PoseGravity: Pose Estimation from Points and Lines with Axis Prior

TL;DR

This work tackles camera pose estimation under an axis prior, such as gravity, which reduces the pose from six to four degrees of freedom and enables efficient algorithms. It unifies point and line features in both minimal and overconstrained configurations, and provides closed-form solutions, including specialized, fast forms for planar and minimal cases. The method hinges on a conic-based loss with a cubic-root solution from a degenerate conic and a circle-intersection step, achieving an O($n$) runtime. Empirical results across synthetic and real-world scenarios show strong accuracy and robustness, with notable gains in planar and minimal configurations and competitive performance against state-of-the-art axis-prior solvers. This approach offers practical benefits for robotics and AR tasks where gravity or axis measurements are readily available and feature sets are mixed.

Abstract

This paper presents a new algorithm to estimate absolute camera pose given an axis of the camera's rotation matrix. Current algorithms solve the problem via algebraic solutions on limited input domains. This paper shows that the problem can be solved efficiently by finding the intersection points of a hyperbola and the unit circle. The solution can flexibly accommodate combinations of point and line features in minimal and overconstrained configurations. In addition, the two special cases of planar and minimal configurations are identified to yield simpler closed-form solutions. Extensive experiments validate the approach.

Figures (5)

• Figure 1: Examples of problem loss spaces with relevant objects in the $x{\text{-}}y$ plane. The darker regions correspond to lower loss values over objective function $\mathbf{\Omega}$, the red circle is the unit circle, and the green dots are the global minimums of $\mathbf{\Omega}$ on the unit circle. (a), (b) show general problems. The red hyperbola corresponds to the derivative conic $\mathbf{\Lambda}$. The dashed red lines are the lines constituting the degenerate conic $\mathbf{\Sigma}$. (a) has four intersections (stationary points) while (b) only has two. (c), (d) show minimal configurations. The dashed line here is the zero level curve of the degenerate loss conic $\mathbf{\Omega}$ (single double line). In (c), the line intersects the circle for two solutions while in (d) a solution is recovered from an infeasible problem with no intersections. (e) shows a planar configuration. The dashed line here is the eigenvector corresponding to the smallest eigenvalue of $\mathbf{\Omega'}$. Note this line goes through the origin.
• Figure 2: Performance of proposed algorithm on various input types, configurations, and levels of $\theta_{noise}$. Left: rotation error $\theta_{err}$, Right: translation error $T_{err}$. Configurations - Top: Image Plane, Middle: Spherical, Bottom: Planar.
• Figure 3: Performance of the algorithm in image plane configuration under different levels of $\theta_{noise}$ compared to general solvers for various levels of $\epsilon_{noise}$. Left: rotation error $\theta_{err}$, Right: translation error $T_{err}$. Top: $n=3$ points, Bottom: $n=20$ points. For our solvers, the number in legend refers to standard deviation of $\theta_{noise}$ applied. P3P from LambdaTwist, PnP from SQPnP.
• Figure 4: Examples of basketball court registration using the proposed algorithm on point detections. (a) shows the captured image with the green dots marking the three detected landmarks. (b), (c) shows the image projected onto the 3D court ground plane using the estimated camera pose. A good registration aligns the court's boundaries well with the projected image edges showing a rectified birdseye view of the court. (b) uses two of the detections (backboard rim points) while (c) uses all three
• Figure 5: Examples of basketball court registration from lines formed from manually annotated contours. (a) shows the captured image with noisy court boundary annotations marked with red dots. (b), (c) show a similar projection as Figures \ref{['fig:4b']}/\ref{['fig:4c']}. (b) estimates pose without the use of the gravity vector while (c) uses the proposed algorithm and is more robust to label noise.