Characterizing 3D Shapes Using Fractal Dimension

  • André Ricardo Backes
  • Danilo Medeiros Eler
  • Rosane Minghim
  • Odemir Martinez Bruno
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6419)

Abstract

Developments in techniques for modeling and digitizing have made the use of 3D models popular to a large number of new applications. With the diffusion and spreading of 3D models employment, the demand for efficient search and retrieval methods is high. Researchers have dedicated effort to investigate and overcome the problem of 3D shape retrieval. In this work, we propose a new way to employ shape complexity analysis methods, such as the fractal dimension, to perform the 3D shape characterization for those purposes. This approach is described and experimental results are performed on a 3D models data set. We also compare the technique to two other known methods for 3D model description, reported in literature, namely shape histograms and shape distributions. The technique presented here has performed considerably better than any of the others in the experiments.

Keywords

Fractal dimension complexity 3D shape descriptor 

References

  1. 1.
    Osada, R., Funkhouser, T., Chazelle, B., Dobkin, D.: Matching 3D models with shape distributions. In: SMI 2001: Proceedings of the International Conference on Shape Modeling & Applications, Washington, DC, USA, p. 154. IEEE Computer Society, Los Alamitos (2001)CrossRefGoogle Scholar
  2. 2.
    Yang, Y., Lin, H., Zhang, Y.: Content-based 3-D model retrieval: A survey. IEEE Transactions on Systems, Man, and Cybernetics 37(6), 1081–1098 (2007)CrossRefGoogle Scholar
  3. 3.
    Bimbo, A.D., Pala, P.: Content-based retrieval of 3d models. ACM Trans. Multimedia Comput. Commun. Appl. 2(1), 20–43 (2006)CrossRefGoogle Scholar
  4. 4.
    Tangelder, J.W., Veltkamp, R.C.: A survey of content based 3d shape retrieval methods. Multimedia Tools Appl. 39(3), 441–471 (2008)CrossRefGoogle Scholar
  5. 5.
    Tricot, C.: Curves and Fractal Dimension. Springer, Heidelberg (1995)CrossRefMATHGoogle Scholar
  6. 6.
    Backes, A.R., Casanova, D., Bruno, O.M.: Plant leaf identification based on volumetric fractal dimension. IJPRAI 23(6), 1145–1160 (2009)Google Scholar
  7. 7.
    da Costa, L.F., Cesar Jr., R.M.: Shape Analysis and Classification: Theory and Practice. CRC Press, Boca Raton (2000)CrossRefMATHGoogle Scholar
  8. 8.
    Carlin, M.: Measuring the complexity of non-fractal shapes by a fractal method. PRL: Pattern Recognition Letters 21(11), 1013–1017 (2000)CrossRefMATHGoogle Scholar
  9. 9.
    Chen, X., Golovinskiy, A., Funkhouser, T.: A benchmark for 3D mesh segmentation. ACM Transactions on Graphics (Proc. SIGGRAPH) 28(3) (2009)Google Scholar
  10. 10.
    Sarkar, N., Chaudhuri, B.B.: An efficient approach to estimate fractal dimension of textural images. Pattern Recognition 25(9), 1035–1041 (1992)CrossRefGoogle Scholar
  11. 11.
    de Plotze, R.O., Falvo, M., Pádua, J.G., Bernacci, L.C., Vieira, M.L.C., Oliveira, G.C.X., Bruno, O.M.: Leaf shape analysis using the multiscale Minkowski fractal dimension, a new morphometric method: a study with passiflora (passifloraceae). Canadian Journal of Botany 83(3), 287–301 (2005)CrossRefGoogle Scholar
  12. 12.
    Bruno, O.M., de Plotze, R.O., Falvo, M., de Castro, M.: Fractal dimension applied to plant identification. Information Sciences 178, 2722–2733 (2008)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Backes, A.R., de Sa Jr., J.J.M., Kolb, R.M., Bruno, O.M.: Plant species identification using multi-scale fractal dimension applied to images of adaxial surface epidermis. In: Jiang, X., Petkov, N. (eds.) CAIP 2009. LNCS, vol. 5702, pp. 680–688. Springer, Heidelberg (2009)Google Scholar
  14. 14.
    Emerson, C.W., Lam, N.N., Quattrochi, D.A.: Multi-scale fractal analysis of image texture and patterns. Photogrammetric Engineering and Remote Sensing 65(1), 51–62 (1999)Google Scholar
  15. 15.
    Gonzalez, R.C., Woods, R.E.: Digital Image Processing, 2nd edn. Prentic-Hall, New Jersey (2002)Google Scholar
  16. 16.
    Smith, G.D.: Numerical Solution of Partial Differential Equations: Finite Difference Methods, 3rd edn., Oxford (1986)Google Scholar
  17. 17.
    Everitt, B.S., Dunn, G.: Applied Multivariate Analysis, 2nd edn. Arnold, London (2001)MATHGoogle Scholar
  18. 18.
    Fukunaga, K.: Introduction to Statistical Pattern Recognition, 2nd edn. Academic Press, London (1990)MATHGoogle Scholar
  19. 19.
    Ankerst, M., Kastenmüller, G., Kriegel, H.P., Seidl, T.: 3D shape histograms for similarity search and classification in spatial databases. In: Güting, R.H., Papadias, D., Lochovsky, F.H. (eds.) SSD 1999. LNCS, vol. 1651, pp. 207–226. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  20. 20.
    Osada, R., Funkhouser, T., Chazelle, B., Dobkin, D.: Shape distributions. ACM Transactions on Graphics 21(4), 807–832 (2002)MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Bruno, O.M., da Fontoura Costa, L.: A parallel implementation of exact Euclidean distance transform based on exact dilations. Microprocessors and Microsystems 28(3), 107–113 (2004)CrossRefGoogle Scholar
  22. 22.
    Fabbri, R., da Fontoura Costa, L., Torelli, J.C., Bruno, O.M.: 2D Euclidean distance transform algorithms: A comparative survey. ACM Computing Surveys 40(1), 1–44 (2008)CrossRefGoogle Scholar
  23. 23.
    Shilane, P., Min, P., Kazhdan, M., Funkhouser, T.: The Princeton shape benchmark. In: SMI 2004: Proceedings of the Shape Modeling International 2004, Washington, DC, USA, pp. 167–178. IEEE Computer Society, Los Alamitos (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • André Ricardo Backes
    • 1
  • Danilo Medeiros Eler
    • 2
  • Rosane Minghim
    • 2
  • Odemir Martinez Bruno
    • 3
  1. 1.Faculdade de ComputaçãoUniversidade Federal de UberlândiaUberlândiaBrasil
  2. 2.Instituto de Ciências Matemáticas e de Computação (ICMC)Universidade de São Paulo (USP)São CarlosBrazil
  3. 3.Instituto de Física de São Carlos (IFSC)Universidade de São Paulo (USP)São CarlosBrazil

Personalised recommendations