Local decomposition of invariant lattice transforms

Jennifer L. Davidson

doi:10.1117/12.23611

1 November 1990 Local decomposition of invariant lattice transforms

Jennifer L. Davidson

Author Affiliations +

Proceedings Volume 1350, Image Algebra and Morphological Image Processing; (1990) https://doi.org/10.1117/12.23611
Event: 34th Annual International Technical Symposium on Optical and Optoelectronic Applied Science and Engineering, 1990, San Diego, CA, United States

Abstract

Lattice transformations are a class of nonlinear image processing transforms that include mathematical morphology transforms as a subclass. By using a matrix representation lattice transforms may apply results established in minimax algebra a matrix algebra originally developed for operations research. This paper presents a strong decomposition technique for a translation invariant template that is a lattice transform using a minimax matrix approach. The factors of the decomposition correspond to variant templates. This method is particularly suited for implementation on multiple-instruction multiple-data (MIMD) architectures. Since the minimax algebra is a subalgebra of the Air Force image algebra which in turn encompasses mathematical morphology this technique provides another tool for template decomposition which in particular can be applied to morphology transforms.

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Jennifer L. Davidson "Local decomposition of invariant lattice transforms", Proc. SPIE 1350, Image Algebra and Morphological Image Processing, (1 November 1990); https://doi.org/10.1117/12.23611

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