Adaptive Filtering Using Channel Representations

  • Michael Felsberg
Part of the Computational Imaging and Vision book series (CIVI, volume 41)


This review article gives an overview on adaptive filtering methods based on channel representations. The framework of channel representations and its relation to density estimation is introduced. The fast and accurate scheme of virtual shift decoding is introduced and applied in several variants of channel smoothing:
  • channel smoothing with alpha-synthesis for improving stability of edge-enhancing filtering

  • orientation adaptive channel smoothing with applications to coherence-enhancing filtering

  • channel smoothing using graph-cuts for improving filtering results at corners

  • channel-coded feature maps (CCFMs) which lead to a significant speed-up of channel averaging

  • CCFM-based smoothing based on optimal parameters derived from a novel uncertainty relation

For each method, an algorithmic description and some examples of results are provided, together with discussions and references of the original papers. Cross connections to other articles in this volume are given where appropriate.


Scale Space Channel Average Channel Vector Orientation Channel Channel Decode 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The author would like to thank P.-E. Forssén for various discussions about the paper, in particular on alpha-synthesis. The research leading to these results has received funding from the European Community’s Seventh Framework Programme (FP7/2007-2013) under grant agreements no 215078 (DIPLECS) and 247947 (GARNICS) as well as the VR project 2009-4282.


  1. 52.
    Boykov, Y., Kolmogorov, V.: An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision. IEEE Trans. Pattern Anal. Mach. Intell. 26(9), 1124–1137 (2004) CrossRefGoogle Scholar
  2. 63.
    Burt, P.J., Adelson, E.H.: The Laplacian pyramid as a compact image code. IEEE Trans. Commun. 31(4), 532–540 (1983) CrossRefGoogle Scholar
  3. 92.
    Daubechies, I.: Orthonormal bases of compactly supported wavelets. Commun. Pure Appl. Math. 41(7), 909–996 (1988) CrossRefzbMATHMathSciNetGoogle Scholar
  4. 116.
    Duits, R., Florack, L., de Graaf, J., ter Haar Romeny, B.: On the axioms of scale space theory. J. Math. Imaging Vis. 20(3), 267–298 (2004) CrossRefGoogle Scholar
  5. 117.
    Duits, R., Felsberg, M., Granlund, G., ter Haar Romeny, B.M.: Image analysis and reconstruction using a wavelet transform constructed from a reducible representation of the Euclidean motion group. Int. J. Comput. Vis. 72(1), 79–102 (2007) CrossRefGoogle Scholar
  6. 126.
    Elder, J.H., Zucker, S.W.: Local scale control for edge detection and blur estimation. IEEE Trans. Pattern Anal. Mach. Intell. 20(7), 699–716 (1998) CrossRefGoogle Scholar
  7. 132.
    Felsberg, M.: Wiener channel smoothing: Robust Wiener filtering of images. In: DAGM 2005. Lecture Notes in Computer Science, vol. 3663, pp. 468–475. Springer, Berlin (2005) Google Scholar
  8. 133.
    Felsberg, M.: Extending graph-cut to continuous value domain minimization. In: Proceedings of the 4th Canadian Conference on Computer and Robot Vision, pp. 274–281 (2007) Google Scholar
  9. 134.
    Felsberg, M.: On the relation between anisotropic diffusion and iterated adaptive filtering. In: 30th DAGM Symposium Mustererkennung. Lecture Notes in Computer Science, vol. 5096, pp. 436–445. Springer, Berlin (2008) Google Scholar
  10. 135.
    Felsberg, M.: Spatio-featural scale-space. In: Tai, X.-C., Mørken, K., Lysaker, M., Lie, K.-A. (eds.) Scale Space and Variational Methods in Computer Vision: Proceedings of the 2nd International Conference, SSVM 2009, Voss, Norway, June 1–5, 2009. Lecture Notes in Computer Science, vol. 5567, pp. 808–819. Springer, Berlin (2009) CrossRefGoogle Scholar
  11. 136.
    Felsberg, M., Granlund, G.: Anisotropic channel filtering. In: Proceedings of the 13th Scandinavian Conference on Image Analysis. Lecture Notes in Computer Science, vol. 2749, pp. 755–762 (2003) Google Scholar
  12. 137.
    Felsberg, M., Granlund, G.: P-channels: robust multivariate M-estimation of large datasets. In: Proceedings of the 18th International Conference on Pattern Recognition, ICPR’06, Hong Kong, August 20–24, 2006, pp. 262–267 (2006) Google Scholar
  13. 138.
    Felsberg, M., Sommer, G.: The monogenic scale-space: a unifying approach to phase-based image processing in scale-space. J. Math. Imaging Vis. 21, 5–26 (2004) CrossRefMathSciNetGoogle Scholar
  14. 139.
    Felsberg, M., Forssén, P.-E., Scharr, H.: Channel smoothing: efficient robust smoothing of low-level signal features. IEEE Trans. Pattern Anal. Mach. Intell. 28(2), 209–222 (2006) CrossRefGoogle Scholar
  15. 140.
    Felsberg, M., Kalkan, S., Krüger, N.: Continuous dimensionality characterization of image structures. Image Vis. Comput. 27(6), 628–636 (2009) CrossRefGoogle Scholar
  16. 159.
    Forssén, P.-E.: Low and medium level vision using channel representations. PhD thesis, Linköping University, Sweden (2004) Google Scholar
  17. 160.
    Forssén, P.-E., Granlund, G.: Robust multi-scale extraction of blob features. In: Proceedings of the 13th Scandinavian Conference on Image Analysis. Lecture Notes in Computer Science, vol. 2749, pp. 11–18 (2003) Google Scholar
  18. 161.
    Förstner, W.: Image preprocessing for feature extraction in digital intensity, color and range images. In: Dermanis, A., Grün, A., Sansò, F. (eds.) Proceedings of the International Summer School on Data Analysis and the Statistical Foundation of Geomatics, Chania, Crete, Greece, May 25–30, 1998. Lecture Notes on Earth Sciences, pp. 165–189. Springer, Berlin (1998) Google Scholar
  19. 171.
    Freeman, W.T., Adelson, E.H.: The design and use of steerable filters. IEEE Trans. Pattern Anal. Mach. Intell. 13(9), 891–906 (1991) CrossRefGoogle Scholar
  20. 188.
    Granlund, G.H.: In search of a general picture processing operator. Comput. Graph. Image Process. 8, 155–173 (1978) CrossRefGoogle Scholar
  21. 189.
    Granlund, G.H.: An associative perception-action structure using a localized space variant information representation. In: Proceedings of the International Workshop on Algebraic Frames for the Perception-Action Cycle. Lecture Notes in Computer Science, vol. 1888, pp. 48–68. Springer, Heidelberg (2000) CrossRefGoogle Scholar
  22. 230.
    Howard, I.P., Rogers, B.J.: Binocular Vision and Stereopsis. Oxford University Press, Oxford (1995) Google Scholar
  23. 232.
    Iijima, T.: Basic theory of pattern observation. In: Papers of Technical Group on Automata and Automatic Control, IECE, Japan, December, 1959 Google Scholar
  24. 241.
    Jonsson, E.: Channel-coded feature maps for computer vision and machine learning. PhD thesis, Linköping University, Sweden, SE-581 83 Linköping, Sweden (February 2008). Dissertation No. 1160, ISBN 978-91-7393-988-1 Google Scholar
  25. 242.
    Jonsson, E., Felsberg, M.: Reconstruction of probability density functions from channel representations. In: Proceedings of the 14th Scandinavian Conference on Image Analysis (2005) Google Scholar
  26. 243.
    Jonsson, E., Felsberg, M.: Accurate interpolation in appearance-based pose estimation. In: Ersbøll, B.K., Steenstrup Pedersen, K. (eds.) Proceedings of the 15th Scandinavian Conference on Image Analysis, Aalborg, Denmark, June 10–14, 2007. Lecture Notes in Computer Science, vol. 4522, pp. 1–10. Springer, Berlin (2007) Google Scholar
  27. 244.
    Jonsson, E., Felsberg, M.: Efficient computation of channel-coded feature maps through piecewise polynomials. Image Vis. Comput. 27(11), 1688–1694 (2009) CrossRefGoogle Scholar
  28. 258.
    Knutsson, H., Westin, C.-F.: Normalized convolution: technique for filtering incomplete and uncertain data. In: Høgda, K.A., Braathen, B., Heia, K. (eds.) Proceedings of the 8th Scandinavian Conference on Image Analysis, Tromsø, Norway, May 25–28, 1993, pp. 997–1006. NOBIM, Tromsø (1993) Google Scholar
  29. 259.
    Knutsson, H., Wilson, R., Granlund, G.H.: Anisotropic non-stationary image estimation and its applications: Part I—restoration of noisy images. IEEE Trans. Commun. COM–31(3), 388–397 (1983) CrossRefGoogle Scholar
  30. 261.
    Koenderink, J.J.: The structure of images. Biol. Cybern. 50, 363–370 (1984) CrossRefzbMATHMathSciNetGoogle Scholar
  31. 264.
    Koenderink, J.J., van Doorn, A.D.: Image processing done right. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) Proceedings of the 7th European Conference on Computer Vision, Copenhagen, Denmark, May–June 2002. Lecture Notes in Computer Science, vols. 2350–2353, pp. 158–172. Springer, Berlin (2002) Google Scholar
  32. 290.
    Lindeberg, T.: Scale-Space Theory in Computer Vision. The Kluwer International Series in Engineering and Computer Science. Kluwer Academic, Dordrecht (1994) Google Scholar
  33. 295.
    Lüdtke, N.L., Wilson, R.C., Hancock, E.R.: Probabilistic population coding of multiple edge orientation. In: Proceedings of the 9th International Conference on Image Processing, Rochester, NY, USA, September 22–25, 2002, pp. 865–868. IEEE Press, New York (2002) Google Scholar
  34. 298.
    Mallat, S.G.: A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans. Pattern Anal. Mach. Intell. 11, 674–693 (1989) CrossRefzbMATHGoogle Scholar
  35. 329.
    Paris, S., Durand, F.: A fast approximation of the bilateral filter using a signal processing approach. Int. J. Comput. Vis. 81(1), 24–52 (2009) CrossRefGoogle Scholar
  36. 334.
    Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell. 12(7), 629–639 (1990) CrossRefGoogle Scholar
  37. 346.
    Portilla, J., Strela, V., Wainwright, J., Simoncelli, E.P.: Image denoising using scale mixtures of Gaussians in the wavelet domain. IEEE Trans. Image Process. 12(11), 1338–1351 (2003) CrossRefMathSciNetGoogle Scholar
  38. 347.
    Pouget, A., Dayan, P., Zemel, R.: Information processing with population codes. Nat. Rev., Neurosci. 1, 125–132 (2000) CrossRefGoogle Scholar
  39. 363.
    Rozenholc, Y., Reiß, M., Balvay, D., Cuenod, C.-A.: Growing time homogeneous neighborhoods for denoising and clustering dynamic contrast enhanced-CT sequences. Technical report, University Paris Descartes (2009) Google Scholar
  40. 372.
    Scharr, H., Felsberg, M., Forssén, P.-E.: Noise adaptive channel smoothing of low-dose images. In: Proceedings of the 2003 Conference on Computer Vision and Pattern Recognition Workshop, CVPRW’03, pp. 1–8 (2003) Google Scholar
  41. 406.
    Therrien, C.W.: Decision, Estimation, and Classification: An Introduction Into Pattern Recognition and Related Topics. Wiley, New York (1989) Google Scholar
  42. 420.
    van den Boomgaard, R.: Nonlinear diffusion in computer vision.
  43. 432.
    Weickert, J.: Theoretical foundations of anisotropic diffusion in image processing. Comput. Suppl. 11, 221–236 (1996) CrossRefGoogle Scholar
  44. 439.
    Weickert, J., Scharr, H.: A scheme for coherence-enhancing diffusion filtering with optimized rotation invariance. J. Vis. Commun. Image Represent. 13(1–2), 103–118 (2002). Special Issue on Partial Differ. Equ. Image Process., Comput. Vis. Comput. Graph. CrossRefGoogle Scholar
  45. 442.
    Weickert, J., Ishikawa, S., Imiya, A.: Linear scale-space has first been proposed in Japan. J. Math. Imaging Vis. 10(3), 237–252 (1999) CrossRefzbMATHMathSciNetGoogle Scholar
  46. 450.
    Witkin, A.P.: Scale-space filtering. In: Proceedings of the International Joint Conference on Artificial Intelligence, Karlsruhe, Germany, pp. 1019–1022 (1983) Google Scholar
  47. 460.
    Zemel, R.S., Dayan, P., Pouget, A.: Probabilistic interpretation of population codes. Neural Comput. 10(2), 403–430 (1998) CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2012

Authors and Affiliations

  1. 1.Computer Vision Laboratory, Department of Electrical EngineeringLinköping UniversityLinköpingSweden

Personalised recommendations