Σ-Δ Background Subtraction and the Zipf Law

  • Antoine Manzanera
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4756)


The Σ-Δ background estimation is a simple non linear method of background subtraction based on comparison and elementary increment/decrement. We propose here some elements of justification of this method with respect to statistical estimation, compared to other recursive methods: exponential smoothing, Gaussian estimation. We point out the relation between the Σ-Δ estimation and a probabilistic model: the Zipf law. A new algorithm is proposed for computing the background/foreground classification as the pixel-level part of a motion detection algorithm. Comparative results and computational advantages of the method are commented.


Image processing Motion detection Background subtraction Σ-Δ modulation Vector data parallelism 


  1. 1.
    Karmann, K.P., von Brandt, A.: Moving Object Recognition Using an Adaptive Background Memory. In: Time-Varying Image Processing and Moving Object Recognition, Elsevier, Amsterdam (1990)Google Scholar
  2. 2.
    Toyoma, K., Krumm, J., Brumitt, B., Meyers, B.: Wallflower: Principles and Practice of Background Maintenance. In: Proc. IEEE ICCV, Kerkyra - Greece, pp. 255–261 (1999)Google Scholar
  3. 3.
    Elgammal, A., Harwood, D., Davis, L.: Non-parametric Model for Background Subtraction. In: Proc. IEEE ECCV, Dublin - Ireland (2000)Google Scholar
  4. 4.
    Piccardi, M.: Background subtraction techniques: a review. In: Proc. of IEEE SMC/ICSMC (October 2004)Google Scholar
  5. 5.
    Cheung, S.C., Kamath, C.: Robust techniques for background subtraction in urban traffic video. In: Proc. SPIE Video Com. and Image Proc. San Jose - CA (2004)Google Scholar
  6. 6.
    McFarlane, N., Schofield, C.: Segmentation and tracking of piglets in images. Machine Vision and Applications 8, 187–193 (1995)CrossRefGoogle Scholar
  7. 7.
    Manzanera, A., Richefeu, J.: A robust and computationally efficient motion detection algorithm based on Σ-Δ background estimation. In: Proc. ICVGIP 2004, pp. 46–51 (December 2004)Google Scholar
  8. 8.
    Manzanera, A., Richefeu, J.: A new motion detection algorithm based on Σ-Δ background estimation. Pattern Recognition Letters 28, 320–328 (2007)CrossRefGoogle Scholar
  9. 9.
    Stauffer, C., Grimson, E.: Learning patterns of activity using real-time tracking. IEEE Trans. on PAMI 22(8), 747–757 (2000)Google Scholar
  10. 10.
    Power, P., Schoonees, J.: Understanding background mixture models for foreground segmentation. In: Imaging and Vision Computing New Zealand, Auckland, NZ (2002)Google Scholar
  11. 11.
    Zipf, G.: Human behavior and the principle of least-effort. Addison-Wesley, New-York (1949)Google Scholar
  12. 12.
    Caron, Y., Makris, P., Vincent, N.: A method for detecting artificial objects in natural environments. In: Int. Conf. in Pattern Recognition, pp. 600–603 (2002)Google Scholar
  13. 13.
    Intel, C.: Intel®C++ Compiler for Linux Systems - User’s Guide (1996-2003) Document number 253254-014Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Antoine Manzanera
    • 1
  1. 1.ENSTA - Elec. and Comp. Sc. lab, 32 Bd Victor, 75015 ParisFrance

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