# Direct Optimization of Frame-to-Frame Rotation

@article{Kneip2013DirectOO, title={Direct Optimization of Frame-to-Frame Rotation}, author={Laurent Kneip and Simon Lynen}, journal={2013 IEEE International Conference on Computer Vision}, year={2013}, pages={2352-2359} }

This work makes use of a novel, recently proposed epipolar constraint for computing the relative pose between two calibrated images. By enforcing the coplanarity of epipolar plane normal vectors, it constrains the three degrees of freedom of the relative rotation between two camera views directly-independently of the translation. The present paper shows how the approach can be extended to n points, and translated into an efficient eigenvalue minimization over the three rotational degrees of…

## 48 Citations

The Probabilistic Normal Epipolar Constraint for Frame-To-Frame Rotation Optimization under Uncertain Feature Positions

- Computer ScienceArXiv
- 2022

The probabilistic normal epipolar constraint (PNEC) is introduced that overcomes this limitation by accounting for anisotropic and inhomogeneous uncertainties in the feature positions and yields more accurate rotation estimates than the original NEC and several popular relative rotation estimation algorithms.

Camera relative pose estimation for visual servoing using quaternions

- Computer ScienceRobotics Auton. Syst.
- 2018

Efficient Computation of Relative Pose for Multi-camera Systems

- Computer Science2014 IEEE Conference on Computer Vision and Pattern Recognition
- 2014

This work factorizes the problem as a low-dimensional, iterative optimization over relative rotation only, directly derived from well-known epipolar constraints, resulting in computational efficiency similar to linear solvers, and accuracy close to bundle adjustment, while using less correspondences.

Globally Optimal Relative Pose Estimation with Gravity Prior

- Computer Science2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)
- 2021

This work proposes a novel globally optimal solver, minimizing the algebraic error in the least squares sense, to estimate the relative pose in the over-determined case, based on the epipolar constraint.

An Efficient Method to Recover Relative Pose for Vehicle-Mounted Cameras Under Planar Motion

- Computer ScienceIEEE Transactions on Systems, Man, and Cybernetics: Systems
- 2021

The proposed 2-point algorithm to estimate the relative pose as well as the absolute scale between two vehicle-mounted cameras efficiently and performs better than many related algorithms including the well-known 5- point algorithm in many cases, especially when the camera’s trajectory contains sharp corners.

Frame-To-Frame Rotation Estimation under Uncertain Feature Positions for Visual Odometry Frame-To-Frame Rotation Estimation under Uncertain Feature Positions for Visual Odometry Bild-zu-Bild Rotationsschätzung unter Unsicheren Featurepositionen für Visuelle Odometrie

- Computer Science
- 2021

A novel objective function is derived that effectively estimates the rotation while maintaining real-time performance and the integration of the PNEC into a state-of-the-art monocular rotation-only odometry system achieves improved results for the real-world KITTI dataset.

Rotation-Only Bundle Adjustment

- Computer Science2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)
- 2021

This work proposes a novel method for estimating the global rotations of the cameras independently of their positions and the scene structure, thereby decoupling the rotation estimation from the translation and structure estimation.

Efficient Ego-Motion Estimation for Multi-Camera Systems With Decoupled Rotation and Translation

- Computer ScienceIEEE Access
- 2020

Novel solutions to estimate the ego-motion of a multi-camera system with a known vertical direction by assuming small camera motion between successive video frames are presented and it is demonstrated that rotation and translation estimation can be decoupled.

Fast and Robust Certifiable Estimation of the Relative Pose Between Two Calibrated Cameras

- Computer ScienceJ. Math. Imaging Vis.
- 2021

This work contributes an efficient algorithm to compute the Relative Pose problem (RPp) between calibrated cameras and certify the optimality of the solution, given a set of pair-wise feature…

The generalized relative pose and scale problem: View-graph fusion via 2D-2D registration

- Computer Science2016 IEEE Winter Conference on Applications of Computer Vision (WACV)
- 2016

By directly employing image information, this work avoids the common noise in point clouds occurring especially along the depth direction by using a simple heuristic global energy minimization scheme based on local minimum suppression, returning outstanding performance in practically relevant scenarios.

## References

SHOWING 1-10 OF 22 REFERENCES

Finding the Exact Rotation between Two Images Independently of the Translation

- Computer ScienceECCV
- 2012

This paper presents a new epipolar constraint for computing the rotation between two images independently of the translation, and shows for the first time how the constraint on the rotation has the advantage of remaining exact even in the case of translations converging to zero.

Estimating Relative Camera Motion from the Antipodal-Epipolar Constraint

- Computer ScienceIEEE Transactions on Pattern Analysis and Machine Intelligence
- 2010

A new formulation based on discrete camera motions, which works over a larger range of motions compared to previous differential techniques using antipodal points, and a new structure-from-motion algorithm that does not require explicitly estimating rotation.

An efficient solution to the five-point relative pose problem

- Computer ScienceIEEE Transactions on Pattern Analysis and Machine Intelligence
- 2004

The algorithm is used in a robust hypothesize-and-test framework to estimate structure and motion in real-time with low delay and is the first algorithm well-suited for numerical implementation that also corresponds to the inherent complexity of the problem.

Global Optimization through Rotation Space Search

- Computer ScienceInternational Journal of Computer Vision
- 2008

A method is developed for the estimation of the essential matrix, giving the first guaranteed optimal algorithm for estimating the relative pose using a cost function based on reprojection errors.

Five-Point Motion Estimation Made Easy

- Computer Science18th International Conference on Pattern Recognition (ICPR'06)
- 2006

This paper provides a simpler algorithm based on the hidden variable resultant technique, which eliminates many unknowns at once in the equation solving stage and compute the minimal singular vector of the coefficient matrix, by which all the unknown parameters can be estimated simultaneously.

Optimization Criteria and Geometric Algorithms for Motion and Structure Estimation

- Computer ScienceInternational Journal of Computer Vision
- 2004

Prevailing efforts to study the standard formulation of motion and structure recovery have recently been focused on issues of sensitivity and robustness of existing techniques. While many cogent…

Essential Matrix Estimation Using Gauss-Newton Iterations on a Manifold

- Mathematics, Computer ScienceInternational Journal of Computer Vision
- 2006

This work proposes three Gauss-Newton type algorithms that have improved convergence properties and reduced computational cost, based on a novel intrinsic Newton method using the normal Riemannian metric on the manifold consisting of all essential matrices.

An Efficient Minimal Solution for Infinitesimal Camera Motion

- Mathematics2007 IEEE Conference on Computer Vision and Pattern Recognition
- 2007

This work presents the first efficient solution to the infinitesimal version of the five-point relative orientation problem, and investigates over which range of motions and scene distances the inf initesimal approximation is valid and shows that it works well in applications such as camera tracking.

Visual odometry

- Computer Science, MathematicsProceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004. CVPR 2004.
- 2004

A system that estimates the motion of a stereo head or a single moving camera based on video input in real-time with low delay and the motion estimates are used for navigational purposes.

Polynomial Eigenvalue Solutions to the 5-pt and 6-pt Relative Pose Problems

- Computer ScienceBMVC
- 2008

This paper shows that the five-point relative pose problem and the six-point focal length problem can easily be formulated as polynomial eigenvalue problems of degree three and two and solved using standard efficient numerical algorithms.