B-code dilation and structuring element decomposition for restricted convex shapes
Tapas Kanungo, Robert M. Haralick, Xinhua Zhuang · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1990
A convex, filled polygonal shape in R x R can be uniquely represented in the discrete Zx Z domain by the set of all the lattice points lying in its interior and on its edges. We define a reslricled convex shape as the discrete four connected set of points representing any convex, filled polygon whose vertices lie on the lattice points and whose interior angles are multiples of 450 In this paper we introduce the Boundary Code (B-Code), and we express the morphological dilation operation on the restricted convex shapes with structuring elements that are also restricted convex shapes. The algorithm for this operation is of O( 1) complexity and hence is independent of the size of the object. Further, we show that the algorithmic for the n-fold dilation is of 0(1) complexity. We prove that there is an unique set of thirteen shapes {K1 ,K2, . . . , "13) such that any given restricted convex shape, K, is expressible as K = K' K . . . K3 where K, represents the ni-fold dilation of K. We also derive a finite step algorithm to find this decomposition.