Abstract
A problem of linear Procrustes transformation of common (two-dimensional) matrices has been formulated and solved. An approach is proposed and an algorithm is developed for the Application of linear Procrustes transformation to letter recognition. The results of the recognition of printed Latin letters subjected to rotation and reflections are cited.
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Andrade, J.M., Gomez-Carracedo, M.P., Krzanowski, W., and Kubista, M., Procrustes Rotation in Analytical Chemistry, a Tutorial, Chemometrics Intell. Labor. Systems, 2004, vol. 72, no. 2, pp. 123–132.
Schneider, J.W. and Borlund, P., Matrix Comparison, Part 2: Measuring the Resemblance between Proximity Measures or Ordination Results by Use of the Mantel and Procrustes Statistics, J. Am. Soc. Inform. Sci. Techn., 2007, vol. 58, no. 11, pp. 1596–1609.
Hurley, J.R. and Cattell, R.B., The Procrustes Program: Producing Direct Rotation to Test a Hypothesized Factor Structure, Behav. Sci., 1962, no. 7, pp. 258–262.
Crosilla, F., Procrustes Analysis and Geodetic Sciences, Technical Report. Part 1. Stuttgart: Univ. of Stuttgart, 1999, pp. 69–78.
Kroonenberg, P.M., Dunn III, W.J., and Commandeur, J.J.F., Consensus Molecular Alignment Based on Generalized Procrustes Analysis, J. Chem. Inform. Comp. Sci., 2003, vol. 43, pp. 2025–2032.
Schonemann, P.H., A Generalized Solution of the Orthogonal Procrustes Problem, Psychometrika, 1966, vol. 31, no. 1, pp. 1–10.
Schonemann, P.H. and Carroll, R.M., On Fitting One Matrix to Another under Choice of a Central Dilation Transformation and a Rigid Motion, Psychometrika, 1970, vol. 35, pp. 245–255.
Horn, R.A. and Johnson, Ch.R., Topics in Matrix Analysis, New York: Cambr. Univ. Press, 1991; Moscow: Mir, 1989.
Mukha, V.S., Linear Procrustes Transformation of Two-Dimensional Matrixes, Informatika, 2010, no. 3, pp. 97–102.
Ten Berge, J.M.F., Orthogonal Procrustes Rotation for Two or More Matrices, Psychometrica, 1977, vol. 42, no. 2, pp. 267–276.
Kudryavtsev, L.D., Kurs matematicheskogo analiza. T.1, (Course of Mathematical Analysis. Vol. 1.), Moscow: Vyssh. Shkola, 1981.
Korneev, A.P., Ivanova, A.A., and Prokdi, R.G., Programma FineReader. Rukovodstvo (Fine Reader Program. A Tutorial), St. Petersburg: Nauka i Tekhnika, 2010.
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Original Russian Text © V.S. Mukha, 2012, published in Avtomatika i Vychislitel’naya Tekhnika, 2012, No. 3, pp. 36–48.
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Mukha, V.S. Linear procrustes transformation for letter recognition. Aut. Conrol Comp. Sci. 46, 119–129 (2012). https://doi.org/10.3103/S0146411612030066
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DOI: https://doi.org/10.3103/S0146411612030066