Decomposition methods for convolution operators II

Zohra Z. Manseur; David C. Wilson

doi:10.1117/12.23613

1 November 1990 Decomposition methods for convolution operators II

Zohra Z. Manseur, David C. Wilson

Proceedings Volume 1350, Image Algebra and Morphological Image Processing; (1990) https://doi.org/10.1117/12.23613
Event: 34th Annual International Technical Symposium on Optical and Optoelectronic Applied Science and Engineering, 1990, San Diego, CA, United States

Abstract

This paper begins by reviewing methods recently developed by the authors for the decomposition of twodimensional shift-invariant convolution operators of size (2m + 1) x (2n + 1) into sums and products of 3x3 operators. Results include the fact that every 5x5 operator can be decomposed into the sum and product of at most five 3 x 3 operators and a theorem giving a characterization for those 5 x 5 operators which can be decomposed into the sum and product of at most three 3x3 operators. The focus of the new theorems presented here will center on the problem of extending results valid for shift-invariant operators to non shift-invariant operators. The image algebra developed by G. X. Ritter will provide the setting for this investigation.

Citation Download Citation

Zohra Z. Manseur and David C. Wilson "Decomposition methods for convolution operators II", Proc. SPIE 1350, Image Algebra and Morphological Image Processing, (1 November 1990); https://doi.org/10.1117/12.23613

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