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 ${\displaystyle {\hat {\mathbf {X} }}}$ recreates the point's true projection ${\displaystyle \mathbf {x} }$. More precisely, let ${\displaystyle \mathbf {P} }$ be the projection matrix of a camera and ${\displaystyle {\hat {\mathbf {x} }}}$ be the image projection of ${\displaystyle {\hat {\mathbf {X} }}}$, i.e. ${\displaystyle {\hat {\mathbf {x} }}=\mathbf {P} \,{\hat {\mathbf {X} }}}$. The reprojection error of ${\displaystyle {\hat {\mathbf {X} }}}$ is given by ${\displaystyle d(\mathbf {x} ,\,{\hat {\mathbf {x} }})}$, where ${\displaystyle d(\mathbf {x} ,\,{\hat {\mathbf {x} }})}$ denotes the Euclidean distance between the image points represented by vectors ${\displaystyle \mathbf {x} }$ and ${\displaystyle {\hat {\mathbf {x} }}}$.

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