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—We consider the problem of estimating a function () on the unit disk (): 2 + 2 1 , given a discrete and noisy data recorded on a regular square grid. An estimate of () based on a class of orthogonal and complete functions over the unit disk is proposed. This class of functions has a distinctive property of being invariant to rotation of axes about the(More)
—In this paper, we give a detailed analysis of the accuracy of Zernike moments in terms of their discretization errors and the reconstruction power. It is found that there is an inherent limitation in the precision of computing the Zernike moments due to the geometric nature of a circular domain. This is explained by relating the accuracy issue to a(More)
An algorithm for high-precision numerical computation of Zernike moments is presented. The algorithm, based on the introduced polar pixel tiling scheme, does not exhibit the geometric error and numerical integration error which are inherent in conventional methods based on Cartesian coordinates. This yields a dramatic improvement of the Zernike moments(More)
In image watermarking, the watermark robustness to geometric transformations is still an open problem. Using invariant image features to carry the watermark is an effective approach to addressing this problem. In this paper, a multibit geometrically robust image watermarking algorithm using Zernike moments is proposed. Some Zernike moments of an image are(More)
Moment features have been applied in pattern recognition systems since the moment method was developed. In this paper, a set of moment features extracted from the newly developed Gegenbauer moment method for Chinese character recognition is proposed. Compared with the results based on other moment methods, the Gegenbauer moments can provide a modest(More)