Abstract
We attack the problem of coordinate frame dependence and gauge freedoms in structure-from-motion. We are able to formulate a bundle adjustment algorithm whose results are independent of both the coordinate frame chosen to represent the scene and the ordering of the images. This method is more efficient that existing approaches to the problem in photogrammetry.
We demonstrate that to achieve coordinate frame independent results, (i) Rotations should be represented by quaternions or local rotation parameters, not angles, and (ii) the translation vector describing the camera/scene motion should be represented in scene 3D coordinates, not camera 3D coordinates, two representations which are normally treated as interchangeable. The algorithm allows 3D point and line features to be reconstructed. Implementation is via the efficient recursive partitioning algorithm common in photogrammetry. Results are presented demonstrating the advantages of the new method in terms of the stability of the bundle adjustment iterations.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
K.B. Atkinson. Close Range Photogrammetry and Machine Vision. Whittles Publishing, Caithness, Scotland, 1996.
A. Azarbayejani and Alex P. Pentland. Recursive estimation of motion, structure, and focal length. IEEE Transactions on Pattern Analysis and Machine Intelligence, 17(6):562–575, 1995.
R. Bergevin, M. Soucy, H. Gagnon, and D. Laurendeau. Towards a general multiview registration technique. IEEE Transactions on Pattern Analysis and Machine Intelligence, 18(5):540–547, May 1996.
A. Gelb (ed). Applied Optimal Estimation. MIT press, 1974.
A.W. Fitzgibbon and A. Zisserman. Automatic camera recovery for closed or open image sequences. In Proc. 5th European Conf. on Computer Vision, Freiburg, volume 1, pages 311–326. Springer-Verlag, June 1998.
G. H. Golub and C. F. van Loan. Matrix Computations, 3rd edition. The John Hopkins University Press, Baltimore, MD, 1996.
J. Heuring and D. W. Murray. Visual head tracking and slaving for visual telepresence. In Proc. IEEE Int’l Conf. on Robotics and Automation, 1996.
Q.-T. Luong and T. Viéville. Canonic representations for the geometries of multiple projective views. In Proc. 3rd European Conf. on Computer Vision, Stockholm, pages 589–599, May 1994.
P. F. McLauchlan. Gauge invariance in projective 3d reconstruction. In IEEE Workshop on Multi-View Modeling and Analysis of Visual Scenes, Fort Collins, CO, June 1999, 1999.
D. Morris and K. Kanatani. Uncertainty modeling for optimal structure from motion. In Proc. ICCV’99 Vision Algorithms Workshop, 1999.
J. L. Mundy and A. P. Zisserman, editors. Geometric Invariance in Computer Vision. MIT Press, Cambridge, MA, 1992.
P.A. Beardsley, A. Zisserman, and D.W. Murray. Sequential updating of projective and affine structure from motion. International Journal of Computer Vision, 23(3), 1997.
X. Pennec and J.P. Thirion. A framework for uncertainty and validation of 3-d registration methods based on points and frames. International Journal of Computer Vision, 25(3):203–229, December1997.
L. Quan and T. Kanade. Affine structure from line correspondences with uncalibrated affine cameras. IEEE Transactions on Pattern Analysis and Machine Intelligence, 19(8):834–845, 1997.
C.J. Taylor and D.J. Kriegman. Structure and motion from line segments in multiple images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 17(11):1021–1032, November 1995.
J. Weng, T. S. Huang, and N. Ahuja. Motion and structure from two perspective views: algorithms, error analysis and error estimation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(5):451–476, 1989.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
McLauchlan, P.F. (2000). Gauge Independence in Optimization Algorithms for 3D Vision. In: Triggs, B., Zisserman, A., Szeliski, R. (eds) Vision Algorithms: Theory and Practice. IWVA 1999. Lecture Notes in Computer Science, vol 1883. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44480-7_12
Download citation
DOI: https://doi.org/10.1007/3-540-44480-7_12
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67973-8
Online ISBN: 978-3-540-44480-0
eBook Packages: Springer Book Archive