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Pasialis, Vasileios; Lampeas, George (2015)
Publisher: Elsevier
Languages: English
Types: Article
Validation of computational solid mechanics simulations requires full-field comparison\ud methodologies between numerical and experimental results. The continuous Zernike and\ud Chebyshev moment descriptors are applied to decompose data obtained from numerical\ud simulations and experimental measurements, in order to reduce the high amount of\ud ‘raw’ data to a fairly modest number of features and facilitate their comparisons. As Zernike\ud moments are defined over a unit disk space, a geometric transformation (mapping) of\ud rectangular to circular domain is necessary, before Zernike decomposition is applied to\ud non-circular geometry. Four different mapping techniques are examined and their decomposition/\ud reconstruction efficiency is assessed. A deep mathematical investigation to the\ud reasons of the different performance of the four methods has been performed, comprising\ud the effects of image mapping distortion and the numerical integration accuracy. Special\ud attention is given to the Schwarz–Christoffel conformal mapping, which in most cases is proven to be highly efficient in image description when combined to Zernike moment descriptors. In cases of rectangular structures, it is demonstrated that despite the fact that Zernike moments are defined on a circular domain, they can be more effective even from Chebyshev moments, which are defined on rectangular domains, provided that appropriate mapping techniques have been applied.
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • 1. E.A. Patterson, M. Feligiotti, E. Hack, On the integration of validation, quality assurance and nondestructive evaluation, J. Str. Anal. 48 (2013) 48-58.
    • 2. P.K. Rastogi, D. Inaudi, Trends in optical non-destructive testing and inspection, first ed., Elsevier, Amsterdam, 2000.
    • 3. G.N. Labeas, V.P. Pasialis, On the use of optical methods in the validation of non-linear dynamic simulations of sandwich structures, J. Terr. Sci. Eng. 5 (2012) 25-31.
    • 4. G.N. Labeas, V.P. Pasialis, A hybrid framework for non-linear dynamic simulations including fullfield optical measurements and image decomposition algorithms, J. Str. Anal. 48 (2013) 5-15.
    • 5. G.A. Papakostas, D.E. Koulouriotis, E.G. Karakasis, Computation strategies of orthogonal image moments: A comparative study, Appl. Math. Comput. 216 (2010) 1-17.
    • 6. L. Kotoulas, I. Andreadis, Image analysis using moments, in: 5th International Conference on Technology and Automation, Thessaloniki, 2005, pp. 360-364.
    • 7. S.X. Liao, Accuracy Analysis of Moment Functions, in: G.A. Papakostas (Ed.), Moments and Moment Invariants - Theory and Applications, Science Gate Publishing, Winnipeg-Canada, 2014, pp. 33-56.
    • 8. S.X. Liao, M. Pawlak, A Study of Zernike Moment Computing, in: Lecture Notes in Computer Science. Computer Vision-ACCV'98, 1997, pp. 394-401.
    • 9. Z. Ping, Y. Sheng, Image description with Chebyshev moments, J. Inner Mong. Norm. Univ. 31 (2002).
    • 10. C. Singh, R. Upneja, Fast and accurate method for high order Zernike moments computation, Appl. Math. Comput. 218 (2012) 7759-7773.
    • 11. W. Wang, J.E. Mottershead, C. Mares, Mode-shape recognition and finite element model updating using the Zernike moment descriptor, J. Mech. Syst. Signal Process. 23 (2009) 2088-2112.
    • 12. R. Mukundan, K.R. Ramakrishnan, Fast computation of Legendre and Zernike moments, Pattern Recognit. 28 (1995) 1433-1442.
    • 13. T. J. Rivlin, The Chebyshev Polynomials. John Wiley & Sons, 1974.
    • 14. Z. Shao, H. Shu, J. Wu, B. Chen, J.L. Coatrieux, Quaternion Bessel-Fourier moments and their invariant descriptors for object reconstruction and recognition, Pattern Recognit. 47(2014) 603-611.
    • 15. E.G. Karakasis, G.A. Papakostas, D.E. Koulouriotis, V.D.Tourassis, A unified methodology for computing accurate quaternion color moments and moment invariants, IEEE Trans. Image Process. 23(2014) 596-611.
    • 16. L. Guo, M. Dai, M. Zhu., Quaternion moment and its invariants for color object classification, Inf. Sci. 273(2014) 132-143
    • 17. T.A. Driscoll, L.N. Trefethen, Schwarz-Christoffel Mapping. Cambridge University Press, 2002.
    • 18. J.P. Boyd, F.Yu, Comparing seven spectral methods for interpolation and for solving the Poisson equation in a disk: Zernike polynomials, Logan-Shepp ridge polynomials, Chebyshev-Fourier Series, cylindrical Robert functions, Bessel-Fourier expansions, square-to-disk conformal mapping and radial basis functions, J. Comput. Phys. 230 (2011) 1408-1438.
    • 19. L.N. Trefethen, Numerical Computation of the Schwarz-Christoffel transformation, J. Sci. and Stat. Comput. 1 (1980) 82-102.
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