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Intrinsic scale space for images on surfaces: The geodesic curvature flow

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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 scale space for images painted on surfaces is introduced. Based on the geodesic curvature flow of the iso-gray level contours of an image painted on the given surface, the image is evolved and forms the natural geometric scale space. Its geometrical properties are discussed as well as the intrinsic nature of the proposed flow. I.e. the flow is invariant to the bending of the surface.

This work is supported in part by the Applied Mathematics Subprogram of the Office of Energy Research under DE-AC03-76SFOOO98, and ONR grant under NOOO14-96-1-0381.

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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. D. L. Chopp and J. A. Sethian. Flow under curvature: Singularity formation, minimal surfaces, and geodesies. Jour. Exper. Math., 2(4):235–255, 1993.

    Google Scholar 

  4. C. L. Epstein and M. Gage. The curve shortening flow. In A. Chorin and A. Majda, editors, Wave Motion: Theory, Modeling, and Computation. Springer-Verlag, New York, 1987.

    Google Scholar 

  5. 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 

  6. D. Gabor. Information theory in electron microscopy. Laboratory Investigation, 14(6):801–807, 1965.

    Google Scholar 

  7. M. Gage and R. S. Hamilton. The heat equation shrinking convex plane curves. J. Diß. Geom., 23, 1986.

    Google Scholar 

  8. M. A. Grayson. The heat equation shrinks embedded plane curves to round points. J. Diff. Geom., 26, 1987.

    Google Scholar 

  9. M. A. Grayson. Shortening embedded curves. Annals of Mathematics, 129:71–111, 1989.

    Google Scholar 

  10. R. Kimmel and A. M. Bruckstein. Shape offsets via level sets. CAD, 25(5):154–162, March 1993.

    Google Scholar 

  11. R. Kimmel and N. Kiryati. Finding shortest paths on surfaces by fast global approximation and precise local refinement. Int. J. of Pattern Rec. and AI, to appear 1996.

    Google Scholar 

  12. R. Kimmel and G. Sapiro. Shortening three dimensional curves via two dimensional flows. International Journal: Computers & Mathematics with Applications, 29(3):49–62, March 1995.

    Google Scholar 

  13. R. Kimmel, N. Sochen, and R. Malladi. From high energy physics to low level vision. In Lecture Notes In Computer Science (this collection). Springer-Verlag, 1997.

    Google Scholar 

  14. M. Lindenbaum, M. Fischer, and A. M. Bruckstein. On Gabor's contribution to image enhancement. Pattern Recognition, 27(1):1–8, 1994.

    Google Scholar 

  15. S. J. Osher and J. A. Sethian. Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations. J. of Comp. Phys., 79:12–49, 1988.

    Google Scholar 

  16. In B. M. ter Haar Romeny, editor, Geometric-Driven Diffusion in Computer Vision. Kluwer Academic Publishers, The Netherlands, 1994.

    Google Scholar 

  17. G. Sapiro and A. Tannenbaum. On invariant curve evolution and image analysis. Indiana University Mathematics Journal, 42(3), 1993.

    Google Scholar 

  18. J. A. Sethian. A review of recent numerical algorithms for hypersurfaces moving with curvature dependent speed. J. of Diff. Geom., 33:131–161, 1990.

    Google Scholar 

  19. 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 

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Authors and Affiliations

  1. Lawrence Berkeley National Laboratory, University of California, 94720, Berkeley, CA

    Ron Kimmel

  2. Dept. of of Mathematics, University of California, 94720, Berkeley, CA

    Ron Kimmel

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  1. Ron Kimmel
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Editor information

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. (1997). Intrinsic scale space for images on surfaces: The geodesic curvature flow. 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_52

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  • DOI: https://doi.org/10.1007/3-540-63167-4_52

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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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