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In this paper we develop a novel approach called the compensated HS (CHS) optical flow estimation algorithm to improve the precision of the large displacement optical flow field. For the lack of the higher order term in the optical flow constraint equation, the traditional optical flow estimation based on the first-order gradient always produce the optical flow field with obvious error in the case of large image displacement. We compensate the optical flow constraint equation with the fitted higher-order term through matching the corner points extracted by the Harris detector. And then, we use it to construct the new energy function and derive the new Gauss-Seidel iterative solution of the optical flow. To the existence of multi-motion pattern, we adopt k-means algorithm to cluster these pattern and point-by-point fit the higher order terms of different pattern. The final experiments show that this algorithm could obviously improve the precision of the large displacement optical flow and of the optical flow in the smooth region.