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

By Juliusz Kulikowski

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

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18) and that the cartesian product of relations is identical with I II the disjunction of relations if= excepting the situation R if one of the components ~esian product is no~ 1 or R" is an empty relation; the ca! defined in this last case. 19) of relations full it is possible to postulate that Rx9 = 9xR = R. On the other hand, the convolution of relations I II is empty if the factors R , R do not 11 overlap 11 ; it does mean that some of the relations are empty, even/ or no pairs of their realizations have common elements on the non-empty conjunction of their set families.

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) = , A Coincidence Measure 39 where a, b are some positive coefficients. The invariance of a detection procedure with respect to the optical transformations can be illustrated in the following example. The two pictures describing the same pattern (a letter "L") should be classified as belonging to the same class, in spite of the fact that they are.

0 0 0 1 0 0 0 1 0 0 0 0 0 0 f 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 . 0. 0. 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 . . . . showing off the distortions together with the informative local features. The situation can be improved if an integrative algorithm is used instead of this one based on local picture analysis. Let us proceed the former example. 22) = Taking m = 2,4,6,8, ... , n • = 2,4,6,8, ... [z•(4,2)] 1al[z'(4,4)] The noisy version of the picture given in the ex ample gives us then the matrix: 0 5 2 6 4 6 5 1 3 2 2 t 3 1 1 t Let us shortly denote the components of the last matrix by 1At~j'~·1,2,3, ...

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