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
x
.
More precisely, let
be the projection matrix of a camera and
{\displaystyle {\hat {\mathbf {x} }}}
be the image projection of
The reprojection error of
denotes the Euclidean distance between the image points represented by vectors
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
and pairs of perfectly matched points
, i.e. points that satisfy
that minimize the reprojection error function given by 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