A model building approach to property measurement in black and white pictures

Abstract

A method is described for extracting geometric and topological information from a picture that is represented as a matrix of black and white points. Essentially, a modified maxtrix of points is partitioned into subsets, each of which resembles a contour on a topological contour map. From this, a tree is created in which each node represents a contour and a downward sloping are indicates that one contour directly contains a second contour. A variety of picture properties can be obtained by examining the tree produced from a picture. In particular, it is possible to predict how the topological structure of the picture would change if the picture were subjected to thickening or thinning operations. Because the effect of operations on the picture can be predicted from the tree, the tree is called a model of the picture. This paper is primarily concerned with explaining the model building process and showing how picture properties can be extracted from the model. A variety of assertions about the model as well as the model building process are stated without proof. A more formal treatment of these assertions will appear in a subsequent paper.