Parallax beam: a vision-based motion estimation method robust to nearly planar scenes

International audience; In computer vision, the epipolar geometry embeds the geometrical relationship between two views of a scene. This geometry is degenerated for planar scenes as they do not provide enough constraints to estimate it without ambiguity. Nearly planar scenes can provide the necessary constraints to resolve the ambiguity. But classic estimators such as the 5-point or 8-point algorithm combined with a random sampling strategy are likely to fail in this case because a large part of the scene is planar and it requires lots of trials to get a nondegenerated sample. However, the planar part can be associated with a homographic model and several links exist between the epipolar geometry and homographies. The epipolar geometry can indeed be recovered from at least two homographies or one homgraphy and two noncoplanar points. The latter fits a wider variety of scenes, as it is unsure to be able to find a second homography in the noncoplanar points. This method is called plane-and-parallax. The equivalence between the parallax and the epipolar lines allows to recover the epipole as their common intersection and the epipolar geometry. Robust implementations of the method are rarely given, and we encounter several limitations in our implementation. Noisy image features and outliers make the lines not to be concurrent in a common point. Also off-plane features are unequally influenced by the noise level. We noticed that the bigger the parallax is, the lesser the noise influence is. We, therefore, propose a model for the parallax that takes into account the noise on the features location to cope with the previous limitations. We call our method the “parallax beam.” The method is validated on the KITTI vision benchmark and on synthetic scenes with strong planar degeneracy. The results show that the parallax beam improves the estimation of the camera motion in the scene with planar degeneracy and remains usable when there is not any particular planar structure in the scene.