Certifiably Optimal Non-minimal Relative Pose Estimation without Disambiguation

Core Concepts

This paper presents a novel approach for directly estimating the correct relative camera pose from correspondences without the need for a post-processing step to enforce the cheirality constraint. The method formulates the relative pose estimation as a Quadratically Constrained Quadratic Program (QCQP) and applies appropriate constraints to ensure the estimation of a camera pose that corresponds to a valid 3D geometry and is globally optimal when certified.

Abstract

The paper addresses the problem of estimating the relative pose between two calibrated views, which is a fundamental task in computer vision with applications in Structure from Motion (SfM) and Simultaneous Localization And Mapping (SLAM).
The traditional approach involves two steps: 1) estimating the essential matrix between the views, and 2) disambiguating among the four candidate relative poses that satisfy the epipolar geometry. The paper proposes a novel method, called C2P, that bypasses the second stage and directly estimates the correct relative camera pose from correspondences without needing a post-processing step to enforce the cheirality constraint.
The key contributions are:

C2P formulates the relative pose estimation as a QCQP and applies appropriate constraints to ensure the estimation of a camera pose that corresponds to a valid 3D geometry and is globally optimal when certified.
The paper derives a novel characterization of the normalized essential manifold that is needed to enforce a geometrically valid solution.
C2P can directly detect near-pure rotational motions, which is known to be challenging for existing methods.
Extensive experiments on synthetic and real-world data demonstrate the efficacy, efficiency, and accuracy of the proposed approach compared to state-of-the-art methods.

Stats

The paper does not provide any specific numerical data or statistics. The experiments focus on evaluating the accuracy and runtime performance of the proposed C2P method compared to existing approaches.

Quotes

None.

Key Insights Distilled From

From Correspondences to Pose

by Javi... at arxiv.org 03-29-2024

https://arxiv.org/pdf/2312.05995.pdf

Deeper Inquiries

How could the proposed C2P method be extended to handle outliers in the input correspondences

To extend the C2P method to handle outliers in the input correspondences, we can incorporate robust estimation techniques. One approach could be to use robust cost functions, such as Huber or Tukey loss functions, during the optimization process. These cost functions can down-weight the influence of outliers, leading to more robust estimates. Additionally, techniques like RANSAC (Random Sample Consensus) can be integrated into the method to iteratively fit the model to a subset of inlier correspondences, effectively filtering out outliers. By combining robust cost functions and robust estimation strategies, the C2P method can be enhanced to handle outliers effectively.

What are the potential limitations or failure cases of the C2P approach, and how could they be addressed in future work

While the C2P approach offers significant advantages in terms of efficiency, accuracy, and global optimality, there are potential limitations and failure cases to consider. One limitation is the assumption of noise-free correspondences, which may not hold true in practical scenarios. To address this, future work could focus on incorporating robust estimation techniques to handle noisy data effectively. Another limitation could be the scalability of the method to very large datasets, as the computational complexity may increase significantly with a large number of correspondences. This could be addressed by exploring parallel computing strategies or optimizing the algorithm for scalability. Additionally, the method may struggle with extreme cases of outliers or incorrect correspondences, which could be mitigated by developing more sophisticated outlier rejection mechanisms or data preprocessing steps.

What other computer vision tasks beyond relative pose estimation could benefit from the insights and techniques developed in this paper

The insights and techniques developed in the C2P paper have broader implications beyond relative pose estimation and could benefit various computer vision tasks. One such task is Structure from Motion (SfM), where estimating camera poses and reconstructing 3D scenes from images are fundamental. By leveraging the efficient and globally optimal optimization framework of C2P, SfM algorithms could achieve more accurate and robust reconstructions. Additionally, Simultaneous Localization And Mapping (SLAM) systems could benefit from the direct estimation of camera poses without the need for disambiguation, leading to more efficient and reliable localization and mapping in real-time applications. Other tasks like object tracking, visual odometry, and scene understanding could also leverage the insights from C2P to improve their performance and robustness.