On Image Analysis by the Methods of Moments
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
The asymptotic zero distribution of orthogonal polynomials with varying recurrence coefficients
Journal of Approximation Theory
Image analysis by discrete orthogonal Racah moments
Signal Processing
Image analysis by discrete orthogonal dual Hahn moments
Pattern Recognition Letters
Application of a new type of singular points in fingerprint classification
Pattern Recognition Letters
Some Aspects of Gaussian-Hermite Moments in Image Analysis
ICNC '07 Proceedings of the Third International Conference on Natural Computation - Volume 02
Image analysis by Tchebichef moments
IEEE Transactions on Image Processing
Image analysis by Krawtchouk moments
IEEE Transactions on Image Processing
Image quality assessment: from error visibility to structural similarity
IEEE Transactions on Image Processing
Some computational aspects of discrete orthonormal moments
IEEE Transactions on Image Processing
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The problem of image reconstruction from its statistical moments is particularly interesting to researchers in the domain of image processing and pattern recognition. Compared to geometric moments, the orthogonal moments offer the ability to recover much more easily the image due to their orthogonality, which allows reducing greatly the complexity of computation in the phase of reconstruction. Since the 1980s, various orthogonal moments, such as Legendre moments, Zernike moments and discrete Tchebichef moments have been introduced early or late to image reconstruction. In this paper, another set of orthonormal moments, the Gaussian-Hermite moments, based on Hermite polynomials modulated by a Gaussian envelope, is proposed to be used for image reconstruction. Especially, the paper's focus is on the determination of the optimal scale parameter and the improvement of the reconstruction result by a post-processing which make Gaussian-Hermite moments be useful and comparable with other moments for image reconstruction. The algorithms for computing the values of the basis functions, moment computation and image reconstruction are also given in the paper, as well as a brief discussion on the computational complexity. The experimental results and error analysis by comparison with other moments show a good performance of this new approach.