(N,0) motion-compensated lifting-based wavelet transform

Motion compensation has been widely used in both DCT- and wavelet-based video coders for years. The recent success of temporal wavelet transform based on motion-compensated lifting suggests that a high-performance, scalable wavelet video coder may soon outperform best DCT-based coders. As recently shown, however, the motion-compensated lifting does not implement exactly its transversal equivalent unless certain conditions on motion are satisfied. In this paper, we review those conditions, and we discuss their importance. We derive a new class of temporal transforms, the so-called 1-N transversal or (N,0) lifting transforms, that are particularly interesting if those conditions on motion are not satisfied. We compare experimentally the 1-3 and 5-3 motion-compensated wavelet transforms for the ubiquitous block-motion model used in all video compression standards. For this model, the 1-3 transform outperforms the 5-3 transform due to the need to transmit additional motion information in the later case. This interesting result, however, does not extend to motion models satisfying the transversal/lifting equivalence conditions.