Uncertainty ellipsoids calculations for complex 3D reconstructions

Many methods exist for the automatic and optimal 3D reconstruction of camera motion and scene structure from image sequence (´structure from motion´ or SfM). The solution to this problem is not unique: we obtain an other solution by changing the coordinate system where points and cameras are defined. On the other hand, existing methods provide some measure of confidence or uncertainty for the estimation when the ground truth is not available, using a gauge constraint which settle the reconstruction coordinate system. Here we justify and describe a method which estimate the uncertainty ellipsoids, when previous methods are not straightforward to use due to a huge number of parameters to fit. Many examples are given and discussed for big reconstructions