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From high energy physics to low level vision

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Scale-Space Theory in Computer Vision (Scale-Space 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1252))

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Abstract

A geometric framework for image scale space, enhancement, and segmentation is presented. We consider intensity images as surfaces in the (x, I) space. The image is thereby a 2D surface in 3D space for gray level images, and a 2D surface in 5D for color images. The new formulation unifies many classical schemes and algorithms via a simple scaling of the intensity contrast, and results in new and efficient schemes. Extensions to multi dimensional signals become natural and lead to powerful denoising and scale space algorithms. Here, we demonstrate the proposed framework by applying it to denoise and improve gray level and color images.

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References

  1. L. Alvarez, F. Guichard, P. L. Lions, and J. M. Morel. Axioms and fundamental equations of image processing. Arch. Rational Mechanics, 123, 1993.

    Google Scholar 

  2. L. Alvarez, P. L. Lions, and J. M. Morel. Image selective smoothing and edge detection by nonlinear diffusion. SIAM J. Numer. Anal, 29:845–866, 1992.

    Google Scholar 

  3. A. Blake and A. Zisserman. Visual Reconstruction. MIT Press, Cambridge, Massachusetts, 1987.

    Google Scholar 

  4. P. Blomgren and T. F. Chan. Color TV: Total variation methods for restoration of vector valued images. cam TR, UCLA, 1996.

    Google Scholar 

  5. V. Caselles, R. Kimmel, G. Sapiro, and C. Sbert. Minimal surfaces: A geometric three dimensional segmentation approach. Numerische Mathematik, to appear, 1996.

    Google Scholar 

  6. A. Chambolle. Partial differential equations and image processing. In Proceedings IEEE ICIP, Austin, Texas, November 1994.

    Google Scholar 

  7. D. L. Chopp. Computing minimal surfaces via level set curvature flow. J. of Computational Physics, 106(1):77–91, May 1993.

    Google Scholar 

  8. S. Di Zenzo. A note on the gradient of a multi image. Computer Vision, Graphics, and Image Processing, 33:116–125, 1986.

    Google Scholar 

  9. A. I. El-Fallah, G. E. Ford, V. R. Algazi, and R. R. Estes. The invariance of edges and corners under mean curvature diffusions of images. In Processing III SPIE, volume 2421, pages 2–14, 1994.

    Google Scholar 

  10. L. M. J. Florack, A. H. Salden, B. M. ter Haar Romeny, J. J. Koendrink, and M. A. Viergever. Nonlinear scale-space. In B. M. ter Haar Romeny, editor, Geometric-Driven Diffusion in Computer Vision. Kluwer Academic Publishers, The Netherlands, 1994.

    Google Scholar 

  11. R. Kimmel. What is a natural norm for multi channel image processing. LBNL report, Berkeley Labs. UC, CA 94720, March 1997.

    Google Scholar 

  12. R. Kimmel, N. Sochen, and R. Malladi. On the geometry of texture. Report LBNL-39640, UC-405, Berkeley Labs. UC, CA 94720, November 1996.

    Google Scholar 

  13. R. Kimmel, N. Sochen, and R. Malladi. Images as embedding maps and minimal surfaces: Movies, color, and volumetric medical images. In Proc. of IEEE CVPR'97, Puerto Rico, June 1997.

    Google Scholar 

  14. E. Kreyszing. Differential Geometry. Dover Publications, Inc., New York, 1991.

    Google Scholar 

  15. R. Malladi and J. A. Sethian. Image processing: Flows under min/max curvature and mean curvature. Graphical Models and Image Processing, 58(2):127–141, March 1996.

    Google Scholar 

  16. D. Mumford and J. Shah. Boundary detection by minimizing functionals. In Proceedings of CVPR, Computer Vision and Pattern Recognition, San Francisco, 1985.

    Google Scholar 

  17. P. Perona and J. Malik. Scale-space and edge detection using anisotropic diffusion. IEEE-PAMI, 12:629–639, 1990.

    Google Scholar 

  18. A. M. Polyakov. Physics Letters, 103B:207, 1981.

    Google Scholar 

  19. T. Richardson and S. Mitter. Approximation, computation, and distoration in the variational formulation. In B. M. ter Haar Romeny, editor, Geometric-Driven Diffusion in Computer Vision. Kluwer Academic Publishers, The Netherlands, 1994.

    Google Scholar 

  20. L. Rudin, S. Osher, and E. Fatemi. Nonlinear total variation based noise removal algorithms. Physica D, 60:259–268, 1992.

    Google Scholar 

  21. G. Sapiro and D. L. Ringach. Anisotropic diffusion in color space. IEEE Trans. Image Proc., to appear, 1996.

    Google Scholar 

  22. G. Sapiro and A. Tannenbaum. Affine invariant scale-space. International Journal of Computer Vision, 11(1):25–44, 1993.

    Google Scholar 

  23. J. Shah. Curve evolution and segmentation functionals: Application to color images. In Proceedings IEEE ICIP'96, pages 461–464, 1996.

    Google Scholar 

  24. N. Sochen, R. Kimmel, and R. Malladi. From high energy physics to low level vision. Report LBNL 39243, LBNL, UC Berkeley, CA 94720, August 1996. http://www.lbl.gov/~ron/belt-html.html.

    Google Scholar 

  25. M. Spivak. A Comprehensive Introduction to Differential Geometry. Publish or Perish, Inc., Berkeley, 1979.

    Google Scholar 

  26. S. D. Yanowitz and A. M. Bruckstein. A new method for image segmentation. Computer Vision, Graphics, and Image Processing, 46:82–95, 1989.

    Google Scholar 

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Bart ter Haar Romeny Luc Florack Jan Koenderink Max Viergever

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© 1997 Springer-Verlag Berlin Heidelberg

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Kimmel, R., Sochen, N., Malladi, R. (1997). From high energy physics to low level vision. In: ter Haar Romeny, B., Florack, L., Koenderink, J., Viergever, M. (eds) Scale-Space Theory in Computer Vision. Scale-Space 1997. Lecture Notes in Computer Science, vol 1252. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63167-4_54

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  • DOI: https://doi.org/10.1007/3-540-63167-4_54

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63167-5

  • Online ISBN: 978-3-540-69196-9

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