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The reprojection error is a geometric error corresponding to the image distance between a projected point and a measured one. It is used to quantify how closely an estimate of a 3D point recreates the point's true projection . More precisely, let be the projection matrix of a camera and be the image projection of , i.e. . The reprojection error of is given by , where denotes the Euclidean distance between the image points represented by vectors and .
Minimizing the reprojection error can be used for estimating the error from point correspondences between two images. Suppose we are given 2D to 2D point imperfect correspondences . We wish to find a homography and pairs of perfectly matched points and , i.e. points that satisfy that minimize the reprojection error function given by
So the correspondences can be interpreted as imperfect images of a world point and the reprojection error quantifies their deviation from the true image projections