Towards a minimal solution for the relative pose between axial cameras

Abstract

The problem of estimating the relative pose between axial cameras from pairwise point correspondences is still open to improvement. The state-of-the-art solutions are either too specific in its scope, assuming certain types of correspondences; too broad, dealing with all types of generalized cameras and failing to address the specific issues of axial cameras; or non-minimal linear solutions. The aim of this paper is to pursue new insights on axial cameras that can lead to a suitable minimal solution for this problem. We propose a new formulation for modeling the intersection of back-projection rays of axial cameras through a 5×5 essential matrix that enables a better understanding of some particular axial configurations and leads to a new set of polynomial equations that proves to be useful in constraining the motion estimation. These equations enable to compute a solution from 10 correspondences, an improvement over the 16-point algorithm, which is the state-of-the-art solution within our aimed scope. Both synthetic and real experiments show that our algorithm achieves a better performance than the 16-point algorithm in the context of robust optimization with RANSAC.

Relative Pose Estimation From Image Correspondences Under a Remote Center of Motion Constraint

“…7(c), it is very challenging for our method (as well as the 5-point algorithm) to work reliably in video sequences with high frame rates. The next step is therefore to extend the remote center of motion constraint to other components of SfM/SLAM systems, such as the ressectioning (pnp) problem [23], the relative pose between stereo pairs [24], and multi-view bundle adjustment [25].…”

Automatic Camera Calibration Using Multiple Sets of Pairwise Correspondences

“…There is a minimal solution for the relative pose between stereo pairs using 6 pairwise correspondences [16] that estimates an up-to scale relative pose solution using 5 correspondences with one camera [25] and solves the scale factor with an additional correspondence from another camera. A non-minimal solution using 10 correspondences was also proposed for the case of any arbitrary combination of correspondences between the 4 views of two stereo rigs [17]. Since in this paper we focus on both intrinsic and extrinsic calibration from pairwise correspondences, the above mentioned works relate but do not directly apply.…”

“…Thus, we propose a modified RANSAC version specifically designed to simultaneously sample multiple datasets. The usefulness of such RANSAC extension goes beyond the calibration problem at hands and can benefit other algorithms such as Structure-from-Motion (SfM) using stereo cameras [16], [17], multi-view camera rigs [18], [19], or a mixture of point and plane correspondences [20], [21]. The contributions in this paper can be summarised as follows:…”

Rolling Shutter Camera Relative Pose: Generalized Epipolar Geometry

“…Difference with axial camera An axial camera is a particular case of non-central cameras where all the backprojection rays intersect a line in 3D (the axis) [26]. The linear rolling shutter camera give rise to an axis where every back-projection ray intersects (center of projection).…”

“…The linear rolling shutter camera give rise to an axis where every back-projection ray intersects (center of projection). However, the temporal-dynamic nature of linear rolling shutter camera distinguishes itself from the axial camera [26], where the internal displacement (linear velocity) is unknown and to estimate. Even though our linear RS essential matrix shares the same size as axial camera essential matrix [25], the detailed structure is different.…”