Fast computation of Legendre moments of polyhedra

Abstract The three-dimensional (3D) orthogonal moments are an efficient tool for object reconstruction and 3D image analysis. However, until now, 3D orthogonal moments have not been analysed in detail from the point of view of reducing the computational complexity. In this paper, we present a recursive algorithm for fast computation of Legendre moments of polyhedra. First, a Gaussian theorem is employed to transform the volume integral into a surface one. The double integral can then be deduced from the simple integral by a Green's theorem. Finally, the recursive relationship is investigated. As one can see, the proposed method decreases the computational complexity tremendously.