<title>Recursive operations in image algebra</title>

Abstract

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 and the multiplicative maximum These are used to realize various nonrecursive image transformations e. g. DFT edge detection and morphological operations. Along with nonrecursive transformations a class of recursive transformations are also widely used in signal and image processing e. g. hR filters sequential block labeling predictive coding etc. . In this paper a couple of new recursive operations are introduced which allow the image algebra to express a set of linear and nonlinear recursive transformations. Algebraic properties of these recursive operations are given which provide a mathematical basis for recursive template composition and decomposition. Also some applications of recursive operations in image processing are presented.