Lie Group Transformation Models for Predictive Video Coding

We propose a new method for modeling the temporal correlation in videos, based on local transforms realized by Lie group operators. A large class of transforms can be theoretically described by these operators; however, we propose to learn from natural movies a subset of transforms that are statistically relevant for video representation. The proposed transformation modeling is further exploited to remove inter-view redundancy, i.e., as the prediction step of video encoding. Since the Lie group transformation coefficients are continuous, a quantization step is necessary for each transform. Therefore, we derive theoretical bounds on the distortion due to coefficient quantization. The experimental results demonstrate that the new prediction method with learned transforms leads to better rate-distortion performance at higher bit-rates, and competitive performance at lower bit-rates, compared to the standard prediction based on block-based motion estimation.