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Combing a Porcupine via Stereographic Direction Difusion

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Scale-Space and Morphology in Computer Vision (Scale-Space 2001)

Part of the book series: Lecture Notes in Computer Science 2106 ((LNCS,volume 2106))

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Abstract

This paper addresses the problem of feature enhancement in noisy images when the feature is known to be constrained to a manifold. As an example, we study the problem of direction denoising. This problem was treated recently and several solutions were proposed. The various solutions share the same structure. They are composed of two terms: A difusion term and a projection term. Analytically, the solutions differ in the difusion part. The projection part is equivalent in all works. Yet, as it is often the case, the analytically equivalent projection terms differ from a numerical viewpoint. We present in this work a new parameterization of the problem that enables us to work always in a numerically stable way.

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References

  1. T. Chan and J. Shen, “Variational restoration of non-.at image features: Models and algorithms”, SIAM J. Appl. Math., to appear.

    Google Scholar 

  2. A. Cumani, “Edge detection in multi-spectral images”, CVGIP: Graphical Models and Image Processing 53 (1991) no.1 40–51.

    Article  MATH  Google Scholar 

  3. R. Kimmel and N. Sochen, “Orientation Difusion or How to Comb a Porcupine?”, special issue on PDEs in Image Processing, Computer Vision and Computer Graphics, Journal of Visual Communication and Image Representation, to appear.

    Google Scholar 

  4. R. Kimmel and R. Malladi and N. Sochen, “Images as Embedding Maps and Minimal Surfaces: Movies, Color, Texture, and Volumetric Medical Images”, International Journal of Computer Vision 39(2) (2000) 111–129.

    Article  MATH  Google Scholar 

  5. E. Kreyszig, “Differential Geometry”, Dover Publications, Inc., New York, 1991.

    Google Scholar 

  6. A.M. Polyakov, “Quantum geometry of bosonic strings”, Physics Letters, 103B (1981) 207–210.

    MathSciNet  Google Scholar 

  7. P. Perona, “Orientation Difusion” IEEE Trans. on Image Processing, 7 (1998) 457–467.

    Article  Google Scholar 

  8. N. Sochen and R.M. Haralick and Y.Y. Zeevi, “A Geometric functional for Derivatives Approximation” EE-Technion Report, April 1999.

    Google Scholar 

  9. N. Sochen and R. Kimmel and A.M. Bruckstein, “Difusions and confusions in signal and image processing”, accepted to Journal of Mathematical Imaging and Vision.

    Google Scholar 

  10. N. Sochen and R. Kimmel and R. Malladi, “From high energy physics to low level vision”, Report, LBNL, UC Berkeley, LBNL 39243, August, Presented in ONR workshop, UCLA, Sept. 5 1996.

    Google Scholar 

  11. N. Sochen and R. Kimmel and R. Malladi, “A general framework for low level vision”, IEEE Trans. on Image Processing, 7 (1998) 310–318.

    Article  MathSciNet  MATH  Google Scholar 

  12. N. Sochen, “Stochastic processes in vision I: From Langevin to Beltrami”, CCIT Technion technical report No. 245

    Google Scholar 

  13. N. Sochen and Y.Y. Zeevi, “Representation of colored images by manifolds embedded in higher dimensional non-Euclidean space”, Proc. IEEE ICIP’98, Chicago, 1998.

    Google Scholar 

  14. B. Tang and G. Sapiro and V. Caselles, “Direction difusion”, International Conference on Computer Vision, 1999.

    Google Scholar 

  15. B. Tang and G. Sapiro and V. Caselles, “Color image enhancement via chromaticity difusion” Technical report, ECE-University of Minnesota, 1999.

    Google Scholar 

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© 2001 Springer-Verlag Berlin Heidelberg

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Sochen, N.A., Kimmel, R. (2001). Combing a Porcupine via Stereographic Direction Difusion. In: Kerckhove, M. (eds) Scale-Space and Morphology in Computer Vision. Scale-Space 2001. Lecture Notes in Computer Science 2106, vol 2106. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47778-0_28

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  • DOI: https://doi.org/10.1007/3-540-47778-0_28

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42317-1

  • Online ISBN: 978-3-540-47778-5

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