Abstract
This study presents the exact Legendre–Fourier moments and a novel arrangement of polar pixels that allows calculating orthogonal moments defined in a unit radius more accurately than traditional methods. This arrangement simplifies implementation and preserves the values of the pixels of the image during the calculation of the moments. Moreover, the exact Legendre–Fourier moments use the weighted substituted radial shifted Legendre polynomials as kernel, which has the ability to accurately calculate the circular moments. Finally, the author presents a comparative analysis of the reconstruction error with existing configurations and other families of circular moments. The results indicate that the mehod provides a significant advantage.
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