Algebraic Methods in Pattern Recognition: Course held at the - download pdf or read online

By Juliusz Kulikowski

ISBN-10: 3211811281

ISBN-13: 9783211811283

ISBN-10: 3709128846

ISBN-13: 9783709128848

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

Sample text

4 structure. This general concept can be improved by additional indexing of the nodes: the nodes corresponding to the relations mutually isomorphic may have assigned the same index of the class of isomorphic relations. In the above-given example the same additional index should be attached to the nodes corresponding to the relations Rt andRe • 5. Formal languages for image processing. In the last years a growing attention was paid to the concept of pattern recognition systems based on the principle of man-computer interaction.

II The relation I R and are then mutually isomorphic. This kind of an isomorphism may be called a "shiftening". -ays) will be called an automorphism. The relation ~,. , '-' ,~ ' are automorphic to each other: the first relation describes a horizontal line-segment, while the seccnd one describes a verti~ cal line-segment. 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.

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.

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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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