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

Abstract

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 non-degenerated 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 non-coplanar points. The latter fits a wider variety of scenes, as it is unsure to be able to find a second homography in the non-coplanar 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 so 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, the lesser the noise influence. We therefore propose a new 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 n synthetic scenes with strong planar degeneracy. The results show that the parallax beam improves the estimation of the camera motion in scene with planar degeneracy and remains usable when there is not any particular planar structure in the scene.

Trajectory Recovery and Terrain Reconstruction Based on Descent Images under Dual-Restrained Conditions: Tianwen-1

“…Based on the obtained homography matrix, the corresponding fundamental matrix is estimated according to the relationship between the fundamental matrix and the homography matrix if the data provide sufficient constraints. Specifically, the robust fundamental matrix is estimated from the points (may including some mismatching points) located outside the plane corresponding to the obtained homography matrix using the epipoles constrained parallax beam method [38]. The robust motion is obtained by decomposing the fundamental matrix.…”

“…For simplicity, let x i and Hx i have the same point error that has a distribution area of the circle of radius ε with the point as the center since ε (figured out from AC-RANSAC) represents point error more accurately. The parallax beams [38] of x i and Hx i are drawn to judge if they cover e 1 or e 2 . Set the initial values of two counters N F 1 and N F 2 to be zero.…”

“…The scene of the Tianwen-1 descent images is predominantly but not entirely planar, which is (quasi-) degenerate data for robust geometry model estimation. Rebert et al proposed a parallax beam algorithm to process the degenerate planar scene [38]. RANSAC for the (Quasi-) Degenerate data (QDEGSAC) algorithm solves the degenerate plane problem by running the RANSAC algorithm multiple times to calculate the rank of the data matrix [39].…”

Learning-based risk assessment and motion estimation by vision for unmanned aerial vehicle landing in an unvisited area

“…The planar area can be extracted through the homography estimation. 8,9 Without the need for a region extraction process, the roughness estimation from the optical flow field was proposed to measure the planarity of the surface. 10 In addition, researchers addressed the learning process to yield more practical versatility for UAV applications, such as supervised learning for texture classification, 11 neural network policy for navigation, 12 and deep reinforcement learning for marker recognition.…”