Image characterisation by fast calculation of Legendre moments

How to calculate Legendre moments of images by less computation is a very important problem for the application of orthogonal moments in pattern recognition and image processing. In the present paper we propose the fast calculation to characterise I-D signals and 2-D images by Legendre moments. We present at first the projections of I-D signals onto Legendre polynomials and deduce their recursive calculation, We then introduce the scaled Legendre polynomials, the Legendre moments of I-D signals with arbitrary window size and their fast calculation. The implementation in discrete cases is presented and its computational complexity is analysed as well. To apply our method to 2-D image processing and recognition, the recursive algorithm is generalized to 2-D cases. With the approach presented the computational complexity to characterise images by Legendre moments is greatly reduced and the implementation is simple. As the moments are widely used in image filtering, image segmentation, texture analysis and pattern recognition, the we of the algorithm proposed could greatly reduce the computational complexity of such tasks.