How is the reprojection error calculated in Matlab's triangulate function? Sadly, the documentation gives no mathematical formula
How is the reprojection error calculated in Matlab's triangulate function?
Sadly, the documentation gives no mathematical formula.
It only says: The vector contains the average reprojection error for each M world point.
What is the procedure/Matlab uses when calculating this error?
I searched SOF but found nothing on this IMHO important question.
UPDATE: How can they use this error to filter out bad matches here : http://se.mathworks.com/help/vision/examples/sparse-3-d-reconstruction-from-two-views.html
Answer
AFAIK The reprojection error is calculated always in the same way (in the field of computer vision in general).
The reprojection is (as the name says) the error between the reprojected point in the camera and the original point.
So from 2 (or more) points in the camera you triangulate and get 3D points in the world system. Due to errors in the calibration of the cameras, the point will not be 100% accurate. What you do is take the result 3D point (P) and with the camera calibration parameters project it in the cameras again, obtaining new points (\hat{p}) near the original ones (p).
Then you calculate the euclidean distance between the original point and the "reprojected" one.
In case you want to know a bit more about the method used by Matlab, I'll enhance the bibliography they use giving you also the page number:
Multiple View Geometry in Computer Vision by Richard Hartley and Andrew Zisserman (p312). Cambridge University Press, 2003.
But basically it is a least squares minimization, that has no geometrical interpretation.