%0 Journal Article %1 HARTLEY1997146 %A Hartley, Richard I. %A Sturm, Peter %D 1997 %J Computer Vision and Image Understanding %K 3D-mesh %N 2 %P 146 - 157 %R https://doi.org/10.1006/cviu.1997.0547 %T Triangulation %U http://www.sciencedirect.com/science/article/pii/S1077314297905476 %V 68 %X In this paper, we consider the problem of finding the position of a point in space given its position in two images taken with cameras with known calibration and pose. This process requires the intersection of two known rays in space and is commonly known as triangulation. In the absence of noise, this problem is trivial. When noise is present, the two rays will not generally meet, in which case it is necessary to find the best point of intersection. This problem is especially critical in affine and projective reconstruction in which there is no meaningful metric information about the object space. It is desirable to find a triangulation method that is invariant to projective transformations of space. This paper solves that problem by assuming a Gaussian noise model for perturbation of the image coordinates. The triangulation problem may then be formulated as a least-squares minimization problem. In this paper a noniterative solution is given that finds the global minimum. It is shown that in certain configurations, local minima occur, which are avoided by the new method. Extensive comparisons of the new method with several other methods show that it consistently gives superior results.

@article{HARTLEY1997146, abstract = {In this paper, we consider the problem of finding the position of a point in space given its position in two images taken with cameras with known calibration and pose. This process requires the intersection of two known rays in space and is commonly known as triangulation. In the absence of noise, this problem is trivial. When noise is present, the two rays will not generally meet, in which case it is necessary to find the best point of intersection. This problem is especially critical in affine and projective reconstruction in which there is no meaningful metric information about the object space. It is desirable to find a triangulation method that is invariant to projective transformations of space. This paper solves that problem by assuming a Gaussian noise model for perturbation of the image coordinates. The triangulation problem may then be formulated as a least-squares minimization problem. In this paper a noniterative solution is given that finds the global minimum. It is shown that in certain configurations, local minima occur, which are avoided by the new method. Extensive comparisons of the new method with several other methods show that it consistently gives superior results.}, added-at = {2019-10-31T12:31:39.000+0100}, author = {Hartley, Richard I. and Sturm, Peter}, biburl = {https://www.bibsonomy.org/bibtex/28288554b083f47bdbaf4d8b73dcba69d/cychapman}, description = {Triangulation - ScienceDirect}, doi = {https://doi.org/10.1006/cviu.1997.0547}, interhash = {705653f5b5e77defcd240a49127ea8be}, intrahash = {8288554b083f47bdbaf4d8b73dcba69d}, issn = {1077-3142}, journal = {Computer Vision and Image Understanding}, keywords = {3D-mesh}, number = 2, pages = {146 - 157}, timestamp = {2019-10-31T12:31:39.000+0100}, title = {Triangulation}, url = {http://www.sciencedirect.com/science/article/pii/S1077314297905476}, volume = 68, year = 1997 }