Algebraic Methods in Pattern Recognition: Course held at the by Juliusz Kulikowski

By Juliusz Kulikowski

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

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Rn,? 1are performed. A question then arises of what is the "highest order" relation between the relations P and T. For example, they are overlap- ping in the former sense. Investigations of this kind of relations between the random variables may be interesting from the point of view of an analysis of an informational system structure. However, this is not a problem of pattern recognition. 3. Structural approach to the recognition patterns. An automatic classification of composite patterns consists of several levels of picture processing.

Let us denote by 'I' a one-to-one pr£ jection of into . Let projections of the form {cpJx:)} be a family of one-to-one 52 Chap. 4) 'f'(U) . Otherwise speaking, '~(x) ing u~ into v~ is a function projec! if u~ and v~ correspond to each other in the "'' - projection sense. It is evident, that the set families and as well as the corresponding sets U~ , V ~ are pairwise of the same powers. Let us suppose that the set families and are linearly ordered. We will say that the one-to-one projection 'f preserves the orders if for any Ur

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. 13) e(z*,z) = -logzg(z*,z) . The main distress of the detection procedures ba~ ed on the distance measures consists in the fact that the deci sions are not invariant with respect to the so called optical transformations of the pictures. 14) T(z) =

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