Detection of Surface Creases in Range Data

  • Alexander Belyaev
  • Elena Anoshkina
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3604)


We propose a fully automatic and view-independent computational procedure for detecting salient curvature extrema in range data. Our method consists of two major steps: (1) smoothing given range data by applying a nonlinear diffusion of normals with automatic thresholding; (2) using a Canny-like non-maximum suppression and hysteresis thresholding operations for detecting crease pixels. A delicate analysis of curvature extrema properties allows us to make those Canny-like image processing operations orientation-independent. The detected patterns of creases can be considered as ‘shape fingerprints’. The proposed method can be potentially used for shape recognition, quality evaluation, and matching purposes.


Range Data Range Image Intersection Curve Positive Maximum Smoothing Procedure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Gullstrand, A.: Zur Kenntnis der Kreispunkte. Acta Mathematica 29, 59–100 (1904)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Ramsay, J.G.: Folding and Fracturing of Rocks. McGraw-Hill, New York (1967)Google Scholar
  3. 3.
    Hoffman, D.D., Richards, W.A.: Parts of recognition. cognition 18, 65–96 (1985)CrossRefGoogle Scholar
  4. 4.
    DeCarlo, D., Finkelstein, A., Rusinkiewicz, S., Santella, A.: Suggestive contours for conveying shape. ACM Transactions on Graphics 22, 848–855 (2003); In: Proceedings of ACM SIGGRAPH (2003)Google Scholar
  5. 5.
    Hartmann, E.: On the curvature of curves and surfaces defined by normalforms. Comput. Aided Geom. Design 16, 355–376 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Hosaka, M.: Modeling of Curves and Surfaces in CAD/CAM. Springer, Berlin (1992)Google Scholar
  7. 7.
    Ohtake, Y., Belyaev, A., Seidel, H.P.: Ridge-valley lines on meshes via implicit surface fitting. ACM Transactions on Graphics 23, 609–612 (2004); In: Proceedings of ACM SIGGRAPH (2004)CrossRefGoogle Scholar
  8. 8.
    Patrikalakis, N.M., Maekawa, T.: Shape Interrogation for Computer Aided Design and Manufacturing. Springer, Heidelberg (2002)zbMATHGoogle Scholar
  9. 9.
    Stylianou, G., Farin, G.: Crest lines extraction from 3D triangulated meshes. In: Farin, G., Hamann, B., Hagen, H. (eds.) Hierarchical and Geometrical Methods in Scientific Visualization, pp. 269–281. Springer, Heidelberg (2003)Google Scholar
  10. 10.
    Stylianou, G., Farin, G.: Crest lines for surface segmentation and flattening. IEEE Transactions on Visualization and Computer Graphics 10, 536–544 (2004)CrossRefGoogle Scholar
  11. 11.
    Watanabe, K., Belyaev, A.G.: Detection of salient curvature features on polygonal surfaces. Computer Graphics Forum 20, 385–392 (2001); Eurographics 2001 issueCrossRefGoogle Scholar
  12. 12.
    Yoshizawa, S., Belyaev, A.G., Seidel, H.P.: Fast and robust detection of crest lines on meshes. In: ACM Symposium on Solid and Physical Modeling 2005, MIT, Cambridge (2005) (to appear)Google Scholar
  13. 13.
    Hallinan, P.L., Gordon, G.G., Yuille, A.L., Giblin, P., Mumford, D.: Two- and Tree-Dimensional Patterns of the Face. A K Peters, Wellesley (1999)Google Scholar
  14. 14.
    Eberly, D., Gardner, R., Morse, D., Pizer, S., Scharlach, C.: Ridges for image analysis. J. Mathematical Imaging and Vision 4, 353–373 (1994)CrossRefGoogle Scholar
  15. 15.
    Monga, O., Armande, N., Montesinos, P.: Thin nets and crest lines: Application to satellite data and medical images. Computer Vision and Image Understanding: CVIU 67, 285–295 (1997)CrossRefGoogle Scholar
  16. 16.
    Monga, O., Ayache, N., Sander, P.T.: From voxel to intrinsic surface features. Image and Vision Computing 10, 403–417 (1992)CrossRefGoogle Scholar
  17. 17.
    Yuille, A.L.: Zero crossings on lines of curvature. Graphical Models and Image Processing 45, 68–87 (1989)Google Scholar
  18. 18.
    Kent, J.T., Mardia, K.V., West, J.: Ridge curves and shape analysis. In: The British Machine Vision Conference, pp. 43–52 (1996)Google Scholar
  19. 19.
    Little, J.J., Shi, P.: Structural lines, TINs and DEMs. Algorithmica 30, 243–263 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Pennec, X., Ayache, N., Thirion, J.P.: Landmark-based registration using features identified through differential geometry. In: Bankman, I.N. (ed.) Handbook of Medical Imaging, Academic Press, London (2000)Google Scholar
  21. 21.
    Belyaev, A.G., Anoshkina, E.V., Kunii, T.L.: Ridges, ravines, and singularities. In: Fomenko, A.T., Kunii, T.L. (eds.) Topological Modeling for Visualization, ch. 18, pp. 375–383. Springer, Heidelberg (1997)Google Scholar
  22. 22.
    Bruce, J.W., Giblin, P.J., Tari, F.: Ridges, crests and sub-parabolic lines of evolving surfaces. Int. J. Computer Vision 18, 195–210 (1996)CrossRefGoogle Scholar
  23. 23.
    Bruce, J.W., Giblin, P.J., Tari, F.: Families of surfaces: focal sets, ridges and umbilics. Math. Proc. Cambridge Philos. Soc. 125, 243–268 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Cazals, F., Pouget, M.: Differential topology and geometry of smooth embedded surfaces: selected topics. In: Computational Geometry and Applications (2005) ( to appear)Google Scholar
  25. 25.
    Cazals, F., Pouget, M.: Topology driven algorithms for ridge extraction on meshes. Rapport de Recherche RR-5526, INRIA (2005)Google Scholar
  26. 26.
    Koenderink, J.J.: Solid Shape. MIT Press, Cambridge (1990)Google Scholar
  27. 27.
    Porteous, I.R.: Geometric Differentiation for the Intelligence of Curves and Surfaces, 2nd edn. Cambridge University Press, Cambridge (2001)zbMATHGoogle Scholar
  28. 28.
    Yuille, A.L., Leyton, M.: 3D symmetry-curvature duality theorems. Graphical Models and Image Processing 52, 124–140 (1990)MathSciNetGoogle Scholar
  29. 29.
    Faugeras, O.: Three-Dimensional Computer Vision. In: Edge Detection, ch. 4, MIT Press, Cambridge (1993)Google Scholar
  30. 30.
    Belyaev, A.G., Ohtake, Y., Abe, K.: Detection of ridges and ravines on range images and triangular meshes. In: Vision Geometry IX, Proc. SPIE 4117, pp. 2000–146 (2000)Google Scholar
  31. 31.
    Ohtake, Y., Belyaev, A.G., Bogaevski, I.A.: Mesh regularization and adaptive smoothing. Computer-Aided Design 33, 789–800 (2001)CrossRefGoogle Scholar
  32. 32.
    Tasdizen, T., Whitaker, R., Burchard, P., Osher, S.: Geometric surface smoothing via anisotropic diffusion of normals. In: Proceedings of IEEE Visualization 2002, Boston, Massachusetts, pp. 125–132 (2002)Google Scholar
  33. 33.
    Hoover, A., Jean-Baptiste, G., Jiang, X., Flynn, P., Bunke, H., Goldgof, D., Bowyer, K., Eggert, D., Fitzgibbon, A., Fisher, R.: An experimental comparison of range image segmentation algorithms. IEEE Transactions on Pattern Analysis and Machine Intelligence 18, 673–689 (1996)CrossRefGoogle Scholar
  34. 34.
    Lee, K.M., Meer, P., Park, R.H.: Robust adaptive segmentation of range images. IEEE Transactions on Pattern Analysis and Machine Intelligence 20, 200–205 (1998)CrossRefGoogle Scholar
  35. 35.
    Berry, M.V., Hannay, J.H.: Umbilic points on gaussian random surfaces. J. Phys. A 10, 1809–1821 (1977)CrossRefGoogle Scholar
  36. 36.
    Maekawa, T., Wolter, F.E., Patrikalakis, N.M.: Umbilics and lines of curvature for shape interrogation. Computer Aided Geometric Design 13, 133–161 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  37. 37.
    Gordon, G.G.: Face recognition from depth maps and surface curvature. In: Proc. SPIE Geometric Methods in Computer Vision, vol. 1570, pp. 234–247 (1991)Google Scholar
  38. 38.
    Canny, J.: A computational approach to edge detection. IEEE Transactions on Pattern Analysis and Machine Intelligence 8, 679–698 (1986)CrossRefGoogle Scholar
  39. 39.
    Saint-Marc, P., Chen, J.S., Medioni, G.: Adaptive smooting: A general tool for early vision. IEEE Transactions on Pattern Analysis and Machine Intelligence 13, 514–529 (1991)Google Scholar
  40. 40.
    Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE Transactions on Pattern Analysis and Machine Intelligence 12, 629–638 (1990)CrossRefGoogle Scholar
  41. 41.
    Tasdizen, T., Whitaker, R.: Anisotropic diffusion of surface normals for feature preserving surface reconstruction. In: Fourth International Conference on 3-D Digital Imaging and Modeling, pp. 353–360 (2003)Google Scholar
  42. 42.
    Smith, S.M., Brady, J.M.: SUSAN – a new approach to low level image processing. International Journal of Computer Vision 23, 45–78 (1997)CrossRefGoogle Scholar
  43. 43.
    Tomasi, C., Manduchi, R.: Bilateral filtering for gray and color images. In: ICCV 1998: Proceedings of the Sixth International Conference on Computer Vision, pp. 839–846 (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Alexander Belyaev
    • 1
  • Elena Anoshkina
    • 1
  1. 1.Max-Planck-Institut für InformatikSaarbrückenGermany

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