Computer Vision and Image Understanding
Multiple view geometry in computer visiond
Multiple view geometry in computer visiond
Solving the Sum-of-Ratios Problem by an Interior-Point Method
Journal of Global Optimization
Semidefinite Relaxations of Fractional Programs via Novel Convexification Techniques
Journal of Global Optimization
Using concave envelopes to globally solve the nonlinear sum of ratios problem
Journal of Global Optimization
International Journal of Computer Vision - Marr Prize Special Issue
Convex Optimization
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
How Hard is 3-View Triangulation Really?
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 - Volume 01
Globally Optimal Estimates for Geometric Reconstruction Problems
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
Quasiconvex Optimization for Robust Geometric Reconstruction
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
Multiple-View Geometry Under the {$L_\infty$}-Norm
IEEE Transactions on Pattern Analysis and Machine Intelligence
Triangulation of points, lines and conics
SCIA'07 Proceedings of the 15th Scandinavian conference on Image analysis
Practical global optimization for multiview geometry
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
Triangulation of Points, Lines and Conics
Journal of Mathematical Imaging and Vision
Global Optimization through Rotation Space Search
International Journal of Computer Vision
Monocular 3-D tracking of inextensible deformable surfaces under L2-norm
IEEE Transactions on Image Processing
L-infinity norm minimization in the multiview triangulation
AICI'10 Proceedings of the 2010 international conference on Artificial intelligence and computational intelligence: Part I
Camera Models and Fundamental Concepts Used in Geometric Computer Vision
Foundations and Trends® in Computer Graphics and Vision
Efficient Suboptimal Solutions to the Optimal Triangulation
International Journal of Computer Vision
Global optimization for estimating a multiple-lobe analytical BRDF
Computer Vision and Image Understanding
Simultaneous Camera Pose and Correspondence Estimation with Motion Coherence
International Journal of Computer Vision
Monocular template-based tracking of inextensible deformable surfaces under L2-norm
ACCV'09 Proceedings of the 9th Asian conference on Computer Vision - Volume Part II
A QCQP approach to triangulation
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part I
A practical but rigorous approach to sum-of-ratios optimization in geometric applications
Computational Optimization and Applications
Optimization techniques for geometric estimation: beyond minimization
SSPR'12/SPR'12 Proceedings of the 2012 Joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
Verifying Global Minima for L2 Minimization Problems in Multiple View Geometry
International Journal of Computer Vision
Hi-index | 0.00 |
This paper presents a practical method for finding the provably globally optimal solution to numerous problems in projective geometry including multiview triangulation, camera resectioning and homography estimation. Unlike traditional methods which may get trapped in local minima due to the non-convex nature of these problems, this approach provides a theoretical guarantee of global optimality. The formulation relies on recent developments in fractional programming and the theory of convex underestimators and allows a unified framework for minimizing the standard L 2-norm of reprojection errors which is optimal under Gaussian noise as well as the more robust L 1-norm which is less sensitive to outliers. Even though the worst case complexity of our algorithm is exponential, the practical efficacy is empirically demonstrated by good performance on experiments for both synthetic and real data. An open source MATLAB toolbox that implements the algorithm is also made available to facilitate further research.