Reprojection error
The reprojection error is a geometric error corresponding to the image distance between a projected point and a measured one, mostly occurred in old camera and phones. 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. . 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.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
Consequences of reprojection error
There are many consequences of reprojection errors, such as
- White or black lines that resemble hair in the photo, more frequently on patterned objects than others.
- White or black bars covering most part of the photo.
- some part of the photo may appear darker, brighter, or distorted.
- The photo appear entirely black or white.
References
- Richard Hartley and Andrew Zisserman (2003). Multiple View Geometry in computer vision. Cambridge University Press. ISBN 0-521-54051-8.