Image reconstruction from a complete set of similarity invariants extracted from complex moments
Pattern Recognition Letters
Image analysis by discrete orthogonal dual Hahn moments
Pattern Recognition Letters
Image Analysis Using Hahn Moments
IEEE Transactions on Pattern Analysis and Machine Intelligence
Two-variable orthogonal polynomials of big q-Jacobi type
Journal of Computational and Applied Mathematics
Invariant image watermarking using multi-scale Harris detector and wavelet moments
Computers and Electrical Engineering
Monomial orthogonal polynomials of several variables
Journal of Approximation Theory
Higher order orthogonal moments for invariant facial expression recognition
Digital Signal Processing
Orthogonal polynomials in two variables as solutions of higher order partial differential equations
Journal of Approximation Theory
Image analysis by Gaussian-Hermite moments
Signal Processing
Image analysis by discrete orthogonal hahn moments
ICIAR'05 Proceedings of the Second international conference on Image Analysis and Recognition
Image analysis by Tchebichef moments
IEEE Transactions on Image Processing
Texture classification using spectral histograms
IEEE Transactions on Image Processing
Image analysis by Krawtchouk moments
IEEE Transactions on Image Processing
Topology Preserving Non-negative Matrix Factorization for Face Recognition
IEEE Transactions on Image Processing
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This paper addresses bivariate orthogonal polynomials, which are a tensor product of two different orthogonal polynomials in one variable. These bivariate orthogonal polynomials are used to define several new types of continuous and discrete orthogonal moments. Some elementary properties of the proposed continuous Chebyshev-Gegenbauer moments (CGM), Gegenbauer-Legendre moments (GLM), and Chebyshev-Legendre moments (CLM), as well as the discrete Tchebichef-Krawtchouk moments (TKM), Tchebichef-Hahn moments (THM), Krawtchouk-Hahn moments (KHM) are presented. We also detail the application of the corresponding moments describing the noise-free and noisy images. Specifically, the local information of an image can be flexibly emphasized by adjusting parameters in bivariate orthogonal polynomials. The global extraction capability is also demonstrated by reconstructing an image using these bivariate polynomials as the kernels for a reversible image transform. Comparisons with the known moments are performed, and the results show that the proposed moments are useful in the field of image analysis. Furthermore, the study investigates invariant pattern recognition using the proposed three moment invariants that are independent of rotation, scale and translation, and an example is given of using the proposed moment invariants as pattern features for a texture classification application.