Open AccessGeometry of circular vectors and pattern recognition of shape of a boundary
Author(s) -
Calyampudi R. Rao
Publication year - 1998
Publication title -
proceedings of the national academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 5.011
H-Index - 771
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.95.22.12783
Subject(s) - mathematics , boundary (topology) , geometry , invariant (physics) , measure (data warehouse) , point (geometry) , sequence (biology) , mathematical analysis , shape analysis (program analysis) , zero (linguistics) , computer science , data mining , biology , static analysis , programming language , philosophy , genetics , mathematical physics , linguistics
This paper deals with pattern recognition of the shape of the boundary of closed figures on the basis of a circular sequence of measurements taken on the boundary at equal intervals of a suitably chosen argument with an arbitrary starting point. A distance measure between two boundaries is defined in such a way that it has zero value when the associated sequences of measurements coincide by shifting the starting point of one of the sequences. Such a distance measure, which is invariant to the starting point of the sequence of measurements, is used in identification or discrimination by the shape of the boundary of a closed figure. The mean shape of a given set of closed figures is defined, and tests of significance of differences in mean shape between populations are proposed.
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