A Probabilistic Derivative Measure Based on the Distribution of Intensity Difference

  • Youngbae Hwang
  • In-So Kweon
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7577)


In this paper, we propose a novel derivative measure based on the probability of intensity difference that is defined by observed intensities and their true intensities. Because the true intensity cannot be estimated accurately only using two observed intensities, the probability is marginalized to consider an entire set of possible true values. The proposed measure not only considers intensity dependent noise effectively using a distribution of intensity difference, but also computes the relevant difference of two corresponding pixels that have different true intensities by extending the same intensity assumption in previous works. Using the proposed measure, the estimation result of image derivative for synthetic noisy signals is closer to the ground truth than most of previous measures. We apply the proposed measure for block matching and corner detection that compute intensity similarity in the temporal domain and image derivative in the spatial domain, respectively.


  1. 1.
    Canny, J.: A computational approach to edge detection. IEEE Trans. on Pattern Analysis and Machine Intelligence 8(6), 679–698 (1986)CrossRefGoogle Scholar
  2. 2.
    Harris, C., Stephens, M.: A combined corner and edge detector. In: Fourth Alvey Vision Conference, pp. 147–151 (1988)Google Scholar
  3. 3.
    Schmid, C., Mohr, R., Bauckhage, C.: Evaluation of interest point detectors. International Journal of Computer Vision 37(2), 151–172 (2000)zbMATHCrossRefGoogle Scholar
  4. 4.
    Shi, J., Tomasi, C.: Good features to track. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR), pp. 593–600 (1994)Google Scholar
  5. 5.
    Healey, G., Kondepudy, R.: Radiometric CCD camera calibration and noise estimation. IEEE Trans. on Pattern Analysis and Machine Intelligence 16(3), 267–276 (1994)CrossRefGoogle Scholar
  6. 6.
    Freeman, W.T., Pasztor, E.C., Carmichael, O.T.: Learning low-level vision. IJCV 40, 25–47 (2000)zbMATHCrossRefGoogle Scholar
  7. 7.
    Tappen, M., Liu, C., Adelson, E., Freeman, W.: Learning gaussian conditional random fields for low-level vision. In: Proc. of CVPR, p. 7 (2007)Google Scholar
  8. 8.
    Alter, F., Matsushita, Y., Tang, X.: An Intensity Similarity Measure in Low-Light Conditions. In: Leonardis, A., Bischof, H., Pinz, A. (eds.) ECCV 2006, Part IV. LNCS, vol. 3954, pp. 267–280. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  9. 9.
    Matsushita, Y., Li, S.: A probabilistic intensity similarity measure based on noise distributions. In: IEEE Proc. of CVPR (2007)Google Scholar
  10. 10.
    Skellam, J.G.: The frequency distribution of the difference between two poisson variates belonging to different populations. Journal of the Royal Statistical Society: Series A 109(3), 296 (1946)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Liu, C., Szeliski, R., Kang, S.B., Zitnick, C.L., Freeman, W.T.: Automatic estimation and removal of noise from a single image. IEEE Trans. on PAMI 30(2), 299–314 (2008)CrossRefGoogle Scholar
  12. 12.
    Azzabou, N., Paragios, N., Guichard, F., Cao, F.: Variable bandwidth image denoising using image-based noise models. In: IEEE Proc. of CVPR (2007)Google Scholar
  13. 13.
    Hwang, Y., Kim, J.S., Kweon, I.S.: Difference-based image noise modeling using skellam distribution. IEEE Trans. on PAMI 34(7), 1329–1341 (2012)CrossRefGoogle Scholar
  14. 14.
    Rosten, E., Drummond, T.: Machine Learning for High-Speed Corner Detection. In: Leonardis, A., Bischof, H., Pinz, A. (eds.) ECCV 2006, Part I. LNCS, vol. 3951, pp. 430–443. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  15. 15.
    Smith, S.M., Brady, J.M.: Susan – a new approach to low level image processing. IJCV 23(1), 45–78 (1997)CrossRefGoogle Scholar
  16. 16.
    Lowe, D.G.: Distinctive image features from scale-invariant keypoints. IJCV 60, 91–110 (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Youngbae Hwang
    • 1
  • In-So Kweon
    • 2
  1. 1.Korea Electronics Technology Institute (KETI)Korea
  2. 2.Korea Advanced Institute of Science and Technology (KAIST)Korea

Personalised recommendations