A Minimal Solver for Relative Pose Estimation with Unknown Focal Length from Two Affine Correspondences

2025-12-28

AI Summary

This paper addresses the joint estimation of relative pose and focal length in IMU-aided visual systems. We propose a minimal solution requiring only two affine correspondences (ACs), solving for the three degrees-of-freedom relative rotation and unknown focal length under known intrinsic parameters (except focal length) and a vertical prior (i.e., known gravity direction). Our key innovation lies in embedding the vertical prior directly into affine geometric constraints, yielding a compact quartic nonlinear system involving only the focal length and rotation angles. This system is efficiently solved using a polynomial eigenvalue method. To the best of our knowledge, this is the first 2-AC minimal solver leveraging the vertical prior. Extensive evaluations on both synthetic and real-world datasets demonstrate that our method significantly outperforms state-of-the-art approaches in accuracy and robustness.

Technology Category

• Intelligent Robots: State Estimation
• Computer Vision: Motion & Tracking
• Machine Learning: Matrix & Tensor Methods

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

In this paper, we aim to estimate the relative pose and focal length between two views with known intrinsic parameters except for an unknown focal length from two affine correspondences (ACs). Cameras are commonly used in combination with inertial measurement units (IMUs) in applications such as self-driving cars, smartphones, and unmanned aerial vehicles. The vertical direction of camera views can be obtained by IMU measurements. The relative pose between two cameras is reduced from 5DOF to 3DOF. We propose a new solver to estimate the 3DOF relative pose and focal length. First, we establish constraint equations from two affine correspondences when the vertical direction is known. Then, based on the properties of the equation system with nontrivial solutions, four equations can be derived. These four equations only involve two parameters: the focal length and the relative rotation angle. Finally, the polynomial eigenvalue method is utilized to solve the problem of focal length and relative rotation angle. The proposed solver is evaluated using synthetic and real-world datasets. The results show that our solver performs better than the existing state-of-the-art solvers.

Problem

• Estimates relative pose and focal length from two affine correspondences
• Reduces degrees of freedom using known vertical direction from IMU
• Solves polynomial equations for focal length and rotation angle

Innovation

• Estimates 3DOF relative pose and focal length
• Uses two affine correspondences with known vertical direction
• Solves via polynomial eigenvalue method for two parameters