The Number of N-Point Digital Discs
IEEE Transactions on Pattern Analysis and Machine Intelligence
Circularly orthogonal moments for geometrically robust image watermarking
Pattern Recognition
Robust designs for series estimation
Computational Statistics & Data Analysis
Testing for image symmetries: with application to confocal microscopy
IEEE Transactions on Information Theory
Nonlinear Image Processing and Filtering: A Unified Approach Based on Vertically Weighted Regression
International Journal of Applied Mathematics and Computer Science - Applied Image Processing
Image reconstruction with polar zernike moments
ICAPR'05 Proceedings of the Third international conference on Pattern Recognition and Image Analysis - Volume Part II
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We consider the problem of estimating a function f (x, y) on the unit disk f {(x, y): x2+y2≤1}, given a discrete and noisy data recorded on a regular square grid. An estimate of f (x, y) 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 origin of coordinates yielding therefore a rotationally invariant estimate. For-radial functions, the orthogonal set has a particularly simple form being related to the classical Legendre polynomials. We give the statistical accuracy analysis of the proposed estimate of f (x, y) in the sense of the L2 metric. It is found that there is an inherent limitation in the precision of the estimate due to the geometric nature of a circular domain. This is explained by relating the accuracy issue to the celebrated problem in the analytic number theory called the lattice points of a circle. In fact, the obtained bounds for the mean integrated squared error are determined by the best known result so far on the problem of lattice points within the circular domain.