Trifocal Tensor and Relative Pose Estimation with Known Vertical Direction

TL;DR

This work tackles relative pose estimation across three views with known vertical direction from IMUs, reducing the problem to yaw angles and two translations. It introduces a linear closed-form 4-point solver and a minimal 3-point Gröbner-basis solver, both designed for real-time CPU execution and robust within RANSAC. By leveraging IMU alignment, the authors derive a trifocal-tensor-based formulation with efficient constraint enforcement, achieving superior rotation accuracy and competitive translation performance on synthetic data and KITTI. The methods offer a practical fallback option for visual odometry in challenging scenarios where traditional 2-view approaches falter. Overall, the study demonstrates that incorporating vertical direction information yields accurate, fast, and robust three-view pose estimation.

Abstract

This work presents two novel solvers for estimating the relative poses among views with known vertical directions. The vertical directions of camera views can be easily obtained using inertial measurement units (IMUs) which have been widely used in autonomous vehicles, mobile phones, and unmanned aerial vehicles (UAVs). Given the known vertical directions, our lgorithms only need to solve for two rotation angles and two translation vectors. In this paper, a linear closed-form solution has been described, requiring only four point correspondences in three views. We also propose a minimal solution with three point correspondences using the latest Gröbner basis solver. Since the proposed methods require fewer point correspondences, they can be efficiently applied within the RANSAC framework for outliers removal and pose estimation in visual odometry. The proposed method has been tested on both synthetic data and real-world scenes from KITTI. The experimental results show that the accuracy of the estimated poses is superior to other alternative methods.

Figures (7)

• Figure 1: Trifocal tensor using 4 point correspondences or 3 point correspondences in three views.
• Figure 2: Camera alignment with known vertical direction.
• Figure 3: Probability density functions over relative pose estimation errors. (a) Rotation estimation errors. (b)Translation estimation errors. The horizontal axis represents the $log_{10}$ value of the estimated error, and the vertical axis represents the probability density. The narrower the curve, the smaller the data variance, indicating that the algorithm is more stable
• Figure 4: Methods accuracy with image noise. (a) Rotation estimation errors. (b)Translation estimation errors.
• Figure 5: Methods accuracy with IMU angle noise. (a) Rotation estimation errors with IMU pitch angel noise. (b) Translation estimation errors with IMU pitch angel noise. (c) Rotation estimation errors with IMU roll angel noise. (d) Translation estimation errors with IMU roll angel noise.