Efficiency of displacement estimation techniques

An analytical description of displacement estimation which allows an objective evaluation and comparison of various displacement estimation techniques is presented. For evaluation and comparison rate-distortion functions are calculated and by this the impact of the 2D motion model of the displacement estimator and the amplitude and spatial resolution of the estimated sparse displacement vector held can be quantified. The rate-distortion function describes the relationship between the encoding bit-rate required for transmission of the measured displacement vector field and the variance of the displacement error. The impact of the spatial and amplitude resolution of the sparse displacement vector field is described by sampling and quantisation of an exact displacement signal. The 2D motion model is considered by low pass filtering the exact displacement signal before sampling and subsequent spatial interpolation. The analytical description is verified by simulations of various displacement estimation techniques, the 2D motion models of which can be described by the nearest neighbour, affine and bilinear displacement vector interpolation, at different amplitude and spatial resolutions. The analytical description allows one to optimise a displacement estimation technique for motion compensated image sequence coding. (C) 1997 Elsevier Science B.V.