Skip to main content

Feature Preserving Smoothing of Shapes Using Saliency Skeletons

  • Conference paper
Book cover Visualization in Medicine and Life Sciences II

Part of the book series: Mathematics and Visualization ((MATHVISUAL))

Abstract

We present a novel method that uses shape skeletons, and associated quantities, for feature-preserving smoothing of digital (black-and-white) binary shapes. We preserve, or smooth out, features based on a saliency measure that relates feature size to local object size, both computed using the shape’s skeleton. Low-saliency convex features (cusps) are smoothed out, and low-saliency concave features (dents) are filled in, respectively, by inflating simplified versions of the shape’s foreground and background skeletons. The method is simple to implement, works in real time, and robustly removes large-scale contour and binary speckle noise while preserving salient features. We demonstrate the method with several examples on datasets from the shape analysis application domain.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. T. Alter and R. Basri. Extracting salient curves from images: An analysis of the saliency network. Intl. J. of Computer Vision, 27(1):51-69, 1995.

    Article  Google Scholar 

  2. N. Amenta, S. Choi, and K. Kolluri. The power crust. In Proc. Solid Modeling, 249-260. IEEE, 2001.

    Google Scholar 

  3. J. August, K. Siddiqi, and S. W. Zucker. Ligature instabilities in the perceptual organization of shape. CVIU, 76(3):231-249, 1999.

    Google Scholar 

  4. X. Bai, J. Latecki, and W. Y. Liu. Skeleton pruning by contour partitioning with discrete curve evolution. IEEE TPAMI, 29(3):449-462, 2007.

    Article  Google Scholar 

  5. U. Clarenz, U. Diewald, and M. Rumpf. Processing textured surfaces via anisotropic geometric diffusion. IEEE Trans. Image Proc., 13(2):248261, 2004.

    Google Scholar 

  6. U. Clarenz, M. Rumpf, and A. Telea. Robust feature detection and local classification of surfaces based on moment analysis. IEEE TVCG, 10(5):516-524, 2004.

    Google Scholar 

  7. Mathieu Desbrun, Mark Meyer, Peter Schröder, and Alan H. Barr. Implicit fairing of irregular meshes using diffusion and curvature flow. In Proc. ACM SIGGRAPH, 317-324, 1999.

    Google Scholar 

  8. G. Dudek and J. K. Tsotsos. Shape representation and recognition from multiscale curvatures. CVIU, 68(4):170189, 1997.

    Google Scholar 

  9. C. Fernmuller and W. Kropatsch. Multiresolution shape description by corners. In Proc. CVPR, page 271276. IEEE, 1992.

    Google Scholar 

  10. S. Fleishman, I. Drori, and D. Cohen-Or. Bilateral mesh denoising. ACM TOG, 22(3):950953, 2003.

    Google Scholar 

  11. M. Hisada, A. Belyaev, and L. Kunii. A skeleton-based approach for detection of perceptually salient features on polygonal surfaces. Computer Graphics Forum, 21(4):689700, 2002.

    Google Scholar 

  12. A. Jalba, M. Wilkinson, and J. Roerdink. Shape representation and recognition through morphological scale spaces. IEEE Trans. Image Proc., 15(2):331341, 2006.

    Google Scholar 

  13. R. Kimmel, D. Shaked, and N. Kiryati. Skeletonization via distance maps and level sets. CVIU, 62 (3):382391, 1995.

    Google Scholar 

  14. J. J. Koenderink. The structure of images. Biological Cybernetics, 50:363370, 1984.

    MathSciNet  Google Scholar 

  15. H. Moreton and C. Séquin. Functional optimization for fair surface design. In Proc. ACM SIGGRAPH, 167-176, 1992.

    Google Scholar 

  16. R. L. Ogniewicz and O. Kübler. Hierarchic Voronoi skeletons. Pattern Recognition, 28(3):343-359, 1995.

    Google Scholar 

  17. S. Osher and J. Sethian. Fronts propagating with curvature-dependent speed. J. of Computational Physics, 79:1249, 1988.

    Article  MathSciNet  Google Scholar 

  18. J. Peng, V. Strela, and D. Zorin. A simple algorithm for surface denoising. In Proc. IEEE Visualization, page 107112, 2001.

    Google Scholar 

  19. S. M. Pizer, W. R. Oliver, and S. H. Bloomberg. Hierarchical shape description via the multiresolution symmetric axis transform. IEEE TPAMI, 9(4):505511, 1987.

    Google Scholar 

  20. K. Rehm, K. Schaper, J. Anderson, R. Woods, S. Stoltzner, and D. Rottenberg. Putting our heads together: a consensus approach to brain/non-brain segmentation in T1-weighted MR volumes. Neuroimage, 22(3):12621270, 2004.

    Google Scholar 

  21. D. Reniers and A. Telea. Tolerance-based distance transforms. In Advances in Computer Graphics and Computer Vision (eds. J. Braz, A. Ranchordas, H. Araujo, J. Jorge), page 187200.Springer LNCS, 2007.

    Google Scholar 

  22. Dennie Reniers, Jarke Van Wijk, and Alexandru Telea. Computing multiscale curve and surface skeletons of genus 0 shapes using a global importance measure. IEEE TVCG, 14(2):355-368, 2008.

    Google Scholar 

  23. T. B. Sebastian, P. N. Klein, and B. Kimia. Recognition of shapes by editing their shock graphs. IEEE TPAMI, 26(5):550571, 2004.

    Google Scholar 

  24. J. A. Sethian. Level set methods and fast marching methods. Cambridge University Press, 2nd edition, 1999.

    Google Scholar 

  25. M. Shah. MRI brain image segmentation, 2009. www.81bones.net/mri/mri_segmentation.pdf.

  26. K. Siddiqi, A. Shokoufandeh, S. Dickinson, and S. W. Zucker. Shock graphs and shape matching. Intl. J. of Computer Vision, 35(1):1332, 2004.

    Google Scholar 

  27. G. Taubin. Estimating the tensor of curvature of a surface from a polyhedral approximation. In Proc. IEEE ICCV, 992-997, 1995.

    Google Scholar 

  28. H. Tek and B. Kimia. Boundary smoothing via symmetry transforms. J. of Math. Imaging and Vision, 14:211223, 2001.

    Google Scholar 

  29. A. Telea. AFMMStar software, 2009. www.cs.rug.nl/~alext/SOFTWARE/AFMM/afmmstarvdt.zip.

  30. A. Telea and J. J. Van Wijk. An augmented fast marching method for computing skeletons and centerlines. In Proc. Symp. on Data Visualisation (VisSym), 251-259, 2002.

    Google Scholar 

  31. B. ter Haar Romeny. Geometric-Driven Diffusion in Computer Vision. Kluwer, 1994.

    Google Scholar 

  32. J. Weickert. A review of nonlinear diffusion filtering. In Proc. Intl. Conf. on Scale Space, page 328. Utrecht, the Netherlands, 1997.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Alexandru Telea .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Telea, A. (2012). Feature Preserving Smoothing of Shapes Using Saliency Skeletons. In: Linsen, L., Hagen, H., Hamann, B., Hege, HC. (eds) Visualization in Medicine and Life Sciences II. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21608-4_9

Download citation

Publish with us

Policies and ethics