Globally Optimal Estimates for Geometric Reconstruction Problems
International Journal of Computer Vision
Quasiconvex Optimization for Robust Geometric Reconstruction
IEEE Transactions on Pattern Analysis and Machine Intelligence
Triangulation for points on lines
Image and Vision Computing
Practical Global Optimization for Multiview Geometry
International Journal of Computer Vision
Triangulation of Points, Lines and Conics
Journal of Mathematical Imaging and Vision
Fast and Stable Polynomial Equation Solving and Its Application to Computer Vision
International Journal of Computer Vision
Camera Resectioning from a Box
SCIA '09 Proceedings of the 16th Scandinavian Conference on Image Analysis
Globally Optimal Least Squares Solutions for Quasiconvex 1D Vision Problems
SCIA '09 Proceedings of the 16th Scandinavian Conference on Image Analysis
Stabilizing 3D modeling with geometric constraints propagation
Computer Vision and Image Understanding
Fast and robust numerical solutions to minimal problems for cameras with radial distortion
Computer Vision and Image Understanding
Triangulation of points, lines and conics
SCIA'07 Proceedings of the 15th 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
Fast optimal three view triangulation
ACCV'07 Proceedings of the 8th Asian conference on Computer vision - Volume Part II
Predicting corresponding region in a third view using discrete epipolar lines
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
Improve matching results for structure from motion problems
International Journal of Computer Applications in Technology
Globally Optimal Algorithms for Stratified Autocalibration
International Journal of Computer Vision
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
Fast multiple-view L2 triangulation with occlusion handling
Computer Vision and Image Understanding
Efficient Suboptimal Solutions to the Optimal Triangulation
International Journal of Computer Vision
EVP-based multiple-view triangulation
ISVC'10 Proceedings of the 6th international conference on Advances in visual computing - Volume Part III
Practical global optimization for multiview geometry
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
Triangulation for points on lines
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part III
A QCQP approach to triangulation
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part I
Numerically stable optimization of polynomial solvers for minimal problems
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part III
Verifying Global Minima for L2 Minimization Problems in Multiple View Geometry
International Journal of Computer Vision
Hand-Eye calibration without hand orientation measurement using minimal solution
ACCV'12 Proceedings of the 11th Asian conference on Computer Vision - Volume Part IV
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We present a solution for optimal triangulation in three views. The solution is guaranteed to find the optimal solution because it computes all the stationary points of the (maximum likelihood) objective function. Internally, the solution is found by computing roots of multi-variate polynomial equations, directly solving the conditions for stationarity. The solver makes use of standard methods from computational commutative algebra to convert the root-finding problem into a 47 脳 47 non-symmetric eigen-problem. Although there are in general 47 roots, counting both real and complex ones, the number of real roots is usually much smaller. We also show experimentally that the number of stationary points that are local minima and lie in front of each camera is small but does depend on the scene geometry.