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中文摘要：
将极坐标下计算Zernike矩的方法推广到笛卡尔坐标下PHT矩的计算中．对极坐标进行设计和规划，以消除笛卡尔坐标下PHT矩计算中存在的几何误差和积分近似误差．在计算PHT内核系数时利用三角函数的对称性和查找表减少三角函数的计算次数，以提高运算速度并消除迭代累计误差．最后通过实验对提出的快速极坐标PHT方法进行验证，并与笛卡尔坐标下的PHT计算方法进行对比，结果表明，极坐标下的快速PHT算法在重建精度、旋转缩放不变性、计算速度等方面都优于笛卡尔坐标下的PHT计算方法．
英文摘要：
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 approxi- mate 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 algo- rithm 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.
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