A new fast method for computing Legendre moments

Abstract This paper presents a new algorithm for fast and accurate computation of Legendre moments. For a binary image, by use of a Green's theorem, we transform a surface integral to a simple integration along the boundary. The inter-order relationship of Legendre moments is then investigated. As a result, the moments of higher order can be deduced from those of lower order. Based on this relationship, an iterative method is proposed to calculate the Legendre moments from a polygonal approximation of the boundary. Comparison with known methods shows that our algorithm is almost as efficient as the existing method, but is more accurate.