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Efficient Three-view Triangulation Based on 3D Optimization
Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
2008 (English)In: Proceedings of the British Machine Vision Conference 2008, BMVA Press , 2008, 19.1-19.10 p.Conference paper (Refereed)
Abstract [en]

Triangulation of a 3D point from two or more views can be solved inseveral ways depending on how perturbations in the image coordinatesare dealt with.  A common approach is optimal triangulation which minimizes the total L2 reprojection error in the images,corresponding to finding a maximum likelihood estimate of the 3Dpoint assuming independent Gaussian noise in the image spaces.Computational approaches for optimal triangulation have beenpublished for the stereo case and, recently, also for the three-viewcase.  In short, they solve an independent optimization problem foreach 3D point, using relatively complex computations such as findingroots of high order polynomials or matrix decompositions.  Thispaper discuss three-view triangulation and reports the followingresults: (1) the 3D point can be computed as multi-linear mapping(tensor) applied on the homogeneous image coordinates, (2)  the set of triangulation tensors forms a 7-dimensional space determined by the camera matrices, (3) given a set of corresponding 3D/2Dcalibration points, the 3D residual L1 errors can be optimized over the elements in the 7-dimensional space, (4) using theresulting tensor as initial value, the error can be further reducedby tuning the tensor in a two-step iterative process, (5) the 3Dresidual L1 error for a set of evaluation points which lieclose to the calibration set is comparable to the three-view optimalmethod.  In summary, three-view triangulation can be done by firstperforming an optimization of the triangulation tensor and once this is done, triangulation can be made with 3D residual error at thesame level as the optimal method, but at a much lower computationalcost.  This makes the proposed method attractive for real-time three-view triangulation of large data sets provided that thenecessary calibration process can be performed.

Place, publisher, year, edition, pages
BMVA Press , 2008. 19.1-19.10 p.
National Category
Engineering and Technology
URN: urn:nbn:se:liu:diva-50613DOI: 10.5244/C.22.19ISBN: 1-901725-36-7OAI: diva2:271746
British Machine Vision Conference (BMVC)
Available from: 2009-10-13 Created: 2009-10-13 Last updated: 2014-08-26

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