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Density-Based 3D Shape Descriptors

Abstract

We propose a novel probabilistic framework for the extraction of density-based 3D shape descriptors using kernel density estimation. Our descriptors are derived from the probability density functions (pdf) of local surface features characterizing the 3D object geometry. Assuming that the shape of the 3D object is represented as a mesh consisting of triangles with arbitrary size and shape, we provide efficient means to approximate the moments of geometric features on a triangle basis. Our framework produces a number of 3D shape descriptors that prove to be quite discriminative in retrieval applications. We test our descriptors and compare them with several other histogram-based methods on two 3D model databases, Princeton Shape Benchmark and Sculpteur, which are fundamentally different in semantic content and mesh quality. Experimental results show that our methodology not only improves the performance of existing descriptors, but also provides a rigorous framework to advance and to test new ones.

References

  1. 1.

    Bustos B, Keim DA, Saupe D, Schreck T, Vranić DV: Feature-based similarity search in 3D object databases. ACM Computing Surveys 2005,37(4):345–387. 10.1145/1118890.1118893

    Article  Google Scholar 

  2. 2.

    Tangelder JWH, Veltkamp RC: A survey of content based 3D shape retrieval methods. Proceedings of International Conference on Shape Modeling and Applications (SMI '04), June 2004, Genova, Italy 145–156.

    Google Scholar 

  3. 3.

    Campbell RJ, Flynn PJ: A survey of free-form object representation and recognition techniques. Computer Vision and Image Understanding 2001,81(2):166–210. 10.1006/cviu.2000.0889

    Article  Google Scholar 

  4. 4.

    Iyer N, Jayanti S, Lou K, Kalyanaraman Y, Ramani K: Three-dimensional shape searching: state-of-the-art review and future trends. Computer Aided Design 2005,37(5):509–530. 10.1016/j.cad.2004.07.002

    Article  Google Scholar 

  5. 5.

    Shilane P, Min P, Kazhdan M, Funkhouser T: The Princeton shape Benchmark. Proceedings of International Conference on Shape Modeling and Applications (SMI '04), June 2004, Genova, Italy 167–178.

    Google Scholar 

  6. 6.

    Tung T: Indexation 3D de bases de données d'objets par graphes de Reeb améliorés, Ph.D. thesis. Ecole Nationale Supérieure des Télécommunications (ENST), Paris, France; 2005.

    Google Scholar 

  7. 7.

    Vranić DV: 3D model retrieval, Ph.D. thesis. University of Leipzig, Leipzig, Germany; 2004.

    Google Scholar 

  8. 8.

    Horn BKP: Extended Gaussian images. Proceedings of the IEEE 1984,72(12):1671–1686.

    Article  Google Scholar 

  9. 9.

    Kang S, Ikeuchi K: The complex EGI: a new representation for 3-D pose determination. IEEE Transactions on Pattern Analysis and Machine Intelligence 1993,15(7):707–721. 10.1109/34.221171

    Article  Google Scholar 

  10. 10.

    Osada R, Funkhouser T, Chazelle B, Dobkin D: Shape distributions. ACM Transactions on Graphics 2002,21(4):807–832. 10.1145/571647.571648

    MathSciNet  Article  Google Scholar 

  11. 11.

    Paquet E, Rioux M: Nefertiti: a query by content software for three-dimensional models databases management. Proceedings of the 1st International Conference on Recent Advances in 3-D Digital Imaging and Modeling (3DIM '97), May 1997, Washington, DC, USA 345–352.

    Google Scholar 

  12. 12.

    Zaharia T, Prêteux F: Indexation de maillages 3D par descripteurs de forme. Actes 13ème Congrès Francophone AFRIF-AFIA Reconnaissance des Formes et Intelligence Artificielle (RFIA '02), January 2002, Angers, France 48–57.

    Google Scholar 

  13. 13.

    Duda RO, Hart PE, Stork DG: Pattern Classification. Wiley-Interscience, New York, NY, USA; 2000.

    Google Scholar 

  14. 14.

    Härdle W, Müller M, Sperlich S, Werwatz A: Nonparametric and Semiparametric Models, Springer Series in Statistics. Springer, Heidelberg, Germany; 2004.

    Google Scholar 

  15. 15.

    Greengard L, Strain J: The fast Gauss transform. SIAM Journal on Scientific and Statistical Computing 1991,12(1):79–94. 10.1137/0912004

    MathSciNet  Article  Google Scholar 

  16. 16.

    Yang C, Duraiswami R, Gumerov NA, Davis L: Improved fast Gauss transform and efficient kernel density estimation. Proceedings of the 9th IEEE International Conference on Computer Vision (ICCV '03), October 2003, Nice, France 1: 464–471.

    Google Scholar 

  17. 17.

    Siddiqi K, Shokoufandeh A, Dickinson SJ, Zucker SW: Shock graphs and shape matching. Proceedings of the IEEE International Conference on Computer Vision (ICCV '98), January 1998, Bombay, India 222–229.

    Google Scholar 

  18. 18.

    Hilaga M, Shinagawa Y, Kohmura T, Kunii TL: Topology matching for fully automatic similarity estimation of 3D shapes. Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH '01), August 2001, Los Angeles, Calif, USA 203–212.

    Google Scholar 

  19. 19.

    Tung T, Schmitt F: The augmented multiresolution Reeb graph approach for content-based retrieval of 3D shapes. International Journal of Shape Modeling 2005,11(1):91–120. 10.1142/S0218654305000748

    Article  Google Scholar 

  20. 20.

    Sundar H, Silver D, Gagvani N, Dickinson SJ: Skeleton based shape matching and retrieval. Proceedings of International Conference on Shape Modeling and Applications (SMI '03), May 2003, Seoul, Korea 130–139.

    Google Scholar 

  21. 21.

    Ankerst M, Kastenmüller G, Kriegel H-P, Seidl T: 3D shape histograms for similarity search and classification in spatial databases. Proceedings of the 6th International Symposium on Advances in Spatial Databases (SSD '99), July 1999, Hong Kong, Lecture Notes in Computer Science 1651: 207–226.

    Article  Google Scholar 

  22. 22.

    Funkhouser T, Min P, Kazhdan M, et al.: A search engine for 3D models. ACM Transactions on Graphics 2003,22(1):83–105. 10.1145/588272.588279

    Article  Google Scholar 

  23. 23.

    Kazhdan M, Funkhouser T, Rusinkiewicz S: Rotation invariant spherical harmonic representation of 3D shape descriptors. Proceedings of the Eurographics/ACM SIGGRAPH Symposium on Geometry Processing (SGP '03), June 2003, Aachen, Germany 156–164.

    Google Scholar 

  24. 24.

    Vranić DV: An improvement of rotation invariant 3D-shape based on functions on concentric spheres. Proceedings of the IEEE International Conference on Image Processing (ICIP '03), September 2003, Barcelona, Spain 3: 757–760.

    Google Scholar 

  25. 25.

    Comaniciu D, Ramesh V, Meer P: The variable bandwidth mean shift and data-driven scale selection. Proceedings of the 8th International Conference on Computer Vision (ICCV '01), July 2001, Vancouver, BC, Canada 1: 438–445.

    Google Scholar 

  26. 26.

    Press WH, Flannery BP, Teukolsky SA: Numerical Recipes in C: The Art of Scientific Computing. Cambridge University Press, Cambridge, UK; 1992.

    Google Scholar 

  27. 27.

    Goodall S, Lewis PH, Martinez K, et al.: SCULPTEUR: multimedia retrieval for museums. Proceedings of the Image and Video Retrieval: 3rd International Conference (CIVR '04), July 2004, Dublin, Ireland, Lecture Notes in Computer Science 3115: 638–646.

    Article  Google Scholar 

  28. 28.

    Ihler AKernel density estimation toolbox for MATLAB (R13), 2003

    Google Scholar 

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Correspondence to Ceyhun Burak Akgül.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://doi.org/creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Akgül, C.B., Sankur, B., Yemez, Y. et al. Density-Based 3D Shape Descriptors. EURASIP J. Adv. Signal Process. 2007, 032503 (2006). https://doi.org/10.1155/2007/32503

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Keywords

  • Probability Density Function
  • Quantum Information
  • Density Estimation
  • Local Surface
  • Kernel Density