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The knowledge of (relative) distances or angles in the scene can be used to obtain information about the metric structure. One of the easiest means to calibrate the scene at a metric level is the knowledge of the relative position of 5 or more points in general position. Assume the points are the metric coordinates of the projectively reconstructed points , then the transformation which upgrades the reconstruction from projective to metric can be obtained from the following equations

(F1) 
which can be rewritten as linear equations by eliminating .
Boufama et al. [9] investigated how some Euclidean constraints could be imposed on an uncalibrated reconstruction. The constraints they dealt with are known 3D points, points on a ground plane, vertical alignment and known distances between points.
Bondyfalat and Bougnoux [8] recently proposed a method in which the constraints are first processed by a geometric reasoning system so that a minimal representation of the scene is obtained. These constraints can be incidence, parallelism and orthogonality. This minimal representation is then fed to a constrained bundle adjustment.
The traditional approach taken by photogrammetrists [11,41,137,42] consists of immediately imposing the position of known control points during reconstruction. These methods use bundle adjustment [12] which is a global minimization of the reprojection error. This can be expressed through the following criterion:

(F2) 
where is the set of indices corresponding to the points seen in view and
describes the projection of a point with camera taking all distortions into account. Note that is known for control points and unknown for other points. It is clear that this approach results in a huge minimization problem and that, even if the special structure of the Jacobian is taken into account (in a similar way as was explained in Section A.2, it is computationally very expensive.
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Marc Pollefeys
20021122