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Algebra of Relations
Structural Approach to the Recognition
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algebra of relations algorithms binary sets Boolean Boolean algebra Boolean functions called cartesian product composite patterns concept conditional relation conjunction consists corresponding correspondingly detection distance measure empty relation equivalent euclidean euclidean distance euclidean space example will illustrate expressions family of sets following example formal language formally described fuzzy picture Geometrical Languages given graphical higher-level decisions homomorphic horizontal line image processing INTEGER Let us consider Let us denote Let us take line going line-segment logical logical conjunction ments messages meta-relations model of pattern morphisms mutually isomorphic non-empty obtained one-to-one projection optical transformation Otherwise speaking pattern recognition problem PICTURE ALGOL 1204 picture Zl planar languages points belonging random variables realizations satisfying recognition of patterns rela relations described on<U relations Ru retina segment sense sequences set families set of basic set of relations standard procedures statistical dependence structure subfamily of sets subrelation subset symbols take into account tical triangle