A 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 motion compensation between pairs of pictures. The well known 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 motion-compensated orthogonal transform strictly maintains orthogonality for any motion field. Further, the transform is designed with an energy-concentration constraint. The energy of the input pictures is accumulated in the temporal low-band while the temporal high-band is zero if the input pictures are identical up to a known single-connecting motion field. This constraint makes the transform suitable for coding applications