Computer Vision and Image Understanding
Multiple view geometry in computer vision
Multiple view geometry in computer vision
Bundle Adjustment - A Modern Synthesis
ICCV '99 Proceedings of the International Workshop on Vision Algorithms: Theory and Practice
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
Multiple View Geometry and the L_"-norm
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
Practical global optimization for multiview geometry
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
Fast and Stable Polynomial Equation Solving and Its Application to Computer Vision
International Journal of Computer Vision
A Study on Gröbner Basis with Inexact Input
CASC '09 Proceedings of the 11th International Workshop on Computer Algebra in Scientific Computing
Fast multiple-view L2 triangulation with occlusion handling
Computer Vision and Image Understanding
EVP-based multiple-view triangulation
ISVC'10 Proceedings of the 6th international conference on Advances in visual computing - Volume Part III
Approximate and SQP two view triangulation
ACCV'10 Proceedings of the 10th Asian conference on Computer vision - Volume Part III
Computing a structured Gröbner basis approximately
Proceedings of the 36th international symposium on Symbolic and algebraic computation
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We consider the problem of L2-optimal triangulation from three separate views. Triangulation is an important part of numerous computer vision systems. Under gaussian noise, minimizing the L2 norm of the reprojection error gives a statistically optimal estimate. This has been solved for two views. However, for three or more views, it is not clear how this should be done. A previously proposed, but computationally impractical, method draws on Gröbner basis techniques to solve for the complete set of stationary points of the cost function. We show how this method can be modified to become significantly more stable and hence given a fast implementation in standard IEEE double precision. We evaluate the precision and speed of the new method on both synthetic and real data. The algorithm has been implemented in a freely available software package which can be downloaded from the Internet.