A fast method for reconstruction of binary and gray-scale images by the tchebichef moments

The discrete orthogonal moments have been recently introduced in the field of image analysis. It has been shown to have a better ability to represent the image than the continuous orthogonal moments. A problem concerning the use of moments as descriptors is the highest cost of calculation, which may limit their application to the problems in which the calculation online is necessary. In this paper, we present an approach for the rapid calculation of two-dimensional Tchebichef moments by using image block representation for binary images and the slice representation of intensity to gray-scale images. A theoretical analysis shows that the computational complexity of the proposed method is based on the number of blocks of the image, thus, it can accelerate the computational efficiency since the number of blocks is less than the size of the image. Finally, the performances of Tchebichef moments in describing images were measured in terms of the image reconstruction error.