Two new algorithms for efficient computation of Legendre moments

Orthogonal moments have been successfully used in the field of pattern recognition and image analysis. However, the direct computation of orthogonal moments is very expensive. In this paper, we present two new algorithms for fast computing the two-dimensional (2D) Legendre moments. The first algorithm consists of transforming the pixel-based calculation of Legendre moments into the line-segment-based calculation. After all line-segment moments have been calculated, Hatamian's filter method is extended to calculate the one-dimensional Legendre moments. The second algorithm is directly based on the double integral formulation. The 2D shape is considered as a continuous region and the contribution of the boundary points is used for fast calculation of shape moments. The numerical results show that the new algorithms can decrease the computational complexity tremendously, furthermore, they can be used to treat any complicated objects.