Reprojection error

The reprojection error is a "geometric error" corresponding to the image distancebetween a projected point and a measured one. It is used to quantify how closely anestimate of a 3D point $$hat{mathbf{X recreates the point's true projection$$mathbf{x}. More precisely, let $$mathbf{P} be the
projection matrix of a camera and $$hat{mathbf{xbe the image projection of $$hat{mathbf{X, i.e.$$hat{mathbf{x=mathbf{P} , hat{mathbf{X.The reprojection error of $$hat{mathbf{X is given by$$d(mathbf{x}, , hat{mathbf{x), where $$d(mathbf{x}, , hat{mathbf{x)denotes the Euclidean distance between the image points represented by vectors$$mathbf{x} and $$hat{mathbf{x.