Recursive operations in image algebra

Abstract

The image algebra, developed by Ritter et al. at the University of Florida, is an algebraic structure for image processing. The three commonly used high-level image-template operations provided by the image algebra are the generalized convolution ⊕, the additive maximum or generalized lattice convolution {ie23-1}, and the multiplicative maximum {ie23-2}. These are used to realize various nonrecursive image transformations, including morphological transformations. Along with nonrecursive transformations, a class of recursive transformations, such as IIR filters, adaptive dithering, and predictive coding, are also widely used in signal and image processing. In this paper the notions of recursive templates and recursive template operations are introduced; these allow the image algebra to express a set of linear and nonlinear recursive transformations. Algebraic properties of these recursive operations are given, providing a mathematical basis for recursive template composition and decomposition. Finally, applications of recursive template operations in specifying some image processing algorithms are presented.