two consecutive horizontal/vertical grid line. A grid point is the point of intersection of a horizontal and a vertical grid line. A unit grid block (UGB) is the smallest square having its four vertices as four grid points and edges as grid edges.

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