Comparative analysis of pattern reconstruction using orthogonal moments

We present a detailed analysis of the reconstruction of gray-level images using orthogonal moments with respect to the basis sets of Zernike, Fourier-Mellin, Chebyshev-Fourier, and pseudo-Jacobi-Fourier polynomials. As test images, we use Ronchigrams with different numbers of fringes as high-spatial-frequency components. The evaluation of image reconstruction between orthogonal moment sets is made in terms of different metrics. These measurements are the normalized image reconstruction error, the overall activity level in each image with respect to spatial frequency variations, the root-mean-square contrast, the total number of reconstructed fringes, the coordinate transformations of the input image, and the number of moment orders. Moreover, a method of denoising the input image based on the Daubechies wavelet transform is implemented to compute the signal-to-noise ratio. Numerical computations show that, for the Ronchigram reconstructions, the performance of Zernike moments is better than that of the other basis sets of orthogonal moments.

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