Object transformation estimation with reduced searching complexity

Conventional motion estimation algorithms rely on translational motion vectors and thus have limitations in capturing transformations of objects in video scenes such as scaling, rotations and deformations. It has been shown that transformation estimation based on Lie operators on objects can provide more accurate motion estimation, albeit at the expense of remarkably increased computational complexity due to the search of the best transformation parameters for the object. In this paper, we aim to lower the complexity of the transformation estimation so that it can become more suitable for real time video coding systems where low complexity motion estimation is desirable. Our study on the probabilistic distributions of the transformation parameters shows that it is feasible to significantly reduce the total number of candidate parameters to search by considering only those possible transformations with smaller degrees. The resulting loss in the estimation accuracy due to searching only a subset of the candidate parameters that describes the degree of object transformations can be negligible. We propose three methods to reduce the searching complexity and present experimental results quantifying the tradeoffs between the estimation accuracy and the searching complexity for several video sequences.