A Class of Parallel Algorithms for Nonlinear Variational Segmentation: A preprocess for robust feature-based image coding

  • Josef Heers
  • Christoph Schnörr
  • H. Siegfried Stiehl

Abstract

Compact feature-based image coding as well as view-based object representations require a preprocessing step that abstracts from image details while preserving essential signal structures. Variational segmentation and nonlinear diffusion approaches provide powerful methods for the design of such a preprocessing stage. This motivates two investigate parallel numerical schemes to enable preprocessing of large image databases in a reasonable amount of time.

In the present paper we consider a non-quadratic convex variational approach for image segmentation and feature extraction. A class of iterative numerical algorithms is defined that allow for the efficient computation of the unique minimum. These algorithms converge globally and do not depend on the starting point. This is an important feature for (semi-)automated image processing and unsupervised feature extraction tasks. We show that our class covers also two-step optimization approaches that have been proposed in the recent literature in the context of image segmentation and restoration. Empirical results of the performance of various iterative numerical schemes on a parallel architecture are also presented.

Keywords

Resid 

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References

  1. [1]
    A.L. Yuille. Generalized deformable models, statistical physics and matching problems. Neural Сотр., 2:1–24, 1990.CrossRefGoogle Scholar
  2. [2]
    W.J. Christmas, J. Kittler, and M. Petrou. Structural matching in computer vision using probabilistic relaxation. IEEE Trans. Patt. Anal. Mach. Intell., 17(8):749–764, 1995.CrossRefGoogle Scholar
  3. [3]
    D. Geiger and A. Yuille. A common framework for image segmentation. Int. J. of Сотр. Vision, 6(3):227–243, 1991.CrossRefGoogle Scholar
  4. [4]
    J.-M. Morel and S. Solimini. Variational Methods in Image Segmentation. Birkhäuser, Boston, 1995.Google Scholar
  5. [5]
    P. Perona and J. Malik. Scale-space and edge-detection. IEEE Trans. Patt. Anal. Mach. Intell, 12(7):629–639, 1990.CrossRefGoogle Scholar
  6. [6]
    Bart M. ter Haar Romeny, editor. Geometry-Driven Diffusion in Computer Vision, Dordrecht, The Netherlands, 1994. Kluwer Academic Publishers.MATHGoogle Scholar
  7. [7]
    J. Weickert. A Review of Nonlinear Diffusion Filtering, pages 3–28. Volume 1252 of ter Haar Romeny et al. В. ter Haar Romeny, L. Florack, J. Koederink, and M. Viergever, editors. Scale-Space Theory in Computer Vision, volume 1252 of Lect. Not. Сотр. Sci., Berlin, 1997. Springer., 1997.Google Scholar
  8. [8]
    С. Schnörr. Unique reconstruction of piecewise-smooth images by minimizing strictly convex noquadratic functionals. J. of Math. Imag. Vision, 4:189–198, 1994.CrossRefGoogle Scholar
  9. [9]
    D. Mumford and J. Shah. Optimal approximations by piecewiese smooth functions and associated variational problems. Comm. Pure Appl. Math., 42:577–685, 1989.MathSciNetMATHCrossRefGoogle Scholar
  10. [10]
    C. Schnörr. A study of a convex variational approach for image segmentation and feature extraction. J. of Math. Imag. Vision, 8(3):271–292, 1998.MATHCrossRefGoogle Scholar
  11. [11]
    V.V. Shaidurov. Multigrid Methods for Finite Elements. Kluwer Academic Publisher, 1995.MATHGoogle Scholar
  12. [12]
    D. Geman and G. Reynolds. Constrained restoration and the recovery of discontinuites. IEEE Trans. Patt. Anal Mach. Intell, 14:367–383, 1992.CrossRefGoogle Scholar
  13. [13]
    P. Charbonnier, L. Blanc-Feraud, G. Aubert, and M. Barlaud. Determistic edge-preserving regularization in computed imaging. In Proc. 12th Intern. Conference of Pattern Recognition, pages C-188–191, 1994.Google Scholar
  14. [14]
    D. Geman and C. Yang. Nonlinear image recovery with half-quadratic regularization. IEEE Trans. Image Proc, 4:932–945, 1995.CrossRefGoogle Scholar
  15. [15]
    K. Rose, E. Gurewitz, and G.C. Fox. Constrained clustering as an optimization method. IEEE Trans. Patt. Anal Mach. Intell, 15(8):785–794, 1993.CrossRefGoogle Scholar
  16. [16]
    В. ter Haar Romeny, L. Florack, J. Koederink, and M. Viergever, editors. Scale-Space Theory in Computer Vision, volume 1252 of Lect. Not. Сотр. Sci., Berlin, 1997. Springer.Google Scholar

Copyright information

© Springer-Verlag London Limited 1998

Authors and Affiliations

  • Josef Heers
    • 1
  • Christoph Schnörr
    • 1
  • H. Siegfried Stiehl
    • 1
  1. 1.AB Kognitive SystemeFB Informatik Universität HamburgHamburgGermany

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