Segmentation of Coarse and Fine Scale Features Using Multi-scale Diffusion and Mumford-Shah

  • Jeremy D. Jackson
  • Anthony YezziJr.
  • Wes Wallace
  • Mark F. Bear
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2695)

Abstract

Here we present a segmentation algorithm that uses multiscale diffusion with the Mumford-Shah model. The image data inside and outside a surface is smoothed by minimizing an energy functional using a partial differential equation that results in a trade-off between smoothing and data fidelity. We propose a scale-space approach that uses a good deal of diffusion as its coarse scale space and that gradually reduces the diffusion to get a fine scale space. So our algorithm continually moves to a particular diffusion level rather than just using a set diffusion coefficient with the Mumford-Shah model. Each time the smoothing is decreased, the data fidelity term increases and the surface is moved to a steady state. This method is useful in segmenting biomedical images acquired using high-resolution confocal fluorescence microscopy. Here we tested the method on images of individual dendrites of neurons in rat visual cortex. These dendrites are studded with dendritic spines, which have very small heads and faint necks. The coarse scale segments out the dendrite and the brighter spine heads, while avoiding noise. Backing off the diffusion to a medium scale fills in more of the structure, which gets some of the brighter spine necks. The finest scale fills in the small and detailed features of the spines that are missed in the initial segmentation. Because of the thin, faint structure of the spine necks, we incorporate into our level set framework a topology preservation method for the surface which aids in segmentation and keeps a simple topology.

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References

  1. 1.
    Tsai, A., Yezzi A., Wilsky A.: Curve Evolution Implementation of the Mumford-Shah Functional for Image Segmentation, Denoising, Interpolation, and Magnification. IEEE Trans. on Image Processing (2001) 1169–1184Google Scholar
  2. 2.
    Yezzi, A., Tsai, A., Wilsky, A.: A statistical approach to snakes for bimodal and trimodal imagery. Int. Conf. on Computer Vision. (1999) 2 898–903Google Scholar
  3. 3.
    Yezzi, A.: Modified curvature motion for image smoothing and enhancement. IEEE Trans. Image Processing 7 (1998) 345–352CrossRefGoogle Scholar
  4. 4.
    Mumford D., Shah J.: Optimal approximations by piecewise smooth functions and associated variational problems. Commun. Pure Appl. Math (1989)Google Scholar
  5. 5.
    Chan, T.F, Vese, L.A.: Active contours without edges. IEEE Trans. Image Processing 10 (2001) 266–277MATHCrossRefGoogle Scholar
  6. 6.
    Chan, T.F, Vese, L.A.: A level set algorithm for minimizing the Mumford-Shah functional in image processing. IEEE Proc. on Variational and Level Set Meth. in Comp. Vision (2001) 161–168Google Scholar
  7. 7.
    Paragios, N., Deriche, R.: Geodesic active regions for texture segmentation. INRIA, France, Res. Rep. 3440 (1998)Google Scholar
  8. 8.
    Ronfard, R.: Region-based strategies for active contour models. Int. J. Comput. Vis. 13 (1994) 229–251CrossRefGoogle Scholar
  9. 9.
    Zhu, S., Yuille, A.: Region competition: Unifying snakes, region growing, and Bayes/MDL for multiband image segmentation. IEEE Trans. Pattern Anal. Machine Intell. 18 (1996) 884–900CrossRefGoogle Scholar
  10. 10.
    Nimchinsky E. A., Sabatini B.L. and Svoboda K. (2002). “Structure and function of dendritic spines.” Annu. Rev. Physiol. 64: 313–353.CrossRefGoogle Scholar
  11. 11.
    Osher, S., Sethian, J.: Fronts propagation with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations. J. Comput. Physics 79 (1988) 12–49MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    J.A. Sethian: Level Set Methods and Fast Marching Methods: Evolving Interfaces in Geometry, Fluid Mechanics, Computer Vision, and Material Science. Cambridge, U.K.: Cambridge University Press (1999)MATHGoogle Scholar
  13. 13.
    Kass, M., Witkin, A., Terzopoulos, D.: Snakes: Active contour models. Int. J. Comput. Vis 1 (1987) 321–331CrossRefGoogle Scholar
  14. 14.
    Han, X., Xu, C., Tosun, D., Prince, J.L.: Corical Surface Reconstruction Using a Topology Preserving Geometric Model. IEEE Trans. on Medical Imaging (2002) 109–121Google Scholar
  15. 15.
    Malandain, G., Bertrand G.: Fast Characterization of 3D Simple Points. IEEE Pattern Recognition (1992) 232–235Google Scholar
  16. 16.
    Malandain, G., Bertrand G.: A new characterization of three-dimensional simple points. Pattern Recognition Letters 15 (1994) 169–175MATHCrossRefGoogle Scholar
  17. 17.
    Bertrand, G.: Simple points, toplogical numbers and geodesic negihborhoods in cubic grids. Pattern Recognition Letters 15 (1994) 1003–1011CrossRefGoogle Scholar
  18. 18.
    Weinstock, R.: Calculus of Variations: With Applications to Physics and Engineering. New York: Dover Pub. Inc. (1974)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Jeremy D. Jackson
    • 1
  • Anthony YezziJr.
    • 1
  • Wes Wallace
    • 2
  • Mark F. Bear
    • 2
  1. 1.School of Electrical and Computer EngineeringGeorgia Institute of TechnologyAtlanta
  2. 2.Department of NeuroscienceHoward Hughes Medical Institute/Brown UniversityProvidence

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