Efficient closed-form approaches for pose estimation using Sylvester forms

2026-04-16

AI Summary

This work addresses the computationally demanding yet critical nonlinear least-squares problem in pose estimation for real-time computer vision. By introducing a suitable parametrization of rotations, the problem is reformulated as a system of polynomial equations. The authors propose a novel class of resultant solvers based on Sylvester matrices that enable efficient closed-form solutions. This approach substantially reduces computational complexity while preserving high numerical accuracy. Experimental results demonstrate that the method outperforms state-of-the-art techniques in terms of runtime on both 3D–3D and 3D–2D pose estimation tasks, offering a practical solution for time-sensitive applications.

Technology Category

• Intelligent Robots: State Estimation
• Computer Vision: Biometrics, Face, Gesture & Pose
• Machine Learning: Learning with Manifolds

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

Solving non-linear least-squares problem for pose estimation (rotation and translation) is often a time consuming yet fundamental problem in several real-time computer vision applications. With an adequate rotation parametrization, the optimization problem can be reduced to the solution of a~system of polynomial equations and solved in closed form. Recent advances in efficient closed form solvers utilizing resultant matrices have shown a promising research direction to decrease the computation time while preserving the estimation accuracy. In this paper, we propose a new class of resultant-based solvers that exploit Sylvester forms to further reduce the complexity of the resolution. We demonstrate that our proposed methods are numerically as accurate as the state-of-the-art solvers, and outperform them in terms of computational time. We show that this approach can be applied for pose estimation in two different types of problems: estimating a pose from 3D to 3D correspondences, and estimating a pose from 3D points to 2D points correspondences.

Problem

• pose estimation
• non-linear least-squares
• real-time computer vision
• rotation and translation
• 3D-2D correspondences

Innovation

• Sylvester form
• closed-form solver
• pose estimation
• resultant matrix
• polynomial system