Download e-book for kindle: Algebraic Methods in Pattern Recognition: Course held at the by Juliusz Kulikowski

By Juliusz Kulikowski

ISBN-10: 3211811281

ISBN-13: 9783211811283

ISBN-10: 3709128846

ISBN-13: 9783709128848

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

Sample text

0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 1 0 0 0 . . 0 0 0 0 0 1 1 1 1 1 0 0 0 0 1 0 0 0 0 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 1 0 0 0 . and both pictures are ready for the application of the algorithms proving the distinct local relations. The situation gets more complicated if the picture is distorted by noise, as illustrated by the following examples: 44 Chap. 3 - Structural Approach to the Recognition of Patterns fuzzy picture original picture 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 0 1 0 0 1 0 0 1 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 0 1 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 1 0 0 0 1 t 0 0 0 0 0 0 0 t 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 i 0 1 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 t 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 • 0 0 Applying the former algorithm based on the "rust" te-chnique we obtain the result .

0 0 0 0 0 1 1 1 1 1 0 0 0 0 1 0 0 0 0 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 1 0 0 0 . and both pictures are ready for the application of the algorithms proving the distinct local relations. The situation gets more complicated if the picture is distorted by noise, as illustrated by the following examples: 44 Chap. 3 - Structural Approach to the Recognition of Patterns fuzzy picture original picture 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 0 1 1 0 1 1 0 1 1 0 1 0 0 1 0 0 1 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 0 1 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 0 1 0 0 0 1 t 0 0 0 0 0 0 0 t 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 i 0 1 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 t 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 • 0 0 Applying the former algorithm based on the "rust" te-chnique we obtain the result .

Are some expressions, then •q~ expression equivalent to q1 •qz*···•q~*··· and ~q~ pression equivalent to qi xqzX •.. xqi. x •... 2) form a pragmatic field. 27). The pro~ lem of proving the formal identity of expressions plays an important role in the structural pattern recognition technique. It is clear that a given pattern can be formally described in sev- eral ways and it is necessary to prove the fact that a given e~ pression obtained from a recognitive experiment describes the same pattern as defined by a theoretically deducted expression.

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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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