Image Algebra - Induced Operators And Induced Subalgebras

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Abstract
The primary goal of an image algebra is the development of a mathematical environment in which to express the various algorithms employed in image processing. From a practical standpoint, this means that the algorithms should appear as strings in an operational calculus, where each operator can ultimately be expressed as a string composed of some collection of elemental, or "basis," operators and where the action of the string upon a collection of input images is determined by function composition. For instance, rather than defining operations such as convolution and dilation in a pointwise manner, we desire closed-form expressions of these operators in terms of low-level operations that are close to the algebraic structure of the underlying mathematical entities upon which images are modeled. It is precisely such an approach that will yield a natural symbolic language for the expression of image processing algorithms.

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