A Novel Algorithm for Fast Computing Legendre Moments of Gray-Level Images
Yang Guan · Chinese Journal of Computers · 2004
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), ap-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.