Globally Optimal Pose from Orthographic Silhouettes

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.

6-DoF pose estimation is a critical task in autonomous rendezvous and proximity operations. In the case of an unknown target, this task becomes challenging as it shall be paired with the reconstruction of the target shape model. In this article, we propose a novel framework for single-shot shape and pose estimation of unknown spacecraft objects. Given a single image, we first reconstruct a 3D shape model of the target, then estimate the relative six-degrees-of-freedom pose by learning dense 2D-3D correspondences. The image features are extracted using a frozen DINOv3 vision transformer, while the geometric features are computed from the reconstructed point cloud using a trainable dynamic graph convolutional neural network encoder. A dual-stream transformer matcher refines descriptors through alternating self- and cross-attention, producing soft correspondences that are passed to a Perspective-$n$-Point solver for pose recovery. We evaluate the method on the SPE3R dataset and consider FoundationPose as a representative baseline for current state-of-the-art capabilities. Results show reliable pose estimates achieving 0.157 degrees mean pointing error using only a single image and reconstructed geometry, demonstrating strong generalization to unseen spacecraft.

Solving non-linear least-squares problem for pose estimation (rotation and translation) is often a time consuming yet fundamental problem in several real-time computer vision applications. With an adequate rotation parametrization, the optimization problem can be reduced to the solution of a~system of polynomial equations and solved in closed form. Recent advances in efficient closed form solvers utilizing resultant matrices have shown a promising research direction to decrease the computation time while preserving the estimation accuracy. In this paper, we propose a new class of resultant-based solvers that exploit Sylvester forms to further reduce the complexity of the resolution. We demonstrate that our proposed methods are numerically as accurate as the state-of-the-art solvers, and outperform them in terms of computational time. We show that this approach can be applied for pose estimation in two different types of problems: estimating a pose from 3D to 3D correspondences, and estimating a pose from 3D points to 2D points correspondences.