A mathematical structure used to express image processing transforms, the AFATL image algebra has proven itself useful in a wide variety of applications. The theoretical foundation for the image algebra includes many important constructs for handling a wide variety of image processing problems: questions relating to linear and nonlinear transforms, including decomposition techniques; mapping of transformations to computer architectures; neural networks; recursive transforms; and data manipulation on hexagonal arrays. However, statistical notions have been included only on a very elementary level and on a more sophisticated level in the literature. This paper presents an extension of the current image algebra that includes a Bayesian statistical approach. It is shown how images are modeled as random vectors, probability functions or mass functions are modeled as images, and conditional probability functions are modeled as templates. The remainder of the paper gives a brief discussion of the current image algebra, an example of the use of image algebra to express high-level image processing transforms, and the presentation of the statistical development of the image algebra.

Date Published: 1 October 1991
PDF: 10 pages
Proc. SPIE 1569, Stochastic and Neural Methods in Signal Processing, Image Processing, and Computer Vision, (1 October 1991); doi: 10.1117/12.48387

Published in SPIE Proceedings Vol. 1569:
Stochastic and Neural Methods in Signal Processing, Image Processing, and Computer Vision
Su-Shing Chen, Editor(s)