Shape Analysis with Geometric Primitives

  • Fabien Feschet
Part of the Lecture Notes in Computational Vision and Biomechanics book series (LNCVB, volume 2)


In this chapter, a unifying framework is presented for analyzing shapes using geometric primitives. It requires both a model of shapes and a model of geometric primitives. We deliberately choose to explore the most general form of shapes through the notion of connected components in a binary image. According to this choice, we introduce geometric primitives for straightness and circularity which are adapted to thick elements. Starting from a model (the tangential cover) which emerged in the digital geometry community we show how to use Constrained Delaunay Triangulation to represent all shapes as a connected path well adapted to the recognition of geometric primitives. We moreover describe how to map our framework into the class of circular arc graphs. Using this mapping we present a multi-primitives analysis which is suitable for self-organizing a shape with respect to prescribed geometric primitives. Further work and open problems conclude the chapter.


Point Index Steiner Point Open Node Geometric Primitive Constrain Delaunay Triangulation 
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.


  1. 1.
    Andres, E.: Discrete circles, rings and spheres. Comput. Graph. 18(5), 695–706 (1994) CrossRefGoogle Scholar
  2. 2.
    Buzer, L.: Digital line recognition, convex hull, thickness, a unified and logarithmic technique. In: Proceedings of the 11th IWCIA, Berlin, Germany. Lecture Notes in Computer Science, vol. 4040, pp. 189–198 (2006) Google Scholar
  3. 3.
    Charrier, E., Lachaud, J.-O.: Maximal planes and multiscale tangential cover of 3D digital objects. In: Combinatorial Image Analysis, 14th International Workshop, IWCIA. Lecture Notes in Computer Science, vol. 6636, pp. 132–143. Springer, Berlin (2011) CrossRefGoogle Scholar
  4. 4.
    Debled-Rennesson, I., Feschet, F., Rouyer-Degli, J.: Optimal blurred segments decomposition of noisy shapes in linear time. Comput. Graph. 30(1), 30–36 (2006) CrossRefGoogle Scholar
  5. 5.
    Debled-Rennesson, I., Reveillès, J.-P.: A linear algorithm for segmentation of digital curves. Int. J. Pattern Recognit. Artif. Intell. 9(4), 635–662 (1995) CrossRefGoogle Scholar
  6. 6.
    Faure, A., Buzer, L., Feschet, F.: Tangential cover for thick digital curves. Pattern Recognit. 42, 2279–2287 (2009) zbMATHCrossRefGoogle Scholar
  7. 7.
    Faure, A., Feschet, F.: Robust decomposition of thick digital shapes. In: Proceedings of the 12th IWCIA, Buffalo, USA. Lecture Notes in Computer Science, vol. 4958, pp. 148–159 (2008) Google Scholar
  8. 8.
    Faure, A., Feschet, F.: Linear decomposition of planar shapes. In: 20th International Conference on Pattern Recognition, ICPR, pp. 1096–1099. IEEE Press, New York (2010) CrossRefGoogle Scholar
  9. 9.
    Feschet, F.: Canonical representations of discrete curves. Pattern Anal. Appl. 8(1–2), 84–94 (2005) MathSciNetCrossRefGoogle Scholar
  10. 10.
    Feschet, F., Tougne, L.: On the min DSS problem of closed discrete curves. Discrete Appl. Math. 151(1–3), 138–153 (2005) MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Hajdu, A., Pitas, I.: Piecewise linear digital curve representation and compression using graph theory and a line segment alphabet. IEEE Trans. Image Process. 17(2), 126–133 (2008) MathSciNetCrossRefGoogle Scholar
  12. 12.
    Hilaire, X., Tombre, K.: Robust and accurate vectorization of line drawings. IEEE Trans. Pattern Anal. Mach. Intell. 28(6), 890–904 (2006) CrossRefGoogle Scholar
  13. 13.
    Kerautret, B., Lachaud, J.-O.: Curvature estimation along noisy digital contours by approximate global optimization. Pattern Recognit. 42(10), 2265–2278 (2009) zbMATHCrossRefGoogle Scholar
  14. 14.
    Kerautret, B., Lachaud, J.-O.: Multi-scale analysis of discrete contours for unsupervised noise detection. In: Combinatorial Image Analysis, 13th International Workshop, IWCIA. Lecture Notes in Computer Science, vol. 5852, pp. 187–200. Springer, Berlin (2009) CrossRefGoogle Scholar
  15. 15.
    Klette, R., Rosenfeld, A.: Digital Geometry: Geometric Methods for Digital Picture Analysis. Computer Graphics and Geometric Modeling. Morgan Kaufmann, San Francisco (2004) zbMATHGoogle Scholar
  16. 16.
    Lachaud, J.-O., Vialard, A., de Vieilleville, F.: Fast, accurate and convergent tangent estimation on digital contours. Image Vis. Comput. 25(10), 1572–1587 (2007) CrossRefGoogle Scholar
  17. 17.
    Massod, A., Sarfraz, M.: An efficient technique for capturing 2D objects. Comput. Graph. 32, 93–104 (2008) CrossRefGoogle Scholar
  18. 18.
    Mokhtarian, F., Abbasi, S.: Shape similarity retrieval under affine transforms. Pattern Recognit. 35(1), 31–41 (2002) zbMATHCrossRefGoogle Scholar
  19. 19.
    Nguyen, T.P., Debled-Rennesson, I.: A discrete geometry approach for dominant point detection. Pattern Recognit. 44(1), 32–44 (2011) zbMATHCrossRefGoogle Scholar
  20. 20.
    Prasad, L., Rao, R.: A geometric transform for shape feature extraction. In: Vision Geometry 2000. Proceedings of SPIE, vol. 4117, pp. 222–233 (2000) Google Scholar
  21. 21.
    Reveilles, J.-P.: Geometrie discrete, calcul en nombres entiers et algorithmique. These d’Etat (1991) Google Scholar
  22. 22.
    Schlei, B.R.: A new computational framework for 2D shape-enclosing contours. Image Vis. Comput. 27(6), 637–647 (2009) CrossRefGoogle Scholar
  23. 23.
    Sivignon, I., Coeurjolly, D.: Minimal decomposition of a digital surface into digital plane segments is NP-hard. In: Discrete Geometry for Computer Imagery, 13th International Conference, DGCI. Lecture Notes in Computer Science, vol. 4245, pp. 674–685. Springer, Berlin (2006) CrossRefGoogle Scholar
  24. 24.
    Vialard, A.: Geometrical parameters extraction from discrete paths. In: 6th International Workshop DGCI. Lecture Notes in Computer Science, vol. 1176, pp. 24–35. Springer, Berlin (1996) Google Scholar
  25. 25.
    Wagenknecht, G.: A contour tracing and coding algorithm for generating 2D contour codes from 3D classified objects. Pattern Recognit. 40, 1294–1306 (2007) zbMATHCrossRefGoogle Scholar
  26. 26.
    Zhang, D., Lu, G.: Review of shape representation and description techniques. Pattern Recognit. 37(1), 1–19 (2004) zbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.IGCNC - EA 2782Clermont Université, Université d’AuvergneClermont-FerrandFrance

Personalised recommendations