An efficient algorithm for computing moments on a block representation of a grey-scale image

Computing lower order moments is important in image processing. Suppose the input grey image with size N×N has been compressed into the block representation where the number of blocks is K, commonly K<N² due to the compression effect. This correspondence presents an efficient algorithm for computing lower order moments on the block representation directly. Our proposed algorithm takes O(K) time which is proportional to the number of blocks. Experimental results reveal the computational advantage of our proposed algorithm. In addition, the results of this paper can be viewed as a generalization of the previous result by Spiliotis and Mertzios for computing lower order moments from the binary image domain to the grey image domain.