二维Tchebichef正交矩反变换的快速算法

A Method for Efficiently Computing the Two-Dimensional Inverse Tchebichef Orthogonal Moments

提出了一种二维Tchebichef矩反变换的快速算法.借助Clenshaw递推公式,推导了一维Tchebichef矩反变换的快速算法,并将其推广至二维Tchebichef正交矩反变换的计算.与以迭代方式计算Tchebichef多项式进而计算二维Tchebichef矩反变换的方法相比,文中提出的算法有效地减少了算术运算的次数,大幅提高了计算速度.实验结果表明了该方法的有效性.

Tchebichef moment is based on discrete orthogonal Tchebichef polynomials. It avoids any numerical approximations that come from numerical approximation of continuous integrals or coordinates transformation. Now, it is applied more and more widely to the area of image processing and computer vision. The authors use Clenshaw＇s recurrence formula and deduce a fast algorithm for calculating the one-dimensional inverse Tchebichef moments. Then, the authors extend it for the computation of the two-dimensional inverse Tchebichef moments. Experimental results show that the new method reduces the computational complexity greatly compared with the direct method.