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

TL;DR

This paper introduces a minimal solver for estimating relative pose and focal length from two affine correspondences, leveraging known vertical direction to reduce problem complexity and improve accuracy.

Contribution

A novel solver that estimates 3DOF relative pose and focal length using only two affine correspondences with known vertical direction, employing polynomial eigenvalue method.

Findings

Performs better than existing state-of-the-art solvers on synthetic data.

Effective in real-world datasets with unknown focal length.

Reduces problem complexity by utilizing known vertical direction.

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.