From Correspondences to Pose: Non-minimal Certifiably Optimal Relative Pose without Disambiguation (2312.05995v2)

Abstract: Estimating the relative camera pose from $n \geq 5$ correspondences between two calibrated views is a fundamental task in computer vision. This process typically involves two stages: 1) estimating the essential matrix between the views, and 2) disambiguating among the four candidate relative poses that satisfy the epipolar geometry. In this paper, we demonstrate a novel approach that, for the first time, bypasses the second stage. Specifically, we show that it is possible to directly estimate the correct relative camera pose from correspondences without needing a post-processing step to enforce the cheirality constraint on the correspondences. Building on recent advances in certifiable non-minimal optimization, we frame the relative pose estimation as a Quadratically Constrained Quadratic Program (QCQP). By applying the appropriate constraints, we ensure the estimation of a camera pose that corresponds to a valid 3D geometry and that is globally optimal when certified. We validate our method through exhaustive synthetic and real-world experiments, confirming the efficacy, efficiency and accuracy of the proposed approach. Code is available at https://github.com/javrtg/C2P.

• The paper introduces a certifiably optimal approach that directly estimates the relative pose from correspondences, bypassing the traditional two-stage method.
• The methodology frames the pose problem as a Quadratically Constrained Quadratic Program relaxed to a Semidefinite Program to ensure global optimality.
• Experimental results show improved runtime and accuracy over state-of-the-art methods, enhancing real-time performance in SfM and SLAM applications.

Non-minimal Certifiably Optimal Relative Pose Estimation

This paper presents a novel approach to estimating the relative pose between two calibrated camera views, focusing on bypassing the traditional two-stage process. The authors propose a method that directly estimates the correct relative camera pose from correspondences without requiring the disambiguation step typically necessary to enforce the cheirality constraint, which demands that 3D points lie in front of the camera. This paper frames the relative pose estimation problem as a Quadratically Constrained Quadratic Program (QCQP), utilizing advancements in certifiable non-minimal optimization.

Summary of the Approach

The traditional process of estimating relative camera pose involves two stages: first, estimating the essential matrix from at least five correspondences, and second, disambiguating among the four candidate poses satisfying the epipolar geometry. The novel contribution of this paper is the introduction of a certifiably optimal approach that eliminates the need for the second stage. The method leverages the properties of the camera projection geometry to directly solve the relative pose in a single optimization step.

Key to this approach is the integration of geometric constraints into the optimization problem. The authors utilize a QCQP, which is relaxed to a Semidefinite Program (SDP) to ensure a global and certifiable solution. The mathematical framework shows that by incorporating convex optimization techniques, it is feasible to ensure that the estimated pose corresponds to the valid 3D geometry. This is a substantial advancement over methods that separately handle these steps, typically using non-convex optimization strategies.

Results and Implications

The paper provides comprehensive validation of the proposed method through synthetic and real-world experiments. The results demonstrate that the method is both effective and efficient, achieving high accuracy relative to existing approaches. Performance is compared against state-of-the-art methods such as those presented by Briales et al. and Garc�a-Salguero et al., with the novel approach outperforming these in terms of runtime efficiency and pose accuracy.

One of the significant implications of this research is the potential improvements in applications such as Structure from Motion (SfM) and Simultaneous Localization and Mapping (SLAM). By reducing the computational complexity and eliminating the need for post-processing disambiguation of the pose, this method could enhance real-time performance and robustness of localization and mapping systems in dynamic environments.

Future Developments

This research opens new avenues for enhancements in pose estimation algorithms, particularly in the field of incorporating convex optimization schemes to ensure globally optimal solutions without the overhead of iterative disambiguation. Future work could explore the integration of this method into larger SLAM systems and robotic vision applications, as well as extending the technique to incorporate more complex camera models and multi-view scenarios.

Overall, this paper contributes to the corpus of computer vision by simplifying and improving the computational aspects of a foundational problem. The authors have laid groundwork for potentially significant improvements in practical computer vision systems by efficiently solving the relative pose estimation problem with a novel one-step globally optimal approach.