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 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