Identity-plus-row matrix decomposition and its application in design of parallel projection algorithms

Many image processing operations can be abstracted into matrix operations. With the help of matrix analysis, we can understand the inherent properties of the operations and thus design better algorithms. In this paper, we pro pose a matrix decomposition method referred to as identity-plus-row decompo sition, The decomposition is particularly useful in design of parallel proj ection algorithms on mesh-connected computers. Projection is a frequently u sed process in image processing and visualization. In volume graphics, proj ection is used to render the essential content of a three-dimensional volum e onto a two-dimensional image plane. For Radon transform, projection is us ed to transform the image space into a parameter space. By applying the ide ntity-plus-row matrix decomposition method, we solve the data redistributio n problem due to the irregular data access patterns present in those applic ations on single instruction stream, multiple data stream (SIMD) mesh-conne cted computers, developing fast algorithms for volume rendering and Radon t ransform on SIMD mesh-connected computers. (C) 2001 SPIE and IS&T.