Abstract
This paper is focused on error characterization of the factorization approach to shape and motion recovery from image sequence using results from matrix perturbation theory and covariance propagation for linear models. Given the 2-D projections of a set of points across multiple image frames and small perturbation on image coordinates, first order perturbation and covariance matrices for 3-D affine/Euclidean shape and motion are derived and validated with the ground truth. The propagation of the small perturbation and covariance matrix provides better understanding of the factorization approach and its results, provides error sensitivity information for 3-D affine/Euclidean shape and moton subject to small image error. Experimental results are demonstrated to support the analysis and show how the error analysis and error measures can be used.
This work is supported by Siemens Corporate Research, Princeton, NJ 08540
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
C. Tomasi and T. Kanade. Shape and motion from image streams under orthography: A factorization method. International Journal on Computer Vision, 9(2):137–154, November 1992.
Joseph L. Mundy and Andrew Zisserman. Geometric Invariance in Computer Vision. The MIT Press, Cambridge, MA, 1992.
D. Weinshall and C. Tomasi. Linear and incremental acquisition of invariant shape models from image sequences. IEEE Trans. Pattern Analysis Machine Intelligence, 17(5):512–517, May 1995.
C.J. Poelman and T. Kanade. A paraperspective factorization method for shape and motion recovery. IEEE Trans. Pattern Analysis Machine Intelligence, 19(3):206–218, March1997.
L. Quan. Self-calibration of an affine camera from multiple views. International Journal on Computer Vision, 19(1):93–105, July 1996.
P. Sturm and B. Triggs. A factorization based algorithm for multi-image projective structure and motion. In Computer Vision-ECCV’96, volume 1065, pages II:709–720. Springer Verlag, Lecture Notes in Computer Science, 1996.
T. Morita and T. Kanade. A sequential factorization method for recovering shape and motion from image streams. IEEE Trans. Pattern Analysis Machine Intellgence, 19(8):858–867, August1997.
L. Quan and T. Kanade. Affine structure from line correspondences with uncalibrated affine cameras. IEEE Trans. Pattern Analysis Machine Intelligence, 19(8):834–845, August 1997.
Daniel D. Morris and Takeo Kanade. A unified factorization algorithm for points, line segments and planes with uncertainty. In International Conference on Computer Vision, pages 696–702, Bombay, India, 1998.
J. Weng, T. S. Huang, and N. Ahuja. Motion and structure from two perspective views: Algorithms, error analysis and error estimation. IEEE Trans. Pattern Analysis Machine Intelligence, PAMI-11(5):451–476, May 1989.
J. Weng, N. Ahuja, and T.S. Huang. Optimal motion and structure estimation. IEEE Trans. Pattern Analysis Machine Intelligence, 15(9):864–884, September 1993.
C. Tomasi and J. Zhang. Is structure-from-motion worth pursuing. In Seventh International Symposium on Robotics Research, 1995.
K. Daniilidis and M. Spetsakis. Understanding noise sensitivity in structure from motion. In Y. Aloimonos editor, Visual Navigation, pages 61–88. Lawrence Erlbaum Associates, Hillsdale, NJ, 1996.
J. H. Wilkinson. The Algebraic Eigenvalue Problem. Clarendon Press, Oxford, England, 1965.
Gene H. Golub and C. F. van Loan. Matrix computations. Johns Hopkins University Press, Baltimore, Maryland, 1996.
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
Sun, Z., Ramesh, V., Tekalp, A.M. (2000). Error Characterization of the Factorization Approach to Shape and Motion Recovery. 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_14
Download citation
DOI: https://doi.org/10.1007/3-540-44480-7_14
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