Fine estimators of two-dimensional parameters and application to spatial shift estimation

This paper presents a fast technique for fine estimation of two-dimensional (2-D) parameters, based on a parabolic interpolation of the same ambiguity function samples, and aimed at block-oriented estimation of the spatial shift between pairs of images in video sequences. Expressions for the bias and variance of the position error and the prediction error are derived. The method is tested using a synthetically generated autocorrelation function, varying the directionality and the eccentricity factor, in order to compare the performance of the proposed 2-D estimator to the case of two separate one-dimensional (1-D) estimators. The method has also been applied in vision systems, evidencing encouraging results for estimating the parameters of sophisticated global motion models from real images.