Advertisement

Decoupling Fourier components of dynamic image sequences: A theory of signal separation, image segmentation, and optical flow estimation

  • David Vernon
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1407)

Abstract

This paper presents a new Fourier-based approach to the separation or decoupling of m additive images from a time-sequence of the sum of these images where at least m−1 images are translating with distinct and unique velocity. A closed-form solution is presented for the case where m=2. A generalization is then presented which extends the theory to embrace situations where the images are not additive but are, instead, formed by the superposition of an occluding object or objects on an occluded background. That is, the approach is generalized to effect a model-free segmentation of objects undergoing translatory fronto-parallel motion in dynamic image sequences. Object velocities of one pixel per frame are sufficient to guarantee segmentation.

We also show how the technique can be applied on a local basis to compute a dense instantaneous optical flow field for the image sequence, even in relatively featureless regions. The technique is evaluated using Otte's and Nagel's benchmark image sequence, for which ground-truth data is available, and results comparable with the ground-truth flow field are achieved. RMS errors of velocity magnitude and direction are computed and reported.

Keywords

Spatial Frequency Optical Flow Fourier Component Occlude Object Optical Flow Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    D. Vernon, Machine Vision Prentice-Hall International, London (1991).Google Scholar
  2. 2.
    D. Vernon and G. Sandini, Parallel Computer Vision — The VIS a VIS System, Ellis Horwood, London (1992).Google Scholar
  3. 3.
    J.H. Duncan and T.-C. Chou, “On the detection and the computation of optical flow”, IEEE Transactions on Pattern Analysis and Machine Intelligence, 14(3), 346–352 (1992).CrossRefGoogle Scholar
  4. 4.
    H. Shariat and K.E. Price, “Motion estimation with more than two frames”, IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(5), 417–434 (1990).CrossRefGoogle Scholar
  5. 5.
    M.P. Cagigal, L. Vega, P. Prieto, “Object movement characterization from lowlight-level images”, Optical Engineering, 33(8), 2810–2812 (1994).CrossRefGoogle Scholar
  6. 6.
    M.P. Cagigal, L. Vega, P. Prieto, “Movement characterization with the spatiotemporal Fourier transform of low-light-level images”, Applied Optics, 34(11), 1769–1774 (1995).CrossRefGoogle Scholar
  7. 7.
    S. A. Mahmoud, M.S. Afifi, and R. J. Green, “Recognition and velocity computation of large moving objects in images”, IEEE Transactions on Acoustics, Speech, and Signal Processing, 36(11), 1790–1791 (1988).zbMATHCrossRefGoogle Scholar
  8. 8.
    S. A. Mahmoud, “A new technique for velocity estimation of large moving objects”, IEEE Transactions on Signal Processing, 39(3), 741–743 (1991).CrossRefGoogle Scholar
  9. 9.
    S.A. Rajala, A. N. Riddle, and W.E. Snyder, “Application of one-dimensional Fourier transform for tracking moving objects in noisy environments”, Computer Vision, Graphics, and Image Processing, 21, 280–293 (1983).Google Scholar
  10. 10.
    D. Vernon, “Phase-Based Measurement of Object Velocity in Image Sequences using the Hough Transform”, Optical Engineering (1996).Google Scholar
  11. 11.
    D. J. Fleet and A.D. Jepson, “Hierarchical construction of orientation and velocity selective filters”, IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(3), 315–325 (1989).CrossRefGoogle Scholar
  12. 12.
    D. J. Fleet and A.D. Jepson, “Computation of component image velocity from local phase information”, International Journal of Computer Vision, 5, 77–104 (1990).CrossRefGoogle Scholar
  13. 13.
    D. J. Fleet and A.D. Jepson, “Stability in Phase Information”, IEEE Transactions on Pattern Analysis and Machine Intelligence, 15(12), 1253–1268 (1993).CrossRefGoogle Scholar
  14. 14.
    J.L. Barron, D.J. Fleet, and S. Beauchemin, “Performance of optical flow techniques”, Int. Journal of Computer Vision, 12(1), 43–77 (1994).CrossRefGoogle Scholar
  15. 15.
    M. Otte and H.-H. Nagel, “Optical flow estimation: advances and comparisons”, Lecture Notes in Computer Science, J.O. Eklundh (Ed.), Computer Vision — ECCV '94, Springer-Verlag, Berlin, 51–60 (1994).Google Scholar
  16. 16.
    M. Tistarelli, “Multiple constraints for optical flow”, Lecture Notes in Computer Science, J.O. Eklundh (Ed.), Computer Vision — ECCV '94, Springer-Verlag, Berlin, 61–70 (1994).Google Scholar
  17. 17.
    L. Jacobson and H. Wechsler, “Derivation of optical flow using a spatiotemporal-frequency approach”, Computer Vision, Graphics, and Image Processing, 38, 29–65 (1987).Google Scholar
  18. 18.
    D. Vernon, “Decoupling Fourier Components of Dynamic Image Sequences: Theory and Application to Segmentation and Estimation of Optical Flow”, Technical Report, Department of Computer Science, National University of Ireland, Maynooth (1997).Google Scholar
  19. 19.
    D. Vernon, “Segmentation in Dynamic Image Sequences by Isolation of Coherent Wave Profiles”, Proceedings of the 4th European Conference on Computer Vision, Springer-Verlag, 293–303 (1996).Google Scholar
  20. 20.
    P.V.C. Hough, ‘Method and Means for Recognising Complex Patterns’ U.S. Patent 3,069,654, (1962).Google Scholar
  21. 21.
    L. Hahn, Complex Numbers and Geometry, The Mathmatical Association of America, Washington, D.C. (1994).zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • David Vernon
    • 1
  1. 1.Department of Computer ScienceNational University of IrelandMaynoothIreland

Personalised recommendations