A fast computation of Hahn moments for binary and gray-scale images

The discrete orthogonal moments have been introduced in the fields of images analysis (reconstruction, classification, indexation, recognition of shapes, ...). They have excellent capacity of representing the image than the continuous orthogonal moments. The problem that limits the use of moments is the high cost of calculation. So as to resolve the problem, we are going to present, in this paper, a method to accelerate the time of the calculation of Hahn´s moments for binary and gray-scale images. The method is based on the calculation of Hahn´s discrete orthogonal polynomials considering the recurrence relation with respect to variable x and order n, and applying the algorithm image block representation IBR for binary images and PIBR for gray-scale images. The moments of image can be obtained from the moments of all blocks. Thus, it can accelerate the computational efficiency since the number of blocks is less than the size of the image. This method also accelerates the reconstruction´s time of images and the quality of reconstruction which will be evaluated by the calculation of error of reconstruction (mse).