Efficient Legendre moment computation for grey level images

9 Legendre orthogonal moments have been widely used in the field of image analysis. Because their computation by a direct method is very time expensive, recent efforts have been devoted to the reduction of computational complexity. Nevertheless, the existing algorithms11 are mainly focused on binary images. We propose here a new fast method for computing the Legendre moments, which is not only suitable for binary images but also for grey level images. We first establish a recurrence formula of one-dimensional (1D) Legendre13 moments by using the recursive property of Legendre polynomials. As a result, the 1D Legendre moments of order p, Lp = Lp(0), can be expressed as a linear combination of Lp-1(1) and Lp-2(0). Based on this relationship, the 1D Legendre moments Lp(0) can thus be15 obtained from the arrays of L1(a) and L0(a), where a is an integer number less than p. To further decrease the computation complexity, an algorithm, in which no multiplication is required, is used to compu...

• Type: Journal
• Year: 2006
• Where: PR
• Authors: G. Y. Yang, Huazhong Shu, Christine Toumoulin, Guo-Niu Han, Limin Luo
• Keywords: Images, Legendre Moments, Legendre Orthogonal Moments, PR 2006