Data driven composite shape descriptor design for shape retrieval with a VoR-Tree

Article
  • 17 Downloads

Abstract

We develop a data driven method (probability model) to construct a composite shape descriptor by combining a pair of scale-based shape descriptors. The selection of a pair of scale-based shape descriptors is modeled as the computation of the union of two events, i.e., retrieving similar shapes by using a single scale-based shape descriptor. The pair of scale-based shape descriptors with the highest probability forms the composite shape descriptor. Given a shape database, the composite shape descriptors for the shapes constitute a planar point set. A VoR-Tree of the planar point set is then used as an indexing structure for efficient query operation. Experiments and comparisons show the effectiveness and efficiency of the proposed composite shape descriptor.

Keywords

shape descriptor shape retrieval shape analysis data-driven model 

MR Subject Classification

68P20 68U05 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    A Akdogan, U Demiryurek, F Banaei-Kashani, C Shahabi. Voronoi-based geospatial query processing with mapreduce, In: IEEE Second International Conference on Cloud Computing Technology and Science, 2010, 9–16.CrossRefGoogle Scholar
  2. [2]
    CB Akgül, B Sankur, Y Yemez, F Schmitt. Similarity score fusion by ranking risk minimization for 3D object retrieval, In: Proceedings of the 1st Eurographics Conference on 3D Object Retrieval, 2008, 41–48.Google Scholar
  3. [3]
    E Bribiesca. An easy measure of compactness for 2D and 3D shapes, Pattern Recogn, 2008, 41(2): 543–554.CrossRefMATHGoogle Scholar
  4. [4]
    M Chahooki, N Charkari. Shape retrieval based on manifold learning by fusion of dissimilarity measures, IET Image Process, 2012, 6(4): 327–336.MathSciNetGoogle Scholar
  5. [5]
    J Dean, S Ghemawat. MapReduce: simplified data processing on large clusters, Commun ACM, 2008, 51(1): 107–113.CrossRefGoogle Scholar
  6. [6]
    V Dhar. Data science and prediction, Commun ACM, 2013, 56(12): 64–73.CrossRefGoogle Scholar
  7. [7]
    L Dong, Y Wu, S Zhou. Constructing the voronoi diagram of planar point set in parallel, In: International Conference on Computational Intelligence and Software Engineering, 2009, 1–5.Google Scholar
  8. [8]
    Y Fang, J Xie, G Dai, M Wang, F Zhu, T Xu, E Wong. 3D deep shape descriptor, In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 2015, 2319–2328.Google Scholar
  9. [9]
    S Fortune. A sweepline algorithm for Voronoi diagrams, In: Proceedings of the Second Annual Symposium on Computational Geometry, ACM, 1986, 313–322.CrossRefGoogle Scholar
  10. [10]
    LJ Guibas, DE Knuth, M Sharir. Randomized incremental construction of Delaunay and Voronoi diagrams, Algorithmica, 1992, 7(1): 381–413.MathSciNetCrossRefMATHGoogle Scholar
  11. [11]
    A Guttman. R-trees: a dynamic index structure for spatial searching, In: Proceedings of ACM Management of Data (SIGMOD), 1984, 47–57.Google Scholar
  12. [12]
    J Jiang, W Zhu, F Shi, Y Zhang, L Lin, TJ iang. A robust and accurate algorithm for estimating the complexity of the cortical surface, J Neurosci Meth, 2008, 172(1): 122–130.CrossRefGoogle Scholar
  13. [13]
    M Kolahdouzan, C Shahabi. Voronoi-based k nearest neighbor search for spatial network databases, In: Proceedings of the Thirtieth International Conference on Very Large Data Bases, VLDB Endowment, 2004, 840–851.Google Scholar
  14. [14]
    RJ Larsen, ML Marx. An Introduction to Mathematical Statistics and Its Applications, 4th ed, Prentice Hall, 2006.MATHGoogle Scholar
  15. [15]
    J L Rodgers, WA Nicewander. Thirteen ways to look at the correlation coefficient, Amer Statist, 1988, 42(1): 59–66.CrossRefGoogle Scholar
  16. [16]
    Z Lian, A Godil, PL Rosin, X Sun. A new convexity measurement for 3d meshes, In: IEEE Conference on Computer Vision and Pattern Recognition, 2012, 119–126.Google Scholar
  17. [17]
    Z Lian, PL Rosin, X Sun. Rectilinearity of 3D meshes, Int J Comput Vision, 2010, 89(2-3): 130–151.CrossRefGoogle Scholar
  18. [18]
    BB Mandelbrot. The Fractal Geometry of Nature, Macmillan, 1983.Google Scholar
  19. [19]
    J O’Rourke. Computational Geometry in C, Cambridge University Press, 1998.CrossRefMATHGoogle Scholar
  20. [20]
    P Papadakis, I Pratikakis, S Perantonis, T Theoharis. Efficient 3D shape matching and retrieval using a concrete radialized spherical projection representation, Pattern Recogn, 2007, 40(9): 2437–2452.CrossRefMATHGoogle Scholar
  21. [21]
    E Rahtu, M Salo, J Heikkila. A new convexity measure based on a probabilistic interpretation of images, IEEE Trans Pattern Anal, 2006, 28(9): 1501–1512.CrossRefGoogle Scholar
  22. [22]
    M Reuter, FE Wolter, N Peinecke. Laplace-Beltrami spectra as “Shape-DNA” of surfaces and solids, Comput Aided Design, 2006, 38(4): 342–366.CrossRefGoogle Scholar
  23. [23]
    PL Rosin. Measuring shape: ellipticity, rectangularity, and triangularity, Mach Vision Appl, 2003, 14(3): 172–184.CrossRefGoogle Scholar
  24. [24]
    M Sharifzadeh, C Shahabi. Vor-tree: R-trees with voronoi diagrams for efficient processing of spatial nearest neighbor queries, Proc VLDB Endow, 2010, 3(1-2): 1231–1242.CrossRefGoogle Scholar
  25. [25]
    P Shilane, P Min, M Kazhdan, T Funkhouser. The princeton shape benchmark, In: International Conference on Shape Modeling and Applications, 2004, 167–178.Google Scholar
  26. [26]
    JW Tangelder, RC Veltkamp. A survey of content based 3D shape retrieval methods, Multimed Tools Appl, 2008, 39(3): 441–471.CrossRefGoogle Scholar
  27. [27]
    S Wild. Java 7’s Dual Pivot Quicksort, Master Thesis, Technische Universität Kaiserslautern, 2013.MATHGoogle Scholar
  28. [28]
    J Xu, B Zheng, WC Lee, DL Lee. The D-tree: An index structure for planar point queries in location-based wireless services, IEEE Trans Knowl Data Eng, 2004, 16(12): 1526–1542.CrossRefGoogle Scholar
  29. [29]
    S Zhang, M Yang, T Cour, K Yu, DN Metaxas. Query specific fusion for image retrieval, In: Computer Vision-ECCV 2012, Springer, 660–673.Google Scholar
  30. [30]
    J Zunic, PL Rosin. A new convexity measure for polygons, IEEE Trans Pattern Anal, 2004, 26(7): 923–934.CrossRefGoogle Scholar
  31. [31]
    J Zunic, PL Rosin. Rectilinearity measurements for polygons, IEEE Trans Pattern Anal, 2003, 25(9): 1193–1200.CrossRefGoogle Scholar
  32. [32]
    J Zunic, PL Rosin, L Kopanja. On the orientability of shapes, IEEE Trans Image Process, 2006, 15(11): 3478–3487.CrossRefGoogle Scholar

Copyright information

© Editorial Committee of Applied Mathematics-A Journal of Chinese Universities and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematical Science, State Key Lab. of CAD&CGZhejiang UniversityHangzhouChina

Personalised recommendations