On geometric optimization with few violated constraints
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Efficient algorithms for geometric optimization
ACM Computing Surveys (CSUR)
An Interior-Point Algorithm for Nonconvex Nonlinear Programming
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part II
Multiple View Geometry in Computer Vision
Multiple View Geometry in Computer Vision
Convex Optimization
Distinctive Image Features from Scale-Invariant Keypoints
International Journal of Computer Vision
Multiple View Geometry and the L_"-norm
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
Removing Outliers Using The L\infty Norm
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
Reconstruction with Interval Constraints Propagation
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
Uncertainty Models in Quasiconvex Optimization for Geometric Reconstruction
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
Recovering Camera Motion Using L\infty Minimization
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
Quasiconvex Optimization for Robust Geometric Reconstruction
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multiple-View Geometry Under the {$L_\infty$}-Norm
IEEE Transactions on Pattern Analysis and Machine Intelligence
Global Optimization through Rotation Space Search
International Journal of Computer Vision
SCIA'11 Proceedings of the 17th Scandinavian conference on Image analysis
Global Optimization for One-Dimensional Structure and Motion Problems
SIAM Journal on Imaging Sciences
Hi-index | 0.02 |
Recent work on geometric vision problems has exploited convexity properties in order to obtain globally optimal solutions. In this paper we give an overview of these developments and show the tight connections between different types of convexity and optimality conditions for a large class of multiview geometry problems. We also show how the convexity properties are closely linked to different types of optimization algorithms for computing the solutions. Moreover, it is also demonstrated how convexity can be used for detection and removal of outliers. The theoretical findings are accompanied with illustrative examples and experimental results on real data.