PnP*: A certifiable solver for Perspective-n-Point

Multi-camera systems are increasingly adopted in robotics and autonomous navigation for their wide field of view, flexibility, and fault tolerance. Nevertheless, existing PnP solvers fail to handle multiple projection centers. This paper introduces a virtual point formulation that bridges the standard PnP and generalized pose problems, enabling a unified pipeline that transforms existing PnP solvers into generalized pose solvers. Based on this framework, we derive three Virtual-point-based Generalized Pose solvers, namely VGPc, VGPq, and VGPr, leveraging Cayley, quaternion, and rotation-matrix parameterizations, respectively. Extensive experiments demonstrate that the proposed solvers inherit the accuracy and efficiency of original PnP algorithms while significantly outperforming existing generalized solvers. Specifically, VGPc achieves higher estimation accuracy under heteroscedastic noise conditions, VGPq maintains global optimality, whereas VGPr provides superior computational efficiency without accuracy degradation.

We present PnP-Transformer, a neural pose solver designed as an iterative-free, differentiable alternative to classical PnP-RANSAC algorithms. PnP-Transformer regresses the 6D object pose by processing predicted semi-dense 2D-3D correspondence fields alongside confidence scores, while mapping geometric inputs into a continuous latent space. To evaluate its practical utility, we integrate PnP-Transformer into a zero-shot 6D pose estimation pipeline, where the correspondence module and pose solver are trained separately. PnP-Transformer achieves a 41.2% mean AR score with low latency (0.46 s/obj) on seven core BOP benchmark datasets, surpassing all prior baselines (such as RayPose with 39.1% AR) but one (Co-op with 58.4% AR). When the pose solver is replaced with EPnP-RANSAC (similar to Co-op) while keeping the correspondence module unchanged, the RANSAC alternative outperforms PnP-Transformer on six of the seven datasets by reaching 52.2% mean AR at a cost of an additional 60 ms per object, revealing an accuracy-latency trade-off. Code and pretrained models are available at https://github.com/ebylmz/pnp-transformer.

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.