Efficient Solution of Point-Line Absolute Pose (2404.16552v1)

Abstract: We revisit certain problems of pose estimation based on 3D--2D correspondences between features which may be points or lines. Specifically, we address the two previously-studied minimal problems of estimating camera extrinsics from $p \in { 1, 2 }$ point--point correspondences and $l=3-p$ line--line correspondences. To the best of our knowledge, all of the previously-known practical solutions to these problems required computing the roots of degree $\ge 4$ (univariate) polynomials when $p=2$, or degree $\ge 8$ polynomials when $p=1.$ We describe and implement two elementary solutions which reduce the degrees of the needed polynomials from $4$ to $2$ and from $8$ to $4$, respectively. We show experimentally that the resulting solvers are numerically stable and fast: when compared to the previous state-of-the art, we may obtain nearly an order of magnitude speedup. The code is available at \url{https://github.com/petrhruby97/efficient\_absolute}

• The paper presents novel solutions that reduce the polynomial degree to quadratic for P2P1L and quartic for P1P2L, simplifying complex algebraic computations.
• It demonstrates nearly an order of magnitude speedup and enhanced numerical stability compared to prior state-of-the-art methods.
• The work enables robust real-time applications in fields like robotics and augmented reality by delivering efficient and reliable pose estimation.

Simplifying Camera Pose Estimation: A Discussion of New Solutions for Point-Line Correspondences

Overview

Camera pose estimation involving point-line correspondences plays a crucial role in many real-world applications ranging from augmented reality to autonomous driving. This paper proposes new solutions that simplify the mathematical computations involved in this task, specifically for scenarios involving a mix of two points and one line (P2P1L) or one point and two lines (P1P2L). The authors present simplified algebraic solutions that enhance computational efficiency and numerical stability.

Key Contributions

Novel Solutions

Previous methods for handling mixed cases in pose estimation employed solutions that were algebraically complex and computationally demanding. In contrast, this paper introduces solutions that drastically reduce the degree of required polynomial computations:

• For the P2P1L problem, the solution now involves solving a quadratic polynomial, reducing from a degree four.
• For the P1P2L problem, a quartic polynomial solution is used instead of the previously required octic degree.

These simplifications result not only in reduced computational overhead but also in improved numerical stability during the calculations.

Implementation and Evaluation

The solutions have been implemented, and the code is released for public use, increasing transparency and fostering further innovation. The experimental comparisons with state-of-the-art methods demonstrated significant improvements:

• Nearly an order of magnitude speedup was observed compared to existing methods.
• The new solvers exhibited better numerical stability, making these methods suitable for practical applications requiring high reliability.

Practical Implications and Future Prospects

Industry Applications

The need for efficient and robust pose estimation algorithms is pressing in domains like robotics and augmented reality. Faster solutions that do not compromise on accuracy provide an edge by enabling real-time processing and reducing computational costs.

Scope of Improvement

While this research pushes the envelope on simplifying pose estimation problems, the paper also opens several avenues for future exploration:

• Adapting these solutions for more complex scenarios involving more mixed correspondences.
• Further analysis could explore the integration of these solutions with deep learning frameworks to handle cases with noisy or incomplete data.

Closing Thoughts

This paper marks a significant stride in addressing the complexity of pose estimation problems involving mixed correspondences. By providing more computationally efficient and robust solutions, this work not only advances academic understanding but also offers tangible benefits for practical applications. Future work, as suggested by the findings, could help in fine-tuning these solutions to cater to a wider array of real-world applications, driving forward the capabilities of machine vision systems.