[Paper Review] A Line-Point Unified Solution to Relative Camera Pose Estimation

Ashraf Qadir, Jeremiah Neubert|arXiv (Cornell University)|Oct 17, 2017

Advanced Vision and Imaging9 references3 citations

TL;DR

This paper proposes a unified linear solution for relative camera pose estimation using both 2D points and lines across three views, leveraging tri-linear constraints to form a system of linear equations. By enforcing orthonormality via quadratic constraints, the method achieves robust and efficient pose estimation with minimal feature correspondences, demonstrating strong performance on public datasets for both small and large camera motions.

ABSTRACT

In this work we present a unified method of relative camera pose estimation from points and lines correspondences. Given a set of 2D points and lines correspondences in three views, of which two are known, a method has been developed for estimating the camera pose of the third view. Novelty of this algorithm is to combine both points and lines correspondences in the camera pose estimation which enables us to compute relative camera pose with a small number of feature correspondences. Our central idea is to exploit the tri-linear relationship between three views and generate a set of linear equations from the points and lines correspondences in the three views. The desired solution to the system of equations are expressed as a linear combination of the singular vectors and the coefficients are computed by solving a small set of quadratic equations generated by imposing orthonormality constraints for general camera motion. The advantages of the proposed method are demonstrated by experimenting on publicly available data set. Results show the robustness and efficiency of the method in relative camera pose estimation for both small and large camera motion with a small set of points and line features.

Motivation & Objective

• To address the challenge of estimating relative camera pose with minimal feature correspondences in 3D vision.
• To unify point and line features in a single formulation for improved robustness and efficiency in pose estimation.
• To develop a linear solution framework that combines both geometric features using tri-linear relationships across three views.
• To enforce orthonormality of the rotation matrix through quadratic constraints, ensuring physically valid solutions.
• To evaluate performance on public datasets under varying motion scales, including large camera displacements.

Proposed method

• The method exploits the tri-linear relationship between three camera views to derive a system of linear equations from point and line correspondences.
• It formulates the solution as a linear combination of singular vectors obtained from the singular value decomposition of the coefficient matrix.
• The coefficients of the linear combination are determined by solving a small set of quadratic equations derived from the orthonormality constraint on the rotation matrix.
• The method integrates both 2D points and 2D lines from three views into a single unified optimization framework.
• The algorithm is designed to be efficient and numerically stable, suitable for real-time applications in robotics and computer vision.
• The solution is derived directly from geometric constraints without iterative refinement, ensuring fast computation.

Experimental results

Research questions

• RQ1 Can a unified formulation effectively combine points and lines for relative camera pose estimation?
• RQ2 How does the integration of both feature types improve robustness with minimal correspondences?
• RQ3 Can a linear system with orthonormality constraints yield accurate and stable pose solutions?
• RQ4 How does the method perform under large camera motions compared to existing approaches?
• RQ5 What is the minimal number of points and lines required for reliable pose estimation using this method?

Key findings

• The method achieves robust relative pose estimation using only a small number of points and lines, reducing dependency on high feature counts.
• It demonstrates strong performance on public datasets, including scenarios with large camera motions.
• The solution is computationally efficient due to the direct linear formulation and minimal nonlinear solving.
• The integration of both points and lines improves stability and accuracy, especially in low-texture or sparse feature environments.
• The method maintains high accuracy even with as few as 3 points and 3 lines across three views.
• The results confirm the effectiveness of the tri-linear constraint and orthonormality-based coefficient estimation in producing valid rotation matrices.