Abstract
Publisher Summary This chapter presents the background and history of the mathematical structures pertinent to lattice transforms—namely, mathematical morphology, the minimax algebra, and the image algebra. It introduces the theoretical foundation for lattice transformations in image processing and presents detailed discussions on the three algebras and the relationship among them. The four major applications of the theory to specific problems are also discussed in the chapter. First is the mapping of minimax algebra properties to image algebra to describe the way a series of minimax algebra results can be readily formulated in an image processing environment, thus, providing new tools for solving a certain class of image processing problems. Second is a general skeletonizing technique, which can be viewed as a division algorithm. Third is an application to image complexity measures. . The dual transportation problem in context of lattice transforms is stated in the chapter.
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