Symbolic dynamic filtering for image analysis: theory and experimental validation


Recent literature has reported the theory of symbolic dynamic filtering (SDF) of one-dimensional time-series data and its various applications for anomaly detection and pattern recognition. This paper extends the theory of SDF in the two-dimensional domain, where symbol sequences are generated from image data (i.e., pixels). Given the symbol sequence, a probabilistic finite state automaton (PFSA), called the D-Markov machine, is constructed on the principles of Markov random fields to incorporate the spatial information in the local neighborhoods of a pixel. The image analysis algorithm has been experimentally validated on a computer-controlled fatigue test apparatus that is equipped with a traveling optical microscope and ultrasonic flaw detectors. The surface images of test specimens, made of a polycrystalline alloy, are analyzed to detect and quantify the evolution of fatigue damage. The results of two-dimensional SDF analysis are in close agreement with those obtained from analysis of one-dimensional time-series data from the ultrasonic sensor, which are simultaneously generated from the same test specimen.

This is a preview of subscription content, access via your institution.


  1. 1

    Bovik, A. (eds): Handbook of Image and Video Processing. Academic Press, New York (2000)

    MATH  Google Scholar 

  2. 2

    Lee T.: Image representation using 2D Gabor wavelets. IEEE Trans. Pattern Anal. Mach. Intell. 18(10), 959–971 (1996)

    Article  Google Scholar 

  3. 3

    Manjunath B., Ma W.: Texture features for browsing and retrieval of image data. IEEE Trans. Pattern Anal. Mach. Intell. 18(8), 837–842 (1996)

    Article  Google Scholar 

  4. 4

    Li J., Gray R., Olshen R.: Multiresolution image classification by hierarchical modeling with two dimensional hidden Markov models. IEEE Trans. Inform. Theory 46(5), 1826–1841 (2000)

    MATH  Article  MathSciNet  Google Scholar 

  5. 5

    Ray A.: Symbolic dynamic analysis of complex systems for anomaly detection. Signal Process. 84(7), 1115–1130 (2004)

    MATH  Article  Google Scholar 

  6. 6

    Lind D., Marcus M.: An Introduction to Symbolic Dynamics and Coding. Cambridge University Press, Cambridge (1995)

    MATH  Book  Google Scholar 

  7. 7

    Rajagopalan V., Chakraborty S., Ray A.: Estimation of slowly-varying parameters in nonlinear systems via symbolic dynamic filtering. Signal Process. 89(2), 339–348 (2008)

    Article  Google Scholar 

  8. 8

    Samsi R., Ray A., Mayer J.: Early detection of stator voltage imbalance in three-phase induction motors. Electr. Power Syst. Res. 79(1), 239–245 (2009)

    Article  Google Scholar 

  9. 9

    Chakraborty, S., Ray, A., Subbu, A., Keller, E.: Analytic signal space partitioning and symbolic dynamic filtering for degradation monitoring of electric motors. Signal Image Video Process. (2008, to appear)

  10. 10

    Mallapragada, G., Chattopadhyay, I., Ray, A.: Automated behavior recognition in mobile robots using symbolic dynamic filtering. Proceedings of the I Mech E Part I: Journal of Systems & Control Engineering, vol. 222, no. 6, pp. 409–424 (2008)

  11. 11

    Gupta S., Ray A., Keller E.: Symbolic time series analysis of ultrasonic signals for fatigue damage monitoring in polycrystalline alloys. Meas. Sci. Technol. 17(7), 1963–1973 (2006)

    Article  Google Scholar 

  12. 12

    Rao, C., Ray, A., Sarkar, S., Yasar M.: Review and comparative evaluation of symbolic dynamic filtering for detection of anomaly patterns. Signal Image Video Process. (2008). doi:10.1007/s11760-008-0061-8

  13. 13

    Subbu A., Ray A.: Space partitioning via hilbert transform for symbolic time series analysis. Appl. Phys. Lett. 92(8), 084107–10841073 (2008)

    Article  Google Scholar 

  14. 14

    Rajagopalan V., Ray A.: Symbolic time series analysis via wavelet-based partitioning. Signal Process. 86(11), 3309–3320 (2006)

    MATH  Article  Google Scholar 

  15. 15

    Buhl M., Kennel M.: Statistically relaxing to generating partitions for observed time-series data. Phys. Rev. E 71(4), 046213 (2005)

    Article  MathSciNet  Google Scholar 

  16. 16

    Gabor D.: Theory of communication. IEE J. Commun. Eng. 93, 429–457 (1946)

    Google Scholar 

  17. 17

    Cohen L.: Time-Frequency Analysis. Englewood Cliffs, Prentice Hall PTR (1995)

    Google Scholar 

  18. 18

    Havlicek, J., Havlicek, J., Bovik, A.: The analytic image. Image Processing, 1997. Proceedings., International Conference on, October 1997, vol. 2, pp. 446–449

  19. 19

    Hahn S.: Multidimensional complex signals with single-orthant spectra. Proc. IEEE 80(8), 1287–1300 (1992)

    Article  Google Scholar 

  20. 20

    Zhu Y.M., Peyrin F., Goutte R.: The use of a two-dimensional hilbert transform for wigner analysis of 2-dimensional real signals. Signal Process. 19(3), 205–220 (1990)

    MATH  Article  MathSciNet  Google Scholar 

  21. 21

    Stark H.: An extension of the Hilbert transform product theorem. Proc. IEEE 59(9), 1359–1360 (1971)

    Article  MathSciNet  Google Scholar 

  22. 22

    Bose N.: Digital Filters: Theory and Applications. Krieger Publishing Company, New York (1993)

    Google Scholar 

  23. 23

    Havlicek J., Harding D., Bovik A.: The multicomponent AM-FM image representation. IEEE Trans. Image Process. 5(6), 1094–1100 (1996)

    Article  Google Scholar 

  24. 24

    Geman S., Geman D.: Stochastic relaxation, gibbs distributions, and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Mach. Intell. 6(6), 721–741 (1984)

    MATH  Article  Google Scholar 

  25. 25

    Vitria J., Bressan M., Radeva P.: Bayesian classification of cork stoppers using class-conditional independent component analysis. Syst. Man Cybern. Part C IEEE Trans. Appl. Rev. 37(1), 32–38 (2007)

    Article  Google Scholar 

  26. 26

    Kumar A.: Computer-vision-based fabric defect detection: a survey . IEEE Trans. Ind. Electron. 55(1), 348–363 (2008)

    Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Asok Ray.

Additional information

This work has been supported in part by the U.S. Army Research Office under Grant No. W911NF-07-1-0376, and by NASA under Cooperative Agreement No. NNX07AK49A. Any opinions, findings and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the sponsoring agencies.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Subbu, A., Srivastav, A., Ray, A. et al. Symbolic dynamic filtering for image analysis: theory and experimental validation. SIViP 4, 319–329 (2010).

Download citation


  • Image analysis
  • Two-dimensional symbolic analysis
  • Statistical pattern recognition
  • Fatigue damage analysis