Virtual-point-based Solutions to Handle Generalized Absolute Pose Problem

Estimating the relative poses of multi-camera systems is a fundamental problem in computer vision, with critical applications in autonomous vehicles, mobile devices, and unmanned aerial vehicles (UAVs). However, existing solutions often suffer from high computational complexity or rely on an excessive number of point correspondences, limiting their real-world applicability. To address these limitations, we propose two efficient minimal solvers for estimating the relative poses of multi-camera systems using a novel parameterization. The first solver leverages the vertical direction prior provided by Inertial Measurement Units (IMUs), while the second utilizes the rotation axis direction prior from IMUs. Our methods require only four point correspondences and reduce the problem of multi-camera relative pose estimation to solving a univariate 6th-degree polynomial, a significant improvement over existing approaches, which typically involve 8th-degree polynomials. This reduction in computational complexity and correspondence requirements makes our solvers particularly effective when integrated into RANSAC frameworks, demonstrating strong potential for visual odometry applications. Through rigorous evaluations on synthetic data and the KITTI benchmark, our methods achieved superior computational efficiency and competitive accuracy compared to state-of-the-art algorithms.

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.

Multi-camera systems offer rich observation capabilities for visual navigation and 3D scene reconstruction; however, the resulting feature redundancy often compromises computational efficiency. This challenge is particularly pronounced during bundle adjustment, where the non-linear optimization of both system poses and scene points incurs substantial computational overhead. To address this challenge, this paper introduces a pose-only geometric constraint for multi-camera systems and proposes a corresponding pose adjustment algorithm. Specifically, we use generalized camera model to establish a unified representation of the multi-camera system. Building upon this model, we formulate the multi-camera pose-only constraint, which implicitly represents a 3D scene point using two base observations and their associated poses, thereby achieving a pose-only representation of the projection geometry. Subsequently, we introduce a multi-camera pose adjustment algorithm that eliminates 3D points from the parameter space, thereby achieving efficient and focused pose optimization. Experimental results on both synthetic and real-world datasets demonstrate that the proposed algorithm outperforms baseline bundle adjustment methods in computational efficiency, while maintaining or even improving pose estimation accuracy.