Shape descriptors and mapping methods for full-field comparison of experimental to simulation data

Validation of computational solid mechanics simulations requires full-field comparison methodologies between numerical and experimental results. The continuous Zernike and Chebyshev moment descriptors are applied to decompose data obtained from numerical simulations and experimental measurements, in order to reduce the high amount of ‘raw’ data to a fairly modest number of features and facilitate their comparisons. As Zernike moments are defined over a unit disk space, a geometric transformation (mapping) of rectangular to circular domain is necessary, before Zernike decomposition is applied to non-circular geometry. Four different mapping techniques are examined and their decomposition/ reconstruction efficiency is assessed. A deep mathematical investigation to the reasons of the different performance of the four methods has been performed, comprising the effects of image mapping distortion and the numerical integration accuracy. Special 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

Quaternion Bessel-Fourier moments and their invariant descriptors for object reconstruction and recognition

International audienceIn this paper, the quaternion Bessel-Fourier moments are introduced. The significance of phase information in quaternion Bessel-Fourier moments is investigated and an accurate estimation method for rotation angle is described. Furthermore, a new set of invariant descriptors based on the magnitude and the phase information of quaternion Bessel-Fourier moments is derived. Experimental results show that quaternion Bessel-Fourier moments lead to better performance for color image reconstruction than the other quaternion orthogonal moments such as quaternion Zernike moments, quaternion pseudo-Zernike moments and quaternion orthogonal Fourier-Mellin moments. In addition, the angles estimated by the proposed moments are more accurate than those obtained by using other quaternion orthogonal moments. The proposed invariant descriptors show also better robustness to geometric and photometric transformations