Accurate and fast harmonic transform of polar coordinates

作者：Wo, Yan^*; Xu, Jiao

来源：Journal of South China University of Technology(Natural Science Edition), 2012, 40(4): 23-29.

DOI：10.3969/j.issn.1000-565X.2012.04.004

• Cartesian coordinate
• Computation methods
• Geometric invariant
• Harmonic transform
• Orthogonal moments
• Polar coordinate
• Reconstruction accuracy
• Trigonometric functions

This paper deals with the extension of the computation method of Zernike moments in polar coordinates to the computation of PHT moments in Cartesian coordinates. In the investigation, polar coordinates are designed and modulated for the computation of PHT moments, which can eliminate the geometric error and the integral approximate error of the computation in Cartesian coordinates. And, during the calculation of the kernel coefficients of PHT, the symmetry and the inquiry table of trigonometric function are used to reduce the computational complexity. Thus, the computation is accelerated and the iterative cumulative error is eliminated. The proposed fast PHT algorithm based on polar coordinates is finally verified by experiments and is compared with the existing one based on Cartesian coordinates. Experimental results show that the proposed algorithm is superior to the PHT algorithm based on Cartesian coordinates in terms of reconstruction accuracy, rotation scale invariance and calculation speed.

• 出版日期2012-4
• 单位华南理工大学