A Simple Algebraic Solution for Estimating the Pose of a Camera from Planar Point Features

2025-08-03

AI Summary

This paper addresses camera pose estimation from planar point correspondences. We propose a hierarchical algebraic solution: first, the plane’s normal vector is computed algebraically from point correspondences; subsequently, camera position, distance to the plane, and the full 6-DoF pose are recovered sequentially via a linear projection model. To enhance robustness against noise, we introduce a novel normal-vector averaging strategy. Furthermore, we formulate a compact algebraic framework integrating quaternions and linear projection, eliminating the need for iterative optimization and significantly improving computational efficiency. Experimental results demonstrate that the method achieves sub-pixel accuracy and strong robustness under both Gaussian noise and outlier contamination. It is applicable to practical tasks including homography-based calibration, augmented reality registration, and industrial planar localization.

Technology Category

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Abstract

This paper presents a simple algebraic method to estimate the pose of a camera relative to a planar target from $n geq 4$ reference points with known coordinates in the target frame and their corresponding bearing measurements in the camera frame. The proposed approach follows a hierarchical structure; first, the unit vector normal to the target plane is determined, followed by the camera's position vector, its distance to the target plane, and finally, the full orientation. To improve the method's robustness to measurement noise, an averaging methodology is introduced to refine the estimation of the target's normal direction. The accuracy and robustness of the approach are validated through extensive experiments.

Problem

• Estimates camera pose from planar point features
• Determines normal vector, position, distance, orientation
• Improves robustness to noise via averaging

Innovation

• Algebraic method for camera pose estimation
• Hierarchical structure for normal and position
• Averaging methodology to reduce noise impact