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Gaussian Scale Space from Insufficient Image Information

  • Marco Loog
  • Martin Lillholm
  • Mads Nielsen
  • Max A. Viergever
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2695)

Abstract

Gaussian scale space is properly defined and well-developed for images completely knownand defined on the d dimensional Euclidean space ℝd. However, as soon as image information is only partly available, say, on a subset V of ℝd, the Gaussian scale space paradigm is not readily applicable and one has to resort to different approaches to come to a scale space on V. Examples are the theory dealing with scale space on ℤd ⊂ ℝd, i.e., discrete scale space; the approach based on the heat equation satisfying certain boundary conditions; and the ad hoc approaches dealing with (hyper)rectangular images, e.g. zero-padding of the area outside of V, or periodic continuation of the image.

We propose to solve the foregoing problem for general V from a Bayesian viewpoint. Assuming that the observed image is obtained by linearly sampling a real underlying image that is actually defined on the complete d dimensional Euclidean space, we can infer this latter image and from that image build the scale space. Re-sampling this scale space then gives rise to the scale space on V. Necessary for inferring the underlying image is knowledge on the linear apertures (or receptive field) used for sampling this image, and information on the prior over the class of all images.

Keywords

Scale Space Image Information Subset Versus Prior Assumption Dimensional Euclidean Space 
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.

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References

  1. 1.
    S. Chaudhuri. Super-Resolution Imaging, volume 632 of International Series in Engineering and Computer Science. Kluwer Academic Publishers, Boston, 2001.Google Scholar
  2. 2.
    D. J. Field. Relations between the statistics of natural images and the response properties of cortical cells. Journal of the Optical Society of America. A, Optics and Image Science, 4(12):2379–2394, 1987.CrossRefGoogle Scholar
  3. 3.
    L. M. J. Florack. Image Structure, volume 10 of Computational Imaging and Vision. Kluwer, Dordrecht. Boston. London, 1997.Google Scholar
  4. 4.
    C. Fox. An Introduction to the Calculus of Variations. Dover Press, New York, 1987.zbMATHGoogle Scholar
  5. 5.
    J. J. Koenderink. The structure of images. Biological Cybernetics, 50:363–370, 1984.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    M. Lillholm, M. Nielsen, and L. D. Griffin. Feature-based image analysis. International Journal of Computer Vision, in press, 2003.Google Scholar
  7. 7.
    T. Lindeberg. Scale-space for discrete signals. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(3):234–245, 1990.CrossRefGoogle Scholar
  8. 8.
    D. L. Ruderman and W. Bialek. Statistics of natural images: Scaling in the woods. Physical Review Letters, 73(6):100–105, 1994.CrossRefGoogle Scholar
  9. 9.
    J. L. Starck, E. Pantin, and F. Murtagh. Deconvolution in astronomy: A review. Publications of the Astronomical Society of the Pacific, 114:1051–1069, 2002.CrossRefGoogle Scholar
  10. 10.
    S. Zhu, Y. Wu, and D. Mumford. Minimax entropy principle and its application to texture modeling. Neural Computation, 9:1627–1660, 1997.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Marco Loog
    • 1
  • Martin Lillholm
    • 2
  • Mads Nielsen
    • 2
  • Max A. Viergever
    • 1
  1. 1.Image Sciences InstituteUniversity Medical Center UtrechtUtrechtThe Netherlands
  2. 2.Image Processing GroupIT University CopenhagenCopenhagenDenmark

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