Title :
Efficient triangulation based on 3D Euclidean optimization
Author_Institution :
Comput. Vision Lab., Linkoping Univ., Linkoping, Sweden
Abstract :
This paper presents a method for triangulation of 3D points given their projections in two images. Recent results show that the triangulation mapping can be represented as a linear operator K applied to the outer product of corresponding homogeneous image coordinates, leading to a triangulation of very low computational complexity. K can be determined from the camera matrices, together with a so-called blind plane, but we show here that it can be further refined by a process similar to gold standard methods for camera matrix estimation. In particular, it is demonstrated that K can be adjusted to minimize the Euclidean L1 residual 3D error, bringing it down to the same level as the optimal triangulation by Hartley and Sturm. The resulting K optimally fits a set of 2D+2D+3D data where the error is measured in the 3D space. Assuming that this calibration set is representative for a particular application, where later only the 2D points are known, this K can be used for triangulation of 3D points in an optimal way, which in addition is very efficient since the optimization need only be made once for the point set. The refinement of K is made by iteratively reducing errors in the 3D and 2D domains, respectively. Experiments on real data suggests that very few iterations are needed to accomplish useful results.
Keywords :
computational complexity; computational geometry; image reconstruction; iterative methods; mathematical operators; matrix algebra; optimisation; stereo image processing; 3D Euclidean optimization; blind plane; camera matrix estimation; computational complexity; gold standard method; image reconstruction; iterative method; linear operator; stereo image processing; triangulation mapping; Calibration; Cameras; Computational complexity; Computer vision; Coordinate measuring machines; Gold; Laboratories; Measurement errors; Minimization methods; Optimization methods;
Conference_Titel :
Pattern Recognition, 2008. ICPR 2008. 19th International Conference on
Conference_Location :
Tampa, FL
Print_ISBN :
978-1-4244-2174-9
Electronic_ISBN :
1051-4651
DOI :
10.1109/ICPR.2008.4760981