On the importance of motion invertibility in MCTF/DWT video coding

Motion-compensated temporal filtering implemented using lifting is an effective and efficient temporal decomposition tool that facilitates video compression competitive with the current standards. As recently shown, however, in order that a lifting-based motion-compensated discrete wavelet transform indeed implements the intended filtering along motion trajectories, motion transformation must be invertible and motion composition between frames must be well-defined. A departure from these conditions results in the application of sub-optimal subband decomposition filters which, in turn, degrades coding performance, even if prediction-step energy is minimized during motion estimation. We study the impact of motion field invertibility error on the coding performance of an MCTF/DWT video coder. We propose two new motion field inversion methods and compare them to previously reported inversion techniques. We also compare coding results for all inversion algorithms with those of coding based on triangular meshes that are inherently invertible. Our results show that a significant improvement in coding performance is possible with more accurate motion field inversion.