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Proceedings Paper

B-code dilation and structuring element decomposition for restricted convex shapes
Author(s): Tapas Kanungo; Robert M. Haralick; Xinhua Zhuang
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Paper Abstract

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.

Paper Details

Date Published: 1 November 1990
PDF: 12 pages
Proc. SPIE 1350, Image Algebra and Morphological Image Processing, (1 November 1990); doi: 10.1117/12.23609
Show Author Affiliations
Tapas Kanungo, Univ. of Washington (United States)
Robert M. Haralick, Univ. of Washington (United States)
Xinhua Zhuang, Univ. of Missouri/Columbia (United States)

Published in SPIE Proceedings Vol. 1350:
Image Algebra and Morphological Image Processing
Paul D. Gader, Editor(s)

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