SIAM Review
Computer Vision and Image Understanding
Solving the Sum-of-Ratios Problem by an Interior-Point Method
Journal of Global Optimization
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
Globally Optimal Estimates for Geometric Reconstruction Problems
International Journal of Computer Vision
Non-convex quadratic minimization problems with quadratic constraints: global optimality conditions
Mathematical Programming: Series A and B
Practical Global Optimization for Multiview Geometry
International Journal of Computer Vision
A fast optimal algorithm for L2 triangulation
ACCV'07 Proceedings of the 8th Asian conference on Computer vision - Volume Part II
On zero duality gap in nonconvex quadratic programming problems
Journal of Global Optimization
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Triangulation of a three-dimensional point from n≥2 two-dimensional images can be formulated as a quadratically constrained quadratic program. We propose an algorithm to extract candidate solutions to this problem from its semidefinite programming relaxations. We then describe a sufficient condition and a polynomial time test for certifying when such a solution is optimal. This test has no false positives. Experiments indicate that false negatives are rare, and the algorithm has excellent performance in practice. We explain this phenomenon in terms of the geometry of the triangulation problem.