Computer Vision and Image Understanding
International Journal of Computer Vision
Linear Multi View Reconstruction and Camera Recovery Using a Reference Plane
International Journal of Computer Vision
Multiple View Geometry in Computer Vision
Multiple View Geometry in Computer Vision
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
Photo tourism: exploring photo collections in 3D
ACM SIGGRAPH 2006 Papers
Quasiconvex Optimization for Robust Geometric Reconstruction
IEEE Transactions on Pattern Analysis and Machine Intelligence
Practical Global Optimization for Multiview Geometry
International Journal of Computer Vision
Multiple-View Geometry Under the {$L_\infty$}-Norm
IEEE Transactions on Pattern Analysis and Machine Intelligence
Globally Optimal Least Squares Solutions for Quasiconvex 1D Vision Problems
SCIA '09 Proceedings of the 16th Scandinavian Conference on Image Analysis
Optimal algorithms in multiview geometry
ACCV'07 Proceedings of the 8th Asian conference on Computer vision - Volume Part I
A fast optimal algorithm for L2 triangulation
ACCV'07 Proceedings of the 8th Asian conference on Computer vision - Volume Part II
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We consider the least-squares (L2) minimization problems in multiple view geometry for triangulation, homography, camera resectioning and structure-and-motion with known rotation, or known plane. Although optimal algorithms have been given for these problems under an L-infinity cost function, finding optimal least-squares solutions to these problems is difficult, since the cost functions are not convex, and in the worst case may have multiple minima. Iterative methods can be used to find a good solution, but this may be a local minimum. This paper provides a method for verifying whether a local-minimum solution is globally optimal, by providing a simple and rapid test involving the Hessian of the cost function. The basic idea is that by showing that the cost function is convex in a restricted but large enough neighbourhood, a sufficient condition for global optimality is obtained.The method is tested on numerous problem instances of real data sets. In the vast majority of cases we are able to verify that the solutions are optimal, in particular, for small to medium-scale problems.