EMIS ELibM Electronic Journals Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques naturelles / sciences mathematiques
Vol. CXXXIX, No. 34, pp. 17–42 (2009)

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Semi-topological classification of line patterns in the plane

M. M. Marjanovic

Serbian Academy of Sciences and Arts, Knez Mihailova 35, 11000 Beograd, Serbia

Abstract: A large class of patterns, consisted of lines being situated in the plane, is classified into equivalence classes, each of which is a conveyor of meaning of a shape. Invariants of this classification are developed and, in particular, for a more regular subclass of these patterns, invariant matrices are defined being unique arithmetic codes of these shapes. Then, an algorithm is established as the way of transformation of so called associated matrices, formed as a result of local inspection of patterns, into invariant ones which express the global properties of these patterns. Using the language of psychology, we could say that this investigation is the study of percepts and the establishment of their meaning.

Keywords: Semi-topological classification of patterns, Associated and invariant matrices, Transformation of associated matrices into invariant ones

Classification (MSC2000): 68T10

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Electronic fulltext finalized on: 15 Sep 2009. This page was last modified: 20 Jun 2011.

© 2009 Mathematical Institute of the Serbian Academy of Science and Arts
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