Second-Order Polynomial Models for Background Subtraction

  • Alessandro Lanza
  • Federico Tombari
  • Luigi Di Stefano
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6468)


This paper is aimed at investigating background subtraction based on second-order polynomial models. Recently, preliminary results suggested that quadratic models hold the potential to yield superior performance in handling common disturbance factors, such as noise, sudden illumination changes and variations of camera parameters, with respect to state-of-the-art background subtraction methods. Therefore, based on the formalization of background subtraction as Bayesian regression of a second-order polynomial model, we propose here a thorough theoretical analysis aimed at identifying a family of suitable models and deriving the closed-form solutions of the associated regression problems. In addition, we present a detailed quantitative experimental evaluation aimed at comparing the different background subtraction algorithms resulting from theoretical analysis, so as to highlight those more favorable in terms of accuracy, speed and speed-accuracy tradeoff.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Elhabian, S.Y., El-Sayed, K.M., Ahmed, S.H.: Moving object detection in spatial domain using background removal techniques - state-of-art. Recent Patents on Computer Sciences 1, 32–54 (2008)CrossRefGoogle Scholar
  2. 2.
    Stauffer, C., Grimson, W.E.L.: Adaptive background mixture models for real-time tracking. In: Proc. CVPR 1999, vol. 2, pp. 246–252 (1999)Google Scholar
  3. 3.
    Elgammal, A., Harwood, D., Davis, L.: Non-parametric model for background subtraction. In: Proc. ICCV 1999 (1999)Google Scholar
  4. 4.
    Durucan, E., Ebrahimi, T.: Change detection and background extraction by linear algebra. Proc. IEEE 89, 1368–1381 (2001)CrossRefGoogle Scholar
  5. 5.
    Ohta, N.: A statistical approach to background subtraction for surveillance systems. In: Proc. ICCV 2001, vol. 2, pp. 481–486 (2001)Google Scholar
  6. 6.
    Xie, B., Ramesh, V., Boult, T.: Sudden illumination change detection using order consistency. Image and Vision Computing 22, 117–125 (2004)CrossRefGoogle Scholar
  7. 7.
    Mittal, A., Ramesh, V.: An intensity-augmented ordinal measure for visual correspondence. In: Proc. CVPR 2006, vol. 1, pp. 849–856 (2006)Google Scholar
  8. 8.
    Heikkila, M., Pietikainen, M.: A texture-based method for modeling the background and detecting moving objects. IEEE Trans. PAMI (2006)Google Scholar
  9. 9.
    Lanza, A., Di Stefano, L.: Detecting changes in grey level sequences by ML isotonic regression. In: Proc. AVSS 2006, pp. 1–4 (2006)Google Scholar
  10. 10.
    Lanza, A., Tombari, F., Di Stefano, L.: Robust and efficient background subtraction by quadratic polynomial fitting. In: Proc. Int. Conf. on Image Processing ICIP 2010 (2010)Google Scholar
  11. 11.
    Lanza, A., Tombari, F., Di Stefano, L.: Accurate and efficient background subtraction by monotonic second-degree polynomial fitting. In: Proc. AVSS 2010, (2010)Google Scholar
  12. 12.
    Crow, F.: Summed-area tables for texture mapping. Computer Graphics 18, 207–212 (1984)CrossRefGoogle Scholar
  13. 13.
    MUSCLE Network of Excellence (Motion detection video sequences)Google Scholar
  14. 14.
    Bradley, A.P.: The use of the area under the ROC curve in the evaluation of machine learning algorithms. Pattern Recognition 30, 1145–1159 (1997)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Alessandro Lanza
    • 1
  • Federico Tombari
    • 1
  • Luigi Di Stefano
    • 1
  1. 1.DEIS, University of BolognaBolognaItaly

Personalised recommendations