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We present a novel approach for adaptive precision motion estimation based on a classification of the residual error curvature. A fast algorithm is proposed to estimate the curvature of the interpolated residual surface using the error samples after integer precision motion estimation. We also propose an original technique to compute and successively update a set of thresholds using the information from previously coded frames. The optimal motion vector precision is then selected for each block according to the current thresholds. The approach is compared in terms of PSNR of the motion compensated reconstruction against conventional state of the art sub-pel motion estimation algorithms, and it is shown to efficiently reduce complexity and coding times of a typical video encoder with negligible effects on the prediction accuracy.