New relationships in operator-based backward motion compensation

The transmission and storage of digital video at reduced bit rates requires a source coding scheme, which generally contains motion compensated prediction as an essential part. The class of motion estimation algorithms known as backward methods have the advantage of dense motion field sampling, and in coding applications the decoder needs no motion information from the coder. In this paper, we first present an overview of operator based motion compensators with interpolative and non-interpolative kernels. We then proceed with two new results. The first offers a new perspective on the classical pel-recursive methods; one that exposes the weaknesses of traditional approaches and offers an explanation for the improved performance of operator-based algorithms. The second result introduces a minimum norm intra-frame operator and establishes an equivalence relationship between this and the original (least squares) operator. This equivalence induces interesting duality properties that, in addition to offering insights into operator-based motion estimators, can be used to relax either the maximum needed computational power or the frame buffer length.