Arabian Journal for Science and Engineering

, Volume 44, Issue 8, pp 6911–6921 | Cite as

Robust Optical Flow Estimation Using Tchebichef Moment Invariant Feature

  • Vishal Kumar PandeyEmail author
  • Varun Saxena
  • Jyotsna Singh
Research Article - Electrical Engineering


In this paper, orthogonal moment invariant-based features are used to compute 2D optical flow from sequence of images. The gray level of pixel is described in terms of its local neighborhood using Tchebichef moment invariants rather than its individual intensity value. The description is then normalized in order to make it insensitive to intensity fluctuations due to noise or other perturbations such as varying illumination conditions. The principle of conservation of moment invariance is used to derive overdetermined system of 2D motion constraint equations in local neighborhood of each pixel. The velocity field is then estimated using the least square method. Experimental results are performed on sequential video and thermal image frames under varying environmental conditions. The run time, robustness against noisy and varying illumination conditions and rotation invariance of proposed method are compared with already existing moment and non-moment-based techniques.


Least square estimation Moment invariant Optical flow Tchebichef moment Velocity field Zernike moment 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Horn, B.K.P.: Robot Vision. MIT Press, Cambridge (1986)Google Scholar
  2. 2.
    Horn, B.K.P.; Schunck, B.G.: Determining optical flow. Artif. Intell. 17(1–3), 185–203 (1981)CrossRefGoogle Scholar
  3. 3.
    Nagel, H.H.: Displacement vectors derived from second order intensity variations in image sequence. Comput. Vis. Gr. Image Process. 21(1), 85–117 (1983)CrossRefGoogle Scholar
  4. 4.
    Haralick, R.M.; Lee, J. S.: The facet approach to optic flow. In: Proceedings of lmage Understanding Workshop, Arlington, pp. 84–93 (1983)Google Scholar
  5. 5.
    Tretiak, O.; Pastor, L.: Velocity estimates from image sequences with second-order differential operators. In: Proceedings of IEEE International Conference on Pattern Recognition, pp. 16–19 (1984)Google Scholar
  6. 6.
    Campani, M.; Verri, A.: Computing optic flow from an overconstrained system of linear algebraic equations. In: Proceedings of IEEE International Conference on Computer Vision, pp. 22–26 (1987)Google Scholar
  7. 7.
    Black, M.J.; Fleet, D.J.; Yacoob, Y.: Robustly estimating changes in image appearance. Comput. Vis. Image Underst. 78(1), 8–31 (2000)CrossRefGoogle Scholar
  8. 8.
    Haussecker, H.W.; Fleet, D.J.: Computing optical flow with physical models of brightness variation. IEEE Trans. Pattern Anal. Mach. Intell. 23(6), 671–673 (2001)CrossRefGoogle Scholar
  9. 9.
    Kim, Y.-H.; Martinez, A.M.; Kak, A.C.: Robust motion estimation under varying illumination. Image Vis. Comput. 23(4), 365–375 (2005)CrossRefGoogle Scholar
  10. 10.
    Ghosal, S.; Mehrotra, R.: Robust optical-flow estimation using semi-invariant local features. Pattern Recognit. 30(2), 229–237 (1997)CrossRefGoogle Scholar
  11. 11.
    Liang, M.; Du, J.; Li, X.; Xu, L.; Liu, H.; Li, Y.: Spatio-temporal super-resolution reconstruction based on robust optical flow and Zernike moment for dynamic image sequences. In: 2013 IEEE International Symposium on Industrial Electronics, Taipei, pp. 1–6 (2013)Google Scholar
  12. 12.
    Tavakoli, V.; Sahba, N.; Ahmadian, A.; Alirezaie, J.: An evaluation of different optical flow techniques for myocardial motion analysis in B-Mode echocardiography images. In: Abu Osman, N.A., Ibrahim, F., Wan Abas, W.A.B., Abdul Rahman, H.S., Ting, H.N. (eds.) 4th Kuala Lumpur International Conference on Biomedical Engineering 2008. IFMBE Proceedings, vol. 21, Springer, Berlin, Heidelberg (2008)Google Scholar
  13. 13.
    Clawson, K.; Jing, M.; Scotney, B.; Wang, H.; Liu, J.: Human action recognition in video via fused optical flow and moment features towards a hierarchical approach to complex scenario recognition. In: Gurrin, C., Hopfgartner, F., Hurst, W., Johansen, H., Lee, H., OConnor, N. (eds.) MultiMedia Modeling. MMM 2014. Lecture Notes in Computer Science, vol. 8326. Springer, Cham (2014)Google Scholar
  14. 14.
    Kharbat, M.; Aouf, N.; Tsourdos, A.; White, B.: Robust brightness description for computing optical flow. In: Proceedings of of the British Machine Vision Conference, Sept 2008, pp. 1–10. BMVA Press (2008)Google Scholar
  15. 15.
    Qiuying, Y.; Ying, W.: Zernike moments descriptor matching based symmetric optical flow for motion estimation and image registration. In: Proceedings of International Joint Conference on Neural Networks (IJCNN), Beijing, 6–11 July 2014, pp. 350–357 (2014)Google Scholar
  16. 16.
    Lucas, B.D.; Kanade, T.: An iterative image registration technique with an application in stereo vision. In: Seventh International Joint Conference on Artificial Intelligence (IJCAI-81), Vancouver, pp. 674–679 (1981)Google Scholar
  17. 17.
    Mukundan, R.; Ramakrishnan, K.R.: Moment Functions in Image Analysis-Theory and Applications. World Scientific, Singapore (1998)CrossRefzbMATHGoogle Scholar
  18. 18.
    Mukundan, R.: A new class of rotational invariants using discrete orthogonal moments. In: Proceedings of 6th IASTED Conference on Signal and Image Processing—SIP 2004, Honolulu, Aug 2004, pp. 80–84 (2004)Google Scholar
  19. 19.
    Khotanzad, A.; Yaw, H.H.: Invariant image recognition by Zernike moments. IEEE Trans. Pattern Anal. Mach. Intell. 12(5), 489–497 (1990)CrossRefGoogle Scholar
  20. 20.
  21. 21.
    OTCBVS Benchmark Dataset: Accessed 24 Sept 2018

Copyright information

© King Fahd University of Petroleum & Minerals 2019

Authors and Affiliations

  1. 1.Multimedia Research Lab, ECENetaji Subhas Institute of TechnologyNew DelhiIndia

Personalised recommendations