Practical global optimization for multiview geometry
Research output: Contribution to journal › Journal article › Research › peer-review
Standard
Practical global optimization for multiview geometry. / Kahl, Fredrik; Agarwal, Sameer; Chandraker, Manmohan Krishna; Kriegman, David; Belongie, Serge.
In: International Journal of Computer Vision, Vol. 79, No. 3, 09.2008, p. 271-284.Research output: Contribution to journal › Journal article › Research › peer-review
Harvard
APA
Vancouver
Author
Bibtex
}
RIS
TY - JOUR
T1 - Practical global optimization for multiview geometry
AU - Kahl, Fredrik
AU - Agarwal, Sameer
AU - Chandraker, Manmohan Krishna
AU - Kriegman, David
AU - Belongie, Serge
N1 - Funding Information: Acknowledgements S. Agarwal and S. Belongie are supported by NSF-CAREER #0448615, DOE/LLNL contract no. W-7405-ENG-48 (subcontracts B542001 and B547328), and the Alfred P. Sloan Fellowship. M. Chandraker and D. Kriegman are supported by NSF EIA 0303622 & NSF IIS-0308185. F. Kahl is supported by Swedish Research Council (VR 2004-4579) & European Commission (Grant 011838, SMERobot).
PY - 2008/9
Y1 - 2008/9
N2 - This paper presents a practical method for finding the provably globally optimal solution to numerous problems in projective geometry including multiview triangulation, camera resectioning and homography estimation. Unlike traditional methods which may get trapped in local minima due to the non-convex nature of these problems, this approach provides a theoretical guarantee of global optimality. The formulation relies on recent developments in fractional programming and the theory of convex underestimators and allows a unified framework for minimizing the standard L 2-norm of reprojection errors which is optimal under Gaussian noise as well as the more robust L 1-norm which is less sensitive to outliers. Even though the worst case complexity of our algorithm is exponential, the practical efficacy is empirically demonstrated by good performance on experiments for both synthetic and real data. An open source MATLAB toolbox that implements the algorithm is also made available to facilitate further research.
AB - This paper presents a practical method for finding the provably globally optimal solution to numerous problems in projective geometry including multiview triangulation, camera resectioning and homography estimation. Unlike traditional methods which may get trapped in local minima due to the non-convex nature of these problems, this approach provides a theoretical guarantee of global optimality. The formulation relies on recent developments in fractional programming and the theory of convex underestimators and allows a unified framework for minimizing the standard L 2-norm of reprojection errors which is optimal under Gaussian noise as well as the more robust L 1-norm which is less sensitive to outliers. Even though the worst case complexity of our algorithm is exponential, the practical efficacy is empirically demonstrated by good performance on experiments for both synthetic and real data. An open source MATLAB toolbox that implements the algorithm is also made available to facilitate further research.
KW - Branch and bound
KW - Camera pose
KW - Cameras
KW - Geometry
KW - Global optimization
KW - Multiple view geometry
KW - Reconstruction
KW - Triangulation
UR - http://www.scopus.com/inward/record.url?scp=45049084485&partnerID=8YFLogxK
U2 - 10.1007/s11263-007-0117-1
DO - 10.1007/s11263-007-0117-1
M3 - Journal article
AN - SCOPUS:45049084485
VL - 79
SP - 271
EP - 284
JO - International Journal of Computer Vision
JF - International Journal of Computer Vision
SN - 0920-5691
IS - 3
ER -
ID: 302051326