New PDF release: Algebraic Methods in Pattern Recognition: Course held at the

By Juliusz Kulikowski

ISBN-10: 3211811281

ISBN-13: 9783211811283

ISBN-10: 3709128846

ISBN-13: 9783709128848

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Additional resources for Algebraic Methods in Pattern Recognition: Course held at the Department of Automation and Information July 1971

Example text

Lled a 11 ro- tation 11 • It is also possible to define other kinds of isomorphisms like scale-changing etc. 14) is not an isomorphism of relations in the above-mentioned sense. Let us consider a more detailed general situation. 55 A Homomorphism of the Relations There are given two families of sets , with the relations Ru and Rv , correspondi ngly. Let us suppose that l is an one-to-one projection of into. 4) are unique but not reciprocal. Any realizations of the relation Ru is then supposed to be projected into one and only one realization of Rv and any realization of the relation Rv is supposed to be a projection of at least one realization of Ru .

The problem is usually solved by intuition; some authors tried to solve the problem using more advanced methods [6, 13] . An optimizing procedure is evidently possible if a crite~ rion of optimization is defined. However, choosing the criterion is a serious problem itself, The pattern recognition problem can 35 Reduction of Image Deformation be considered as a problem of reduction of the information redundance. For example, if the retina consists of N elements char acterized by two possible states ( 11 black-white 11 ) and the set of final.

W. ,). 6) \l=i An euclidean distance measure is rather preferable in the case of multi-stage components vectors: ~(z* ,z) 2 1/2. 7) in the case of the binary-components vectors the Hamming 1 s arid the euclidean distances are equivalent. A. Aizerman, E. M. I. Rosoneer [1, 3]. 8) v =i are some real coefficients. Then, the distance measure is defined as 38 Chap. 9) eCz*,z) = [K(z*,z*)+K(z,z)-2K (z*,z)] t/2. 12) g(z*,z) = (z*,z) 11t(z*) + v(z) - (z*,z) and a distance measure (proposed by J. Rogers and T.

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Algebraic Methods in Pattern Recognition: Course held at the Department of Automation and Information July 1971 by Juliusz Kulikowski


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