Abstract
In the Universal Imaging Algebra, the values between 0 and 1, inclusive, denote gray values. This helps in utilizing the structure of fuzzy set theory in the Universal Imaging Algebra. As in any algebra, the Universal Imaging Algebra consists of three items: (1) sets of various sorts, (2) operators mapping elements in some of these sets into an element in another set of some sort, and (3) equational constraints between the operators, such as the commutative or associative laws. Two sets employed in the imaging algebra—the set of images and the set of binary images—are described. The mathematical morphology is applied to binary images. This theory is generalized to images using fuzzy set theory. One of the important concepts in the mathematical morphology, as well as in the signal processing and image processing is the 180°-rotated image. The arithmetic and topological operators in the Universal Imaging Algebra are also presented along with useful properties.
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