A representation of digitized patterns and an edge tracking thinning method

摘要

A representation of digitized patterns by using a cubic spline function is described in this paper. Each black pixel (k, l) is represented by the Cartesian product of the cubic B-splines Bk(x) and Bl(y) and the sum S(x, y) of these Bk(x)×Bl(y) for all nonzero pixels is used for the representation. We prove that if one starts from a pixel located at the right edge of the surface z=s(x, y) and follows the direction of ∇×r where r=(x, y, S(x, y)), then the path stays on the right edge of the surface. This fact is used to derive a very efficient thinning algorithm. A few examples are included to verify our algorithm.