Reprojection error

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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 $\hat{\mathbf{X}}$ 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 $\hat{\mathbf{x}}$ .