Efficient local transformation estimation using Lie operators

Conventional translation-only motion estimation algorithms cannot cope with transformations of objects such as scaling, rotations and deformations. Motion models characterizing non-translation motions are thus beneficial as they offer more accurate motion estimation and compensation. In this paper, we introduce low-complexity transformation estimation methods with four motion models based on Lie operators, which are linear operators that have found applications in optical character recognitions. We show that individual Lie operators are capable of capturing small degrees of object transformations. We propose an efficient local transformation estimation algorithm in order to further improve the accuracy of the translation-only estimation by integrating all four motion models. Simulations with an MPEG-2 video codec on two video sequences show that the proposed transformation estimation approach can noticeably improve the motion compensation performance of the translation-only method by achieving higher PSNR (peak signal-to-noise ratio) values for the predicted frames, with only a small fraction of the complexity required by the translation motion search.