Abstract
A set theoratic model for representing patterns and pattern classes is presented. Accordingly, a pattern P is defined as a finite non-empty set of features where feature element F is a 3-tupple, <Xi,Xj,qk>. The first two components Xi and Xj of the feature tupple F are either primitive patterns or sub-patterns appearing in a given pattern, and the third component qk is a binary predicate satisfied by Xi and Xj. It is then possible to depict P as a semantic net where nodes represent the components Xi and Xj of FεP, and the directed edge from Xi to Xj represent the predicate qk.
Depending on the values of Xi and Xj, it is possible to define a given complex pattern P in more than one way such that if Xi and Xj are primitives, then the representation P° is called the zero-order definition. The n-order definition of P is obtained by utilizing the sub-patterns \( {X_{{{i_n}}}},{X_{{{j_n}}}} \subset {P^{{n - 1}}} \).
Different order representation of patterns lead into the notions of object-equivalence and closure of patterns. Further, with the aid of a probability function, a modeling scheme for pattern classes become possible.
The concepts of null-pattern and null-relation help define simple and complex patterns, which in turn provide a path to the previous work done by the proponents of the statistical and structural approaches to the problem of pattern recognition.
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© 1984 Springer-Verlag Berlin Heidelberg
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Gökeri, A.M. (1984). On Patterns and Pattern Recognition. In: Brady, M., Gerhardt, L.A., Davidson, H.F. (eds) Robotics and Artificial Intelligence. NATO ASI Series, vol 11. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82153-0_7
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DOI: https://doi.org/10.1007/978-3-642-82153-0_7
Publisher Name: Springer, Berlin, Heidelberg
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