Journal of Computational and Applied Mathematics
Comments on: 'Robust Line Fitting in a Noisy Image by the Method of Moments'
IEEE Transactions on Pattern Analysis and Machine Intelligence
On a structure formula for classical q-orthogonal polynomials
Journal of Computational and Applied Mathematics
Distributions of zeros of discrete and continuous polynomials from their recurrence relation
Applied Mathematics and Computation - Orthogonal systems and applications
Analysis for the reconstruction of a noisy signal based on orthogonal moments
Applied Mathematics and Computation
Integrable systems on the lattice and orthogonal polynomials of discrete variable
Journal of Computational and Applied Mathematics - Proceedings of the sixth international symposium on orthogonal polynomials, special functions and their applications
Discrete Cosine Transform: Algorithms, Advantages, Applications
Discrete Cosine Transform: Algorithms, Advantages, Applications
Image analysis by Tchebichef moments
IEEE Transactions on Image Processing
Image analysis by Krawtchouk moments
IEEE Transactions on Image Processing
A modified moment-based edge operator for rectangular pixel image
IEEE Transactions on Circuits and Systems for Video Technology
Image analysis by discrete orthogonal dual Hahn moments
Pattern Recognition Letters
A unified methodology for the efficient computation of discrete orthogonal image moments
Information Sciences: an International Journal
Image analysis by Bessel-Fourier moments
Pattern Recognition
Quaternion Fourier-Mellin moments for color images
Pattern Recognition
Fast computation of tchebichef moments for binary and grayscale images
IEEE Transactions on Image Processing
CIARP'10 Proceedings of the 15th Iberoamerican congress conference on Progress in pattern recognition, image analysis, computer vision, and applications
Rotation and translation invariants of Gaussian-Hermite moments
Pattern Recognition Letters
Image analysis by Gaussian-Hermite moments
Signal Processing
Generalized dual Hahn moment invariants
Pattern Recognition
The fast recursive computation of Tchebichef moment and its inverse transform based on Z-transform
Digital Signal Processing
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Discrete orthogonal moments are powerful tools for characterizing image shape features for applications in pattern recognition and image analysis. In this paper, a new set of discrete orthogonal moments is proposed, based on the discrete Racah polynomials. In order to ensure numerical stability, the Racah polynomials are normalized, thus creating a set of weighted orthonormal Racah polynomials, to define the so-called Racah moments. This new type of discrete orthogonal moments eliminates the need for numerical approximations. The paper also discusses the properties of Racah polynomials such as recurrence relations and permutability property that can be used to reduce the computational complexity in the calculation of Racah polynomials. Finally, we demonstrate Racah moments' feature representation capability by means of image reconstruction and compression. Comparison with other discrete orthogonal transforms is performed, and the results show that the Racah moments are potentially useful in the field of image analysis.