Abstract
This paper formulates the problem of assessing the reflection symmetry of a function f observed in the presence of noise. We consider both univariate and bivariate characteristics representing signal and image functions. First the problem of estimating a parameter defining the reflection symmetry is examined. This is followed by the question of testing the given symmetry type. The estimation/detection procedure is based on minimizing the L 2-distance between empirical versions of f and its reflected version. For univariate functions this distance is estimated by the Fourier series type estimate. In the bivariate case we utilize a class of radial series represented by the Zernike functions. It is shown that the symmetry parameter can be recovered with the parametric optimal rate for all functions f of bounded variation.
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© 2014 Springer International Publishing Switzerland
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Pawlak, M. (2014). Statistical Assessment of Signal and Image Symmetries. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds) Artificial Intelligence and Soft Computing. ICAISC 2014. Lecture Notes in Computer Science(), vol 8467. Springer, Cham. https://doi.org/10.1007/978-3-319-07173-2_49
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DOI: https://doi.org/10.1007/978-3-319-07173-2_49
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-07172-5
Online ISBN: 978-3-319-07173-2
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