Abstract

In this paper, we present a new epipolar constraint for com- puting the rotation between two images independently of the translation. Against the common belief in the field of geometric vision that it is not possible to find one independently of the other, we show how this can be achieved by relatively simple two-view constraints. We use the fact that translation and rotation cause fundamentally different flow fields on the unit sphere centered around the camera. This allows to establish inde- pendent constraints on translation and rotation, and the latter is solved using the Grobner basis method. The rotation computation is completed by a solution to the cheiriality problem that depends neither on trans- lation, nor on feature triangulations. Notably, we show for the first time how the constraint on the rotation has the advantage of remaining ex- act even in the case of translations converging to zero. We use this fact in order to remove the error caused by model selection via a non-linear optimization of rotation hypotheses. We show that our method operates in real-time and compare it to a standard existing approach in terms of both speed and accuracy.