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In this paper, an exact computation of the geometric error for homography is derived. We assume the Gaussian noise model for the perturbation of image coordinates and formulate the problem as a least squares minimization. This paper shows how to compute accurate geometric error through solving a polynomial of degree eight. This approach avoids falling into local minima that may occur when iterative methods are used. An application where this method can improve accuracy is discussed. Experiments comparing the geometric error with its approximation by the Sampson error are presented.