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

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 $\hat$ and pairs of perfectly matched points $\hat$ and $\hat_i'$, i.e. points that satisfy $\hat' = \hat\mathbf$ that minimize the reprojection error function given by
:$\sum_i d(\mathbf, \hat)^2 + d(\mathbf', \hat')^2$
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 $\hat, \hat'$

References

*{{cite book ,
author=Richard Hartley and Andrew Zisserman ,
title=Multiple View Geometry in computer vision ,
publisher=Cambridge University Press,
year=2003 ,
isbn=0-521-54051-8

Geometry in computer vision