Chebyshev-Fourier moments for describing images were proposed. After definition of the moments, the multidistortion invariance of the moments was verified. The performance of the moments in describing images was investigated in terms of the normalized image-reconstruction error and the results of the experiments on the noise sensitivity are given.
We show that the transformation with radial polynomial and circular Fourier kernel of two-dimensional image can generate image moments, which are invariant to rotation, translation and scale changes. Among them the orthogonal Fourier-Mellin moments using the generalized Jacobi radial polynomials show better performance that the Zernike moments. We introduce new Chebyshev-Fourier moments using Chebyshev radial polynomials, which improve the behavior of the orthogonal Fourier-Mellin moments in regions close to the center of image. Experimental results are shown for the image description performance of the Chebyshev-Fourier moments in terms of image reconstruction errors and sensitivity to noise. In the cases of binary or contour shapes the Fourier-Mellin moments of single orders are able to describe and reconstruct the shapes.
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