Operator-Based Backward Motion Estimation

Backward motion estimation consists of the class of motion algorithms that do not transmit motion information directly, but rather compute it at the decoder from already transmitted data. Traditional backward algorithms { also known as pel-recursion { rely on continuous image models, and apply resulting parameters onto sampled data. Within the framework of this approach, it is not feasible to implement a least squared error criterion, or to account for and analyze the eeects of various segments of the algorithm, e.g. interpolation. This paper investigates backward motion estimation directly in a sampled environment, and proposes an operator-based method for motion estimation and compensation. Our re-examination of backward motion compensation indicates that minimum mean squared estimation of pixel intensities in a recursive coder naturally decomposes into two distinct operations: a search on the image lattice and a least squares optimization. We ooer algorithmic solutions to both the least squares and search problems for a variety of cases. We propose and study two interpolation operators. We also investigate families of non-interpolative operators, where computational considerations motivate a recursive least squares (RLS) algorithm. Operator-based methods not only outperform traditional pel-recursion { as indicated by experimental results { they also ooer a much more exible framework to trade complexity vs. performance, or to design hybrid forward/backward algorithms that use partial forward motion information to combat tracking diiculties.