Reprojection error explained
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
} recreates the point's true projection
. More precisely, let
be the
projection matrix of a
camera and
} be the image projection of
}, i.e.
}=\mathbf \, \hat. The reprojection error of
} is given by
}), where
}) denotes the
Euclidean distance between the image points represented by vectors
and
}.
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
} and
}_i', i.e. points that satisfy
}' = \hat\mathbf that minimize the reprojection error function given by
})^2 + d(\mathbf', \hat')^2So 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'
References
- Book: Richard Hartley and Andrew Zisserman . Multiple View Geometry in computer vision . Cambridge University Press. 2003 . 0-521-54051-8.
