Abstract
This paper proposes several algebraic methods aimed at refining the positions of characteristic points (that describe some objects on a pattern) based on the a priori information about their symmetrical position. These methods are known as the symmetrization of characteristic points. We consider symmetrization of points for the cases of vertical and arbitrary symmetry with known parameters of the symmetry axis, as well as more general case of symmetrization with unknown parameters of axial symmetry. The methods under consideration give a solution to the axial symmetrization problem with minimal variation of characteristic points.
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This paper uses the materials of a report that was submitted at the 11th International Conference Pattern Recognition and Image Analysis: New Information Technologies that was held in Samara, Russia on September 23–28, 2013.
Alexander N. Karkishchenko. Born 1956. Graduated from the Taganrog Radio Engineering Institute in 1978. Received Candidate’s degree in 1983 and Doctor’s in 1997. Scientific interests: data mining and pattern recognition, artificial intelligence and decision making, processing and analysis of images. Author of more than 170 publications.
Valeriy B. Mnukhin. Born 1958. Graduated from the Taganrog Radio Engineering Institute in 1979. Received Candidate’s degree in 1985. At present he is an associate professor at the Chair of Higher Mathematics at the Academy of Engineering and Technology of Southern Federal University. Scientific interests: mathematical methods of pattern recognition, algebraic and topological combinatorics, problems of graphs recovery, spectral theory of graphs. Author of more than 60 publications.
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Karkishchenko, A.N., Mnukhin, V.B. Reflective symmetrization of images. Pattern Recognit. Image Anal. 25, 33–40 (2015). https://doi.org/10.1134/S1054661815010071
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DOI: https://doi.org/10.1134/S1054661815010071