Reprojection error

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 formula_1 recreates the point's true projection formula_2. More precisely, let formula_3 be the projection matrix of a camera and formula_4 be the image projection of formula_1, i.e. formula_6. The reprojection error of formula_1 is given by formula_8, where formula_8 denotes the Euclidean distance between the image points represented by vectors formula_2 and formula_4.
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 formula_12. We wish to find a homography formula_13 and pairs of perfectly matched points formula_14 and formula_15, i.e. points that satisfy formula_16 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 formula_18