Image Feature Extraction Using a Method Derived from the Hough Transform with Extended Kalman Filtering

  • Sergio A. Velastin
  • Chengping Xu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4872)


The conventional implementation of the Hough Transform is inadequate in many cases due to its integrative effects of the discrete spaces. The design of an algorithm to extract optimal parameters of curves passing through image points requires a measure of statistical fitness. A strategy for image feature extraction called Tracking Hough Transform (THT) is presented that combines Extended Kalman Filtering with a Hough voting scheme that incorporates a formal noise model. The minimum mean-squares filtering process leads to high accuracy. Computing cost for real-time applications is addressed by introducing a converging sampling scheme. Extensive performance tests show that the algorithm can achieve faster speed, lower storage requirement and higher accuracy than the Standard Hough Transform.


Hough Transform Parametric curve detection line detection Kalman Filtering 


  1. 1.
    Duda, R.O., Hart, P.E.: Use of the Hough transform to detect lines and curves in pictures. Communications of the Association of Computing Machinery 15, 11–15 (1972)Google Scholar
  2. 2.
    Leavers, V.F.: Which Hough transform? Computer Vision, Graphics & Image Processing (CVGIP): Image Understanding 58, 250–264 (1993)CrossRefGoogle Scholar
  3. 3.
    Liang, P.: A new and efficient transform for curve detection. Journal of Robotic Systems 8, 841–847 (1991)CrossRefGoogle Scholar
  4. 4.
    Niblack, W., Petkovic, D.: On improving the accuracy of the Hough transform. Machine Vision and Applications 3, 87–106 (1990)CrossRefGoogle Scholar
  5. 5.
    Weiss, I.: Line fitting in a noisy image. IEEE Transactions on Pattern Analysis and Machine Intelligence 11, 325–329 (1989)zbMATHCrossRefGoogle Scholar
  6. 6.
    Kiryati, N., Bruckstein, A.M.: Antialiasing the Hough Transform. Computer Vision. Graphics and Image Processing: Graphical Models Image Processing 53, 213–222 (1991)Google Scholar
  7. 7.
    Xu, L., Oja, E., Kultanen, P.: A new curve detection method: Randomized Hough Transform (RHT). Pattern Recognition Letters 11, 328–331 (1990)CrossRefGoogle Scholar
  8. 8.
    Kiryati, N., Eldar, Y., Bruckstein, A.M.: A probabilistic Hough transform. Pattern Recognition 24, 303–316 (1991)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Xu, L., Oja, E.: Randomized Hough transform (RHT): Basic mechanisms, algorithms, and computational complexities. Computer Vision, Graphics and Image Processing: Image Understanding 57, 131–154 (1993)CrossRefGoogle Scholar
  10. 10.
    Kalviainen, H., Hirvonen, P., Xu, L., Oja, E.: Comparisons of probabilistic and non-probabilistic Hough transforms. In: Eklundh, J.-O. (ed.) ECCV 1994. LNCS, vol. 801, pp. 351–360. Springer, Heidelberg (1994)Google Scholar
  11. 11.
    Shaked, D., Yaron, O., Kiryati, N.: Deriving stopping rules for the probabilistic Hough transform by Sequential Analysis. Computer Vision and Image Understanding 63, 512–526 (1996)CrossRefGoogle Scholar
  12. 12.
    Behrens, T., Rohr, K., Stiehl, H.S.: Using an extended Hough transform combined with a Kalman filter to segment tubular structures in 3D medical images. In: Proceedings of the Vision, Modelling, and Visualization Conference 2001, pp. 491–498Google Scholar
  13. 13.
    Hills, M., Pridmore, T., Mills, S.: Object tracking through a Hough space. In: VIE 2003. Visual Information Engineering Conference, pp. 53–56. IEE, Guildford (2003)Google Scholar
  14. 14.
    French, A., Mills, S., Pridmore, T.: Condensation tracking through a Hough space. In: ICPR 2004. 17th International Conference on Pattern Recognition, vol. 4, pp. 195–198.Google Scholar
  15. 15.
    Xu, C., Velastin, S.A.: A comparison between the standard Hough transform and the Mahalanobis distance Hough transform. In: Eklundh, J.-O. (ed.) LNCS, vol. 800, pp. 95–100 (1994)Google Scholar
  16. 16.
    Xu, C., Velastin, S.A.: The Mahalanobis Distance Hough Transform with Extended Kalman Filter Refinement. IEEE International Symposium on Circuits & Systems 3, 5–8 (1994)Google Scholar
  17. 17.
    Brown, R.G., Hwang, P.Y.C.: Introduction to Random Signal Analysis and Kalman Filtering, 2nd edn. John Wiley and Sons Inc., Chichester (1992)Google Scholar
  18. 18.
    Gerig, G.: Linking image-space and accumulator-space: A new approach for object-recognition. In: Proceedings of IEEE 1st International Conference on Computer Vision, pp. 112–115 (1987)Google Scholar
  19. 19.
    Dambra, C., Serpico, S.B., Vernazza, G.: A new technique for peak detection in the Hough-transform parameter space. In: Proceedings of Signal Processing V: Theories and Applications, pp. 705–708 (1990)Google Scholar
  20. 20.
    Xu, C.: The Mahalanobis Distance Hough Transform with Kalman Filter Refinement. PhD thesis, King’s College London, University of London (1995) Google Scholar
  21. 21.
    Weiss, R., Boldt, M.: Geometric grouping applied to straight lines. In: ICPR 1986. IEEE International Conference on Pattern Recognition, pp. 489–495.Google Scholar
  22. 22.
    Hare, A.R., Sandler, M.B.: General test framework for straight-line detection by Hough transforms. In: ISCAS 1993. IEEE International Symposium on Circuits and Systems, pp. 239–242.Google Scholar
  23. 23.
    Hunt, D.J., Nolte, L.W.: Performance of the Hough transform and its relationship to statistical signal detection theory. Computer Vision, Graphics and Image Processing 43, 221–238 (1988)CrossRefGoogle Scholar
  24. 24.
    Peterson, W.W., Birdsall, T.G., Fox, W.C.: The theory of signal detectability. IRE Transactions on Information Theory 4, 171–211 (1954)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Sergio A. Velastin
    • 1
  • Chengping Xu
    • 1
  1. 1.Digital Imaging Research Centre, Kingston University, Kingston upon Thames, KT1 2EEUnited Kingdom

Personalised recommendations