This paper discusses possible computation schemes that have been introduced in the past and cope with the efficient computation of the orthogonal image moments. An exhaustive comparative study of these alternatives is performed in order to investigate the conditions under which each scheme ensures high computation rates, for several test images. The present study aims to discover the properties and the behaviour of the different methodologies and it serves as a reference point in the field of moment’s computation. Some useful conclusions are drawn regarding the applicability and the usefulness of the computation strategies in comparison and efficient hybrid methods are proposed to better utilize their advantages.