一种新的快速计算Legendre矩的方法

正交矩在模式识别，图像分析等领域有成功的应用，但由于正交矩的复杂性，有关正交矩的快速算法研究尚未得到很好的解决，该文提出一种 新的快速计算Ｌegendre矩的方法，该方法把基于像素点的二维Ｌegendre矩转换为线段的形式来计算，在计算出所有线段的积分后，使用扩展的Ｈatamian滤波方法来计算一维的Ｌegendre矩。结果显示新的算法有效地降低了计算的复杂度，并且，该方法能用于处理任意形状的物体。

A New Method for Fast Computing Legendre Moments

Various types of moments have been widely used to pattern recognition and image analysis tasks. Moment functions, especially orthogonal moments, are useful tools in the field of pattern recognition and image analysis, such as being used to describe the features of objects, including the shape, area, border, location and orientation, so the orthogonal moments are the emphasis in this paper.As is well known, the computation of image's orthogonal moments, such as Legendre and Zernike ones, if using straightforward method, requires quite excessive additional and multiplicative operations. To solve this problem, many algorithms have been developed to speed up the their calculation. Although, the existing methods are effective, but they may be not suitable to deal with certain kind of images such as the images represented by run length code or chain code. Since the run length code or chain code is a frequent way to represent the images, we present in this paper a new algorithm for fast computing the two dimensional Legendre moments for this kind of images. The method, usually be called delta method, consists of transforming pixel based calculation of Legendre moments into the line segment based calculation. After all line segment integrals have been calculated, Hatamian's filter method is extended to calculate the one dimensional Legendre moments. So we divide our approach into two steps: the calculation of Legendre moments of all line segments, and the calculation of 1D Legendre moments by using Hatamian's filter method.The numerical results show that, contrast to the straightforward method, the new algorithm can decrease the computational complexity tremendously. Furthermore, they can be used to treat any complicated objects and can be extended to 3D objects.