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Proceedings Paper

Decomposition of separable and symmetric convex templates
Author(s): Dong Li; Gerhard X. Ritter
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Paper Abstract

Convolutions are a fundamental tool in image processing. Classical examples of 2-dimensional linear convolutions include image correlation the mean filter the discrete Fourier transform and a multitude of edge mask filers. Nonlinear convolutions are used in such operations as the median filter the medial axis transform and erosions and dilations as defined in mathematical morphology. For large convolution mask the computation cost resulting from implementation can be prohibitive. However in many instances this cost can be significantly reduced by decomposing the masks or templates into a sequence of smaller templates. In addition such decompositions can often be made architecture specific and thus resulting in optimal transform performance. In this paper the issues of template decomposition are discussed in the context of the image algebra. Necessary and sufficient conditions as well as some efficient methods for decomposing rectangular symmetric convex and spherical templates are presented.

Paper Details

Date Published: 1 November 1990
PDF: 11 pages
Proc. SPIE 1350, Image Algebra and Morphological Image Processing, (1 November 1990); doi: 10.1117/12.23608
Show Author Affiliations
Dong Li, Univ. of Florida (United States)
Gerhard X. Ritter, Univ. of Florida (United States)

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

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