Abstract
This chapter discusses graph-theoretic generalization of the grid cell incidence model. It further treats pictures as graph-theoretic objects. The chapter represents the spatial subdivisions with incidence pseudographs. The open and closed subsets of the incidence pseudographs along with their frontiers are also reviewed. The combinatorial formulas for such subsets in regular incidence grids are given and a graph-theoretic treatment of the frontier tracing can be seen. In a labeled incidence pseudograph G = [S, I, dim], each node in G has a label, and the labels belong to a finite set {L0,…, Lmax}. A picture assigns labels (values of pixels or voxels) to all of the principal nodes of S. An ordered labeling of the nodes of an incidence pseudograph is defined by assigning labels to the principal nodes and extending this labeling to the other nodes by applying the maximum-label rule. This rule states that every marginal node should be given the largest label of any of its incident principal nodes.
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