Recursion and feedback in image algebra

Gerhard X. Ritter; Jennifer L. Davidson

doi:10.1117/12.47965

1 April 1991 Recursion and feedback in image algebra

Proceedings Volume 1406, Image Understanding in the '90s: Building Systems that Work; (1991) https://doi.org/10.1117/12.47965
Event: Applied Imaging Pattern Recognition, 1990, McLean, VA, United States

Abstract

Recursion and feedback are two important processes in image processing. Image algebra, a unified algebraic structure developed for use in image processing and image analysis, provides a common mathematical environment for expressing image processing transforms. It is only recently that image algebra has been extended to include recursive operations [1]. Recently image algebra was shown to incorporate neural nets [2], including a new type of neural net, the morphological neural net [3]. This paper presents the relationship of the recursive image algebra to the field of fractions of the ring of matrices, and gives the two dimensional moving average filter as an example. Also, the popular multilayer perceptron with back propagation and a morphology neural network with learning rule are presented in image algebra notation. These examples show that image algebra can express these important feedback concepts in a succinct way.

Citation Download Citation

Gerhard X. Ritter and Jennifer L. Davidson "Recursion and feedback in image algebra", Proc. SPIE 1406, Image Understanding in the '90s: Building Systems that Work, (1 April 1991); https://doi.org/10.1117/12.47965

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