Abstract
The displacement field computed by the method discussed in the previous chapter provides point correspondences for motion and structure analysis. This chapter deals with estimating motion and structure of the scene from point correspondences between two perspective views. First, an algorithm is presented that computes a closed-form solution for motion and structure parameters. The algorithm exploits redundancy in the data to obtain more reliable estimates in the presence of noise. Then, an approach is introduced to estimating the errors in the computed solution. Specifically, standard deviation of the error is estimated in terms of the variance of the errors in the coordinates of the image points. The estimated errors indicate the reliability of the solution, as well as any degeneracy or near degeneracy that causes the failure of the motion estimation algorithm. The presented approach to error estimation is applicable to a wide variety of problems that involve least-squares optimization or pseudo-inverse. Finally, the relationships between errors and other parameters are analyzed.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
G. Adiv: Determining three-dimensional motion and structure from optical flow generated by several moving objects. IEEE Trans. Pattern Anal. Machine Intell., 7, 348–401 (1985)
O. Bottema, B. Roth: Theoretical Kinematics (North-Holland, New York, 1979)
A. R. Bruss, B. K. Horn: Passive navigation. Computer Vision, Graphics and Image Processing, 21, 3–20 (1983)
J. Q. Fang, T. S. Huang: Some experiments on estimating the 3-D motion parameters of a rigid body from two consecutive image frames. IEEE Trans. Pattern Anal. Machine Intell., 6, 547–554 (1984)
O. D. Faugeras, M. Hebert: A 3-D recognition and positioning algorithm using geometrical matching between primitive surfaces, in Proc. 8th Int’l Joint Conf. Artif. Intell. (William Kaufmann, Los Angeles, LA 1983) pp. 996–1002
O. D. Faugeras, F. Lustman, G. Toscani: Motion and structure from point and line matches, in Proc. Int’l Conf. Computer Vision (IEEE Computer Soc. Press, Washington D.C. 1987)
O. D. Faugeras, S. Maybank: Motion from point matches: multiplicity of solutions, in Proc. Workshop on Visual Motion (IEEE Computer Soc. Press, Washington D.C. 1989) pp. 248–255
W. R. Hamilton: Elements of Quaternions, 3rd ed. (Chelsea, New York, 1969)
R. Jain, H. -H. Nagel: On the analysis of accumulative difference pictures from image sequences of real world scenes. IEEE Trans. Pattern Anal. Machine Intell., 1, 206–214 (1979)
H. C. Longuet-Higgins: A computer program for reconstructing a scene from two projections. Nature, 293, 133–135 (1981)
H. C. Longuet-Higgins: The reconstruction of a scene from two projections — configurations that defeat the 8-point algorithm, in Proc. IEEE 1st Conf. on Artif. Intell. Applications (IEEE Computer Soc. Press, Washington D.C. 1984) pp. 395–397
H. C. Longuet-Higgins: Multiple interpretations of a pair of images of a surface. Proc. Royal Society London, A, 418, 1–15 (1988)
S. J. Maybank: The angular velocity associated with the optical flow field arising from motion through a rigid environment. Proc. Royal Society London, A, 401, 317–326 (1985)
A. Mitiche, J. K. Aggarwal: A computational analysis of time- varying images, in Handbook of Pattern Recognition and Image Processing, ed. by T. Y. Young and K. S. Fu (Academic Press, New York, 1986)
S. Negahdaripour: Multiple interpretations of the shape and motion of objects from two perspective images. IEEE Trans. Pattern Anal. Machine Intell., 12, 1025–1039 (1990)
A. N. Netravali, T. S. Huang, A. S. Krishnakumar, R. J. Holt: Algebraic methods in 3D motion estimation from two-view point correspondences. Int’l J. Imaging Systems and Technology, 1, 78–99 (1989)
J. Philip: Estimation of three-dimensional motion of rigid objects from noisy observations. IEEE Trans. Pattern Anal. Machine Intell., 13, 61–66 (1991)
J. W. Roach, J. K. Aggarwal: Determining the movement of objects from a sequence of images. IEEE Trans. Pattern Anal. Machine Intell., 2, 554–562 (1980)
M. D. Shuster: Approximate algorithms for fast optimal attitude computation, in Proc. AIAA Guidance and Control Specialist Conference (Palo Alto, 1978) pp. 88–95
M. E. Spetsakis, J. Aloimonos: Optimal motion estimation, in Proc. Workshop on Visual Motion (IEEE Computer Soc. Press, Washington D.C. 1989) pp. 229–237
R. Y. Tsai, T. S. Huang: Uniqueness and estimation of 3-D motion parameters of rigid bodies with curved surfaces. IEEE Trans. Pattern Anal. Machine Intell., 6, 13–27 (1984)
A. M. Waxman, B. Kamgar-Parsi, M. Subbarao: Closed-form solutions to image flow equations for 3-D structure and motion, Int’l J. Computer Vision, 1, 239–258 (1987)
J. Weng, T. S. Huang, N. Ahuja: Error analysis of motion parameter determination from image sequences, in Proc. 1st Int’l Conf. Computer Vision (IEEE Computer Soc. Press, Washington D.C. 1987) pp. 703–707
J. Weng, T. S. Huang, N. Ahuja: Motion and structure from two perspective views: algorithms, error analysis and error estimation. IEEE Trans. Pattern Anal. Machine Intell., 11, 451–476 (1989)
J. H. Wilkinson, The Algebraic Eigenvalue Problem (Oxford University Press, England, 1965)
B. L. Yen, T. S. Huang: Determining 3-D motion and structure of a rigid body using the spherical projection. Computer Vision, Graphics and Image Processing, 21, 21–32 (1983)
X. Zhuang, R. M. Haralick: Rigid body motion and the optic flow image, in Proc. IEEE 1st Conf. Artif. Intell. Applications (IEEE Computer Soc. Press, Washington D.C. 1984) pp. 366– 375
X. Zhuang, T. S. Huang, R. M. Haralick: Two-view motion Analysis: a unified algorithm. J. Opt. Soc. Amer., A, 3, 1492–1500 (1986)
X. Zhuang, T. S. Huang, N. Ahuja, R. M. Haralick: A simplified linear optic flow-motion algorithm. Computer Vision, Graphics and Image Processing, 42, 334–344 (1988)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Weng, J., Huang, T.S., Ahuja, N. (1993). Two-View Analysis. In: Motion and Structure from Image Sequences. Springer Series in Information Sciences, vol 29. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-77643-4_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-77643-4_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-77645-8
Online ISBN: 978-3-642-77643-4
eBook Packages: Springer Book Archive