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

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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.

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References

  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.

    Chapter  Google Scholar 

  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. E Bribiesca. An easy measure of compactness for 2D and 3D shapes, Pattern Recogn, 2008, 41(2): 543–554.

    Article  MATH  Google Scholar 

  4. M Chahooki, N Charkari. Shape retrieval based on manifold learning by fusion of dissimilarity measures, IET Image Process, 2012, 6(4): 327–336.

    MathSciNet  Google Scholar 

  5. J Dean, S Ghemawat. MapReduce: simplified data processing on large clusters, Commun ACM, 2008, 51(1): 107–113.

    Article  Google Scholar 

  6. V Dhar. Data science and prediction, Commun ACM, 2013, 56(12): 64–73.

    Article  Google Scholar 

  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. 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. S Fortune. A sweepline algorithm for Voronoi diagrams, In: Proceedings of the Second Annual Symposium on Computational Geometry, ACM, 1986, 313–322.

    Chapter  Google Scholar 

  10. LJ Guibas, DE Knuth, M Sharir. Randomized incremental construction of Delaunay and Voronoi diagrams, Algorithmica, 1992, 7(1): 381–413.

    Article  MathSciNet  MATH  Google Scholar 

  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. 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.

    Article  Google Scholar 

  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. RJ Larsen, ML Marx. An Introduction to Mathematical Statistics and Its Applications, 4th ed, Prentice Hall, 2006.

    MATH  Google Scholar 

  15. J L Rodgers, WA Nicewander. Thirteen ways to look at the correlation coefficient, Amer Statist, 1988, 42(1): 59–66.

    Article  Google Scholar 

  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. Z Lian, PL Rosin, X Sun. Rectilinearity of 3D meshes, Int J Comput Vision, 2010, 89(2-3): 130–151.

    Article  Google Scholar 

  18. BB Mandelbrot. The Fractal Geometry of Nature, Macmillan, 1983.

    Google Scholar 

  19. J O’Rourke. Computational Geometry in C, Cambridge University Press, 1998.

    Book  MATH  Google Scholar 

  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.

    Article  MATH  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  23. PL Rosin. Measuring shape: ellipticity, rectangularity, and triangularity, Mach Vision Appl, 2003, 14(3): 172–184.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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. JW Tangelder, RC Veltkamp. A survey of content based 3D shape retrieval methods, Multimed Tools Appl, 2008, 39(3): 441–471.

    Article  Google Scholar 

  27. S Wild. Java 7’s Dual Pivot Quicksort, Master Thesis, Technische Universität Kaiserslautern, 2013.

    MATH  Google Scholar 

  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.

    Article  Google Scholar 

  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. J Zunic, PL Rosin. A new convexity measure for polygons, IEEE Trans Pattern Anal, 2004, 26(7): 923–934.

    Article  Google Scholar 

  31. J Zunic, PL Rosin. Rectilinearity measurements for polygons, IEEE Trans Pattern Anal, 2003, 25(9): 1193–1200.

    Article  Google Scholar 

  32. J Zunic, PL Rosin, L Kopanja. On the orientability of shapes, IEEE Trans Image Process, 2006, 15(11): 3478–3487.

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Mathematical Science, State Key Lab. of CAD&CG, Zhejiang University, Hangzhou, 310027, China

    Zi-hao Wang, Hong-wei Lin & Chen-kai Xu

Authors
  1. Zi-hao Wang
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  2. Hong-wei Lin
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  3. Chen-kai Xu
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Corresponding author

Correspondence to Hong-wei Lin.

Additional information

This work is supported by the National Key R&D Plan of China (2016YFB1001501).

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Wang, Zh., Lin, Hw. & Xu, Ck. Data driven composite shape descriptor design for shape retrieval with a VoR-Tree. Appl. Math. J. Chin. Univ. 33, 88–106 (2018). https://doi.org/10.1007/s11766-018-3536-6

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  • DOI: https://doi.org/10.1007/s11766-018-3536-6

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