Motion-compensated lifted wavelets have received much interest for video compression. While they are biorthogonal, they may substantially deviate from orthonormality due to motion compensation, even if based on an orthogonal or near-orthogonal wavelet. A temporal transform for video sequences that maintains orthonormality while permitting flexible motion compensation would be very desirable. We have recently introduced such a transform for unidirectional motion compensation from one previous frame [1]. See also sample video [avi] comparing to the motion-compensated lifted Haar wavelet.

In [3], we extend the idea to half-pel accurate motion compensation. Orthonormality is maintained for arbitrary half-pel motion compensation by cascading a sequence of incremental orthogonal transforms. The half-pel intensity values are obtained by averaging neighboring integer-pel positions. Depending on the number of averaged integer-pel values, we use different types of incremental transforms. The cascade of incremental transforms allows us to choose in each step the optimal type of incremental transform and, hence, the optimal half-pel position. Half-pel motion-compensated blocks of arbitrary shape and size can be used as the granularity of the cascade can be as small as one pixel. The new half-pel accurate motion-compensated orthogonal video transform compares favorably with the integer-pel accurate orthogonal transform.

In [4], we extend the idea to bidirectional motion compensation. Orthonormality is maintained for arbitrary integer-pixel motion compensation by cascading a sequence of incremental orthogonal 3x3 transforms. The energy of three input pictures is accumulated in two temporal low-bands while the temporal high-band is zero if the input pictures are identical after motion compensation. Further, the motion-compensated orthogonal transforms can be cascaded to build a dyadic wavelet decomposition. The new bidirectionally motion-compensated orthogonal transform compares favorably with the lifted 5/3 wavelet in video coding experiments with integer-pixel motion compensation.