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On Medial Representations

  • Gabriella Sanniti di Baja
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5197)

Abstract

During the last half century, medial representations of objects have been involved in many biological and physical theories, and computer scientists have designed suitable algorithms for their computation. Aim of this paper is to provide a short, non-comprehensive, survey of the most common medial representation systems.

Keywords

Medial Axis Grassfire Shock Graph Voronoi Diagram Skeleton 

References

  1. 1.
    Blum, H.: A transformation for extracting new descriptors of shape. MIT Press, Cambridge (1967)Google Scholar
  2. 2.
    Blum, H., Nagel, R.: Shape Description Using Weighted Symmetric Axis Features. Pattern Recognition 10(3), 167–180 (1978)CrossRefzbMATHGoogle Scholar
  3. 3.
    Kimia, B.B., Tannenbaum, A.R., Zucker, S.W.: Toward a Computational Theory of Shape: An Overview. In: Proceedings of the First European Conference on Computer Vision, Antibes, France, pp. 402–407. Springer, Heidelberg (1990)Google Scholar
  4. 4.
    Kimia, B.B., Tannenbaum, A., Zucker, S.W.: Shape, Shocks, and Deformations I: The Components of Two-Dimensional Shape and the Reaction Diffusion Space. International Journal of Computer Vision 15, 189–224 (1995)CrossRefGoogle Scholar
  5. 5.
    Siddiqi, K., Kimia, B.B.: A Shock Grammar for Recognition. In: Proceedings of the Conference on Computer Vision and Pattern Recognition, pp. 507–513 (1996)Google Scholar
  6. 6.
    Siddiqi, K., Shokoufandeh, A., Dickinson, S.J., Zucker, S.W.: Shock Graphs and Shape Matching. International Journal of Computer Vision 35(1), 13–32 (1999)CrossRefGoogle Scholar
  7. 7.
    Klein, F.: Vollständige Mittelachsenbeschreibung binärer Bildstrukturen mit euklidischer Metrik und korrekter Topologie. Ph.D. thesis, ETH Nr. 8441 (1987)Google Scholar
  8. 8.
    Ogniewicz, R.: Discrete Voronoi Skeletons. Hartung-Gorre Verlag(1993)Google Scholar
  9. 9.
    Arcelli, C., Sanniti di Baja, G.: Computing Voronoi diagrams in digital pictures. Pattern Recognition Letters 4(5), 383–389 (1986)CrossRefGoogle Scholar
  10. 10.
    Brandt, J., Algazi, V.: Continuous Skeleton Computation by Voronoi Diagram. Computer Vision Graphics Image Processing: Image Understanding 55(3), 329–338 (1992)zbMATHGoogle Scholar
  11. 11.
    Attali, D., Montanvert, A.: Semicontinuous skeletons of 2D and 3D shapes. In: Arcelli, C., Cordella, L.P., Sanniti di Baja, G. (eds.) Aspects of Visual Form Processing, pp. 32–41. World Scientific, Singapore (1994)Google Scholar
  12. 12.
    Arcelli, C., Sanniti di Baja, G.: Euclidean skeleton via center-of-maximal-disc extraction. Image and Vision Computing 11, 163–173 (1993)CrossRefGoogle Scholar
  13. 13.
    Sanniti di Baja, G.: Well-shaped, stable and reversible skeletons from the (3,4)-distance transform. Visual Communication and Image Representation 5, 107–115 (1994)CrossRefGoogle Scholar
  14. 14.
    Sanniti di Baja, G., Thiel, E.: Skeletonization algorithm running on path-based distance maps. Image and Vision Computing 14, 47–57 (1997)CrossRefGoogle Scholar
  15. 15.
    Svensson, S., Borgefors, G., Nyström, I.: On reversible skeletonization using anchor-points from distance transforms. Journal of Visual Communication and Image Representation 10, 379–397 (1999)CrossRefGoogle Scholar
  16. 16.
    Sanniti di Baja, G., Svensson, S.: Surface skeletons detected on the D6 distance transform. In: Ferri, F.J., et al. (eds.) Advances in Pattern Recognition. LNCS, vol. 1121, pp. 387–396. Springer, Berlin (2000)CrossRefGoogle Scholar
  17. 17.
    Asada, H., Brady, M.: The Curvature Primal Sketch. IEEE Transactions on Pattern Analysis and Machine Intelligence 8, 2–14 (1983)Google Scholar
  18. 18.
    Leyton, M.: A Process Grammar For Shape. Artificial Intelligence 34, 213–247 (1988)CrossRefGoogle Scholar
  19. 19.
    Leyton, M.: Inferring Causal History From Shape. Cognitive Science 13, 357–387 (1989)Google Scholar
  20. 20.
    Borgefors, G., Nyström, I.: Efficient shape representation by minimizing the set of centers of maximal discs/spheres. Pattern Recognition Letters 18, 465–472 (1997)CrossRefGoogle Scholar
  21. 21.
    Borgefors, G.: Distance transformations in digital images. Computer Vision, Graphics, and Image Processing 34(3), 344–371 (1986)CrossRefGoogle Scholar
  22. 22.
    Borgefors, G.: On digital distance transform in three dimensions. Computer Vision and Image Understanding 64(3), 368–376 (1996)CrossRefGoogle Scholar
  23. 23.
    Aichholzer, O., Alberts, D., Aurenhammer, F., Gartner, B.: A novel type of skeleton for polygons. Journal of Universal Computer Science 1, 752–761 (1995)MathSciNetzbMATHGoogle Scholar
  24. 24.
    Giblin, P.J., Kimia, B.B.: On the local form and transitions of symmetry sets, medial axes, and shocks. International Journal of Computer Vision 54, 143–157 (2003)CrossRefzbMATHGoogle Scholar
  25. 25.
    Giblin, P.J., Kimia, B.B.: A formal classification of 3D medial axis points and their local geometry. In: Proc. CVPR 2000, vol. I, pp. 566–575. IEEE Computer Society, Los Alamitos (2000)Google Scholar
  26. 26.
    Schmitt, M.: Some examples of algorithms analysis in computational geometry by means of mathematical morphology techniques. In: Boissonnat, J.-D., Laumond, J.-P. (eds.) Geometry and Robotics. LNCS, vol. 391, pp. 225–246. Springer, Heidelberg (1989)CrossRefGoogle Scholar
  27. 27.
    Asada, H., Brady, M.: The curvature primal sketch. IEEE Trans. Pattern Analysis Machine Inteligence 8, 2–14 (1986)CrossRefGoogle Scholar
  28. 28.
    Weiss, I.: Shape Reconstruction on a Varying Mesh. IEEE Trans. Pattern Analysis Machine Inteligence 12(4), 345–362 (1990)CrossRefGoogle Scholar
  29. 29.
    Ogniewicz, R.L., Kübler, O.: Hierarchic Voronoi skeletons. Pattern Recognition 28(3), 343–359 (1995)CrossRefGoogle Scholar
  30. 30.
    Szekely, G.: Shape Characterization by Local Symmetries. Habilitationsschrift, Institut fur Kommunikationstechnik, Fachgruppe Bildwissenschaft, ETH Zurich (1996)Google Scholar
  31. 31.
    Näf, M.: Voronoi Skeletons: a semicontinous implementation of the ‘Symmetric Axis Transform’ in 3D space, Ph.D. thesis, ETH Zurich, Commmunication Technology Institue, Image Analysis Group IKT/BIWI (1996)Google Scholar
  32. 32.
    Katz, R., Pizer, S.M.: Untangling the Blum Medial Axis Transform. International Journal of Computer Vision 55(3), 139–153 (2003)CrossRefGoogle Scholar
  33. 33.
    Attali, D., Montanvert, A.: Computing and simplifying 2D and 3D continuous skeletons. Computer Vision and Image Understanding 67(3), 261–273 (1997)CrossRefGoogle Scholar
  34. 34.
    Arcelli, C., Sanniti di Baja, G., Serino, L.: From 3D discrete surface skeletons to curve skeletons. In: Campilho, A., Kamel, M. (eds.) ICIAR 2008. LNCS, vol. 5112, pp. 507–516. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  35. 35.
    Wan, M., Dachille, F., Kaufman, A.: Distance-Field Based Skeletons for Virtual Navigation. In: Proc. IEEE Visualization 2001, pp. 239–246 (2001)Google Scholar
  36. 36.
    Perchet, D., Fetita, C.I., Preteux, F.: Advanced navigation tools for virtual bronchoscopy. In: Proc. SPIE Conf. on Image Processing: Algorithms and Systems III, vol. 5298, pp. 147–158 (2004)Google Scholar
  37. 37.
    Bartz, D., Straßer, W., Skalej, M., Welte, D.: Interactive Exploration of Extra- and Intracranial Blood Vessels. In: Proc. 10th IEEE Visualization (VIS 1999), vol. 5 (1999)Google Scholar
  38. 38.
    Bloomenthal, J.: Medial Based Vertex Deformation. In: Proc. SIGGRAPH/ Eurographics Symp. On Computer Animation, pp. 147–151 (2002)Google Scholar
  39. 39.
    Sundar, H., Silver, D., Gagvani, N., Dickinson, S.: Skeleton based shape matching and retrieval. In: Proc. Shape Modelling and Applications Conference, SMI 2003, pp. 130–139 (2003)Google Scholar
  40. 40.
    Pizer, S.M., Fritsch, D., Yushkevich, P., Johnson, V., Chaney, E.: Segmentation, Registration, and Measurement of Shape Variation via Image Object Shape. IEEE Trans. Medical Imaging 18, 851–865 (1999)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Gabriella Sanniti di Baja
    • 1
  1. 1.Institute of Cybernetics “E. Caianiello”, CNRPozzuoli (Naples)Italy

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