一种新的灰度图像Legendre矩的快速算法

A Novel Algorithm for Fast Computing Legendre Moments of Gray-Level Images

Legendre正交矩在模式识别和图像分析等领域有着广泛的应用 ,但由于计算的复杂性 ,相关的快速算法尚未得到很好的解决 ,已有方法均局限于二值图像 .文章提出了一种灰度图像的Legendre正交矩的快速算法 ,借助于Legendre多项式的递推公式推导出计算一维Legendre矩的递归公式 .利用该关系式 ,一维Legendre矩Lp( 0 )可以用一系列初始值L1(a) ,a <p ,L0 (a) ,a <p - 1来得到 .而二维Legendre矩Lpq可以利用一维算法进行计算 .为了降低算法复杂度 ,文中采用基于Systolic阵列的快速算法进行计算L1(a) ,L0 (a) .与直接方法相比 ,快速算法可以大幅度减少乘法的次数 ,从而达到了降低算法复杂度的目的 .

Legendre orthogonal moments have been successfully used in the field of pattern recognition and image analysis. However, due to its complexity, the research of the fast computing algorithms for Legendre moments has been limited on the binary images. In this paper, a new fast algorithm for computing the Legendre moments of gray-level images is presented. By using the recursive property of Legendre polynomials, the recurrence formulas of 1D Legendre moments can be established. As a result, the 1D Legendre moments L p(0) can be expressed as a linear combination of L p -1(1) and L p -2(0). Based on this relationship, the 1D Legendre moments L p(0) can be calculate by the array of L 1(a), a <p, L 0(a), a<p-1. To reduce the computation complexity, authors adopt an algorithm based on Systolic array for computing L 1(a),L 0(a). Using such a strategy, the multiplication number required in the moment calculation of L p(0) can be reduced significantly. Authors then extend the method to calculate the 2D Legendre moments L p q. Compared with direct methods, the above method is more efficient.