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 $hat\{mathbf\{x$be 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 $hat\{mathbf\{x$.