3D Motion from Image Derivatives Using the Least Trimmed Square Regression

  • Fadi Dornaika
  • Angel D. Sappa
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4153)


This paper presents a new technique to the instantaneous 3D motion estimation. The main contributions are as follows. First, we show that the 3D camera or scene velocity can be retrieved from image derivatives only. Second, we propose a new robust algorithm that simultaneously provides the Least Trimmed Square solution and the percentage of inliers- the non-contaminated data. Experiments on both synthetic and real image sequences demonstrated the effectiveness of the developed method. Those experiments show that the developed robust approach can outperform the classical robust scheme.


Translational Velocity Golden Section Perspective Camera Least Trim Square Image Derivative 
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  1. 1.
    Alon, J., Sclaroff, S.: Recursive estimation of motion and planar structure. In: IEEE Conference on Computer Vision and Pattern Recognition (2002)Google Scholar
  2. 2.
    Weng, J., Huang, T.S., Ahuja, N.: Motion and Structure from Image Sequences. Springer, Berlin (1993)zbMATHGoogle Scholar
  3. 3.
    Brooks, M., Chojnacki, W., Baumela, L.: Determining the egomotion of an uncalibrated camera from instantaneous optical flow. Journal of the Optical Society of America A 14(10), 2670–2677 (1997)CrossRefGoogle Scholar
  4. 4.
    Brodsky, T., Fermuller, C.: Self-calibration from image derivatives. International Journal of Computer Vision 48(2), 91–114 (2002)zbMATHCrossRefGoogle Scholar
  5. 5.
    Fischler, M., Bolles, R.: Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography. Communication ACM 24(6), 381–395 (1981)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Rousseeuw, P.J., Leroy, A.: Robust Regression and Outlier Detection. John Wiley & Sons, New York (1987)zbMATHCrossRefGoogle Scholar
  7. 7.
    Rousseeuw, P.J., Driessen, K.V.: Computing LTS regression for large data sets. Estadistica 54, 163–190 (2002)zbMATHMathSciNetGoogle Scholar
  8. 8.
    Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes in C. Cambridge University Press, Cambridge (1992)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Fadi Dornaika
    • 1
  • Angel D. Sappa
    • 1
  1. 1.Computer Vision Center, Edifici O, Campus UABBellaterra, BarcelonaSpain

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