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1 November 1990 Decomposition of separable and symmetric convex templates
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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.
© (1990) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Dong Li and Gerhard X. Ritter "Decomposition of separable and symmetric convex templates", Proc. SPIE 1350, Image Algebra and Morphological Image Processing, (1 November 1990); https://doi.org/10.1117/12.23608
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