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

By Juliusz Kulikowski

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

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000 . 000 . . . . relations be- ing satisfied. However, usually a picture is not given in such a distinct form, as supposed in the example. The lines are rather 42 Chap. 3 - Structural Approach to the Recognition of Patterns diffused like in the following examples: 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 1 1 0 0 1 1 1 0 0 1 1 1 0 0 0 1 1 0 0 0 1 1 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 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 and a "skeleton" of the picture must be shown off before the lineend is detected.

24 bits). The number H of rows is not limited but by the capacity of the operative-memory. Being realized as a sublanguage imbedded in the ALGOL the PICTURE ALGOL 1204 A has the opportunity of possible realization of its stan~ ard procedures on the INTEGER-type variables instead of the REAL ones. The INTEGER variables M, N as well as some auxiliary var! ables (BOUND and THR) are declared while a PICTURE ALGOL procedure is introduced. 62 Chap. 5 - Formal Languages for Image Processing There are several kinds of standard procedures in the PICTURE ALGOL.

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 (the order being taken in the family sense). (4. 5) (the order being taken in the -family sense).

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