A Double Motion-Compensated Orthogonal Transform with Energy Concentration Constraint

This paper discusses a transform for successive pictures of an image sequence which strictly maintains orthogonality while permitting 2-hypothesis motion compensation between pairs of pictures. We extend previous work on an orthogonal transform for image sequences which uses only 1-hypothesis motion compensation between pairs of pictures. This work is motivated by the well known fact that the motion-compensated lifted Haar wavelet maintains orthogonality only approximately. In the case of zero motion fields, the motion-compensated lifted Haar wavelet is known to be orthogonal. But for complex motion fields with many multi-connected and unconnected pixels, the motion-compensated lifted Haar wavelet cannot accurately maintain its transform property and, hence, suffers a performance degradation. The presented double motion-compensated orthogonal transform strictly maintains orthogonality for any motion field. For the transform, each pixel in the high-band is compensated by a linear combination of two motion-compensated pixels chosen from the corresponding low-band. That is, each pixel in the high-band is associated with two motion vectors. This is in contrast to the previously presented single motion-compensated orthogonal transform where each pixel in the high-band is compensated by only one motion-compensated pixel chosen from the corresponding low-band. In terms of energy concentration, the double motion-compensated orthogonal transform outperforms the single motion-compensated orthogonal transform and compares favorably with the double motion-compensated lifted Haar wavelet.