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1 November 1990 Generalized matrix product and its relation to parallel architecture communication
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The Air Force Image Algebra formalizes the notion of a generalized matrix product (GMP). The GMP is the basis for image-template operations in the Image Algebra. In a mathematical sense the GMP supports the combining of matrices using paradigms other than the dot product approach of linear algebra. This permits one to view linear and non-linear image transformations and mathematical morphology operations as different embodiments of the same concept. The GMP has been implemented on a variety of computers from sequential to massively parallel. Our experience with use of the GMP on parallel machines has shown that the GMP unifies the three concepts of many-to-one one-to-many and one-to-one data transfers (reduction replication and permutation respectively). This paper demonstrates the utility of the generalized mathx product as a tool in algorithm description. It discusses the relationship of the GMP to the three data transfer paradigms of massively parallel machines and shows how GMP mappings and their transposes can be efficiently implemented on massively parallel processors. It also presents code restructuring techniques necessary to implement GMP operations efficiently on sequential computers linking the general problem of serializing parallel programs to implementation of the GMP operation.
© (1990) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Joseph N. Wilson "Generalized matrix product and its relation to parallel architecture communication", Proc. SPIE 1350, Image Algebra and Morphological Image Processing, (1 November 1990);

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