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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics


  • Editor: Gregory W. Faris
  • Vol. 4, Iss. 7 — Jul. 1, 2009

Noise-insensitive image optimal flow estimation using higher-order statistics

El Mehdi Ismaili Alaoui, Elhassane Ibn-elhaj, and El Houssaine Bouyakhf  »View Author Affiliations

JOSA A, Vol. 26, Issue 5, pp. 1212-1220 (2009)

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A new algorithm is presented that estimates the displacement vector field from two successive image frames. In the case where the sequence is severely corrupted by additive (Gaussian or not, colored) noise of unknown covariance, then second-order statistics methods do not work well. However, we have studied this topic from a viewpoint different from the above to explore the fundamental limits in image optimal flow estimation. Our scheme is based on subpixel optimal flow estimation using the bispectrum in the parametric domain. The displacement vector of a moving object is estimated by solving linear equations involving third-order holograms and the matrix containing the Dirac delta function. To prove the feasibility of the proposed method, we compared it with a phase correlation technique and the nonparametric bispectrum method described in Res. Lett. Signal Process., ID 417915 (2008) . Our results show that our method is considerably more immune to the presence of noise.

© 2009 Optical Society of America

OCIS Codes
(100.4145) Image processing : Motion, hyperspectral image processing
(110.4153) Imaging systems : Motion estimation and optical flow

ToC Category:
Imaging Systems

Original Manuscript: May 20, 2008
Revised Manuscript: November 21, 2008
Manuscript Accepted: December 18, 2008
Published: April 20, 2009

Virtual Issues
Vol. 4, Iss. 7 Virtual Journal for Biomedical Optics

El Mehdi Ismaili Alaoui, Elhassane Ibn-elhaj, and El Houssaine Bouyakhf, "Noise-insensitive image optimal flow estimation using higher-order statistics," J. Opt. Soc. Am. A 26, 1212-1220 (2009)

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  1. R. M. Armitano, R. W. Schafer, F. L. Kitson, and V. Bhaskaran, “Robust block-matching motion-estimation technique for noisy sources,” in Proceedings of 1997 IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE, 1997), pp. 2685-2688. [CrossRef]
  2. S. Bhattacharya, N. C. Ray, and S. Sinha, “2-D signal modelling and reconstruction using third-order cumulants,” Signal Process. 62, 61-72 (1997). [CrossRef]
  3. E. M. Ismaili Aalaoui and E. Ibn-Elhaj, “Estimation of subpixel motion using bispectrum,” Res. Lett. Signal Process. , ID 417915 (2008).
  4. J. M. Anderson and G. B. Giannakis, “Image motion estimation algorithms using cumulants,” IEEE Trans. Image Process. 4, 346-357 (1995). [CrossRef] [PubMed]
  5. R. P. Kleihorst, R. L. Lagendijk, and J. Biemond, “Noise reduction of severely corrupted image sequences,” in Proceedings of 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE, 1993), pp. 293-296. [CrossRef]
  6. E. Ibn-elhaj, D. Aboutajdine, S. Pateux, and L. Morin, “HOS-based method of global motion estimation for noisy image sequences,” Electron. Lett. 35, 1320-1322 (1999). [CrossRef]
  7. E. Sayrol, A. Gasull, and J. R. Fonollosa, “Motion estimation using higher order statistics,” IEEE Trans. Image Process. 5, 1077-1084 (1996). [CrossRef] [PubMed]
  8. A. N. Netravali and J. D. Robbins “Motion-compensated television coding: Part I,” Bell Syst. Tech. J. 58, 629-668 (1979).
  9. V. Murino, C. Ottonello, and S. Pagnan, “Noisy texture classification: A higher-order statistics approach,” Pattern Recogn. 31, 383-393 (1998). [CrossRef]
  10. M. R. Raghuveer and C. L. Nikias, “Bispectrum estimation: A parametric approach,” IEEE Trans. Acoust., Speech, Signal Process. ASSP-33, 1213-1230 (1985). [CrossRef]
  11. G. B. Giannakis, “On the identifiability of non Gaussian ARMA models using cumulants,” IEEE Trans. Autom. Control 35, 18-26 (1990). [CrossRef]
  12. J. M. Mendel, “Tutorial on higher order statistics (spectra) in signal processing and systems theory: Theoretical results and some applications,” Proc. IEEE 79, 278-305 (1991). [CrossRef]
  13. C. L. Nikias and R. Pan, “Time delay estimation in unknown Gaussian spatially correlated noise,” IEEE Trans. Acoust., Speech, Signal Process. ASSP-36, 1706-1714 (1988). [CrossRef]
  14. B. M. Sadler and G. B. Giannakis, “Shift- and rotation-invariant object reconstruction using the bispectrum,” J. Opt. Soc. Am. A 9, 57-69 (1992). [CrossRef]
  15. J. Heikkilä, “Image scale and rotation from the phase-only bispectrum,” in Proceedings of the 2004 IEEE International Conference on Image Processing (IEEE, 2004).
  16. A. P. Petropulu and H. Pozidis, “Phase reconstuction from bispectrum slices,” IEEE Trans. Image Process. 46, 527-530 (1998).
  17. C. L. Nikias and A. P. Petropulu, Higher-Order Spectra Analysis: A Nonlinear Signal Processing Framework (Prentice-Hall, 1993).
  18. Y. T. Chan, “Notes on: Time delay estimation, ARMA processes, tracking filters” (Department of Electrical Engineering, Royal Military College Canada, Kingston, Ontario, Canada K7L2W3, April 1985).
  19. G. Madec, “Half pixel accuracy in blockmatching,” in Proceedings of the Picture Coding Symposium (PCS 90), Cambridge, Massachusetts, USA, March 1990.
  20. E. M. Ismaili Aalaoui and E. Ibn-Elhaj, “Estimation of motion fields from noisy image sequences using generalized cross-correlation methods,” in Proceedings of IEEE International Conference on Signal Processing and Communications 2007 (IEEE, 2007).
  21. E. M. Ismaili Aalaoui and E. Ibn-Elhaj, “Estimation of displacement vector field from noisy data using maximum likelihood estimator,” in 14th IEEE International Conference on Electronics, Circuits and Systems (IEEE, 2007).
  22. W. K. Pratt, Digital Image Processing, PIKS Scientific Inside, 4th ed. (Wiley, 2007).
  23. S. G. Johnson and M. Frigo, “A modified split-radix FFT with fewer arithmetic operations,” IEEE Trans. Signal Process. 55, 111-119 (2007). [CrossRef]
  24. K. S. Lii and K. N. Helland, “Cross bispectrum computation and variance estimation,” ACM Trans. Math. Softw. 7, 284-294 (1981). [CrossRef]
  25. J.-M. L. Caillec and R. Garello, “Comparison of statistical indices using third order statistics for nonlinearity detection,” Signal Process. 84, 499-525 (2004). [CrossRef]
  26. S. A. Kruger and A. D. Calway, “A multiresolution frequency domain method for estimating affine motion parameters,” in 1996 Proceedings of International Conference on Image Processing (IEEE, 1996), Vol. 1, 113-116. [CrossRef]
  27. A. K. Jain, Fundamentals of Digital Image Processing (Prentice Hall, 1989).

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