Skip to main content
Log in

Pairwise matching of 3D fragments using fast fourier transform

  • Original Article
  • Published:
The Visual Computer Aims and scope Submit manuscript

Abstract

In this paper, we introduce a new method for pairwise matching of broken fragments from unorganized point clouds. We use a new descriptor that contains not only the cluster of feature points but also curves along the principal directions of the cluster. In our method, feature points are extracted by using the curvature values of points. Curves of the descriptor are approximated using Fourier series. The main idea is motivated by comparing descriptor curves between each cluster of matching faces. For comparing curves, the Fourier coefficients of each curve are computed by using Fast Fourier Transform and total energies of curves are compared.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. Altantsetseg, E., Muraki, Y., Matsuyama, K., Konno, K.: Feature line extraction from unorganized noisy point clouds using truncated Fourier series. Vis. Comput. 29(6–8), 617–626 (2013)

    Article  Google Scholar 

  2. Brigham, E.O.: The Fast Fourier Transform and Applications. Prentice Hall, Englewood Cliffs (1988)

    Google Scholar 

  3. Brown, B.J., Toler-Franklin, C., Nehab, D., Burns, M., Dobkin, D., Vlachopoulos, A., Weyrich, T.: A system for high-volume acquisition and matching of fresco fragments: reassembling Theran wall paintings. ACM Trans. Graph. 27, 3 (2008)

    Article  Google Scholar 

  4. Cohen, F., Liu, Z., Ezgi, T.: Virtual reconstruction of archeological vessels using expert priors and intrinsic differential geometry information. Comput. Graph. 37(1), 41–53 (2013)

    Google Scholar 

  5. Da Gama Leitao, H.C., Stolfi, J.: A multiscale method for the reassembly of fragmented objects. IEEE Trans. Patt. Anal. Mach. Intell. 24(9), 1239–1251 (2002)

    Article  Google Scholar 

  6. Dong, S., Bremer, P.-T., Garland, M., Pascucci, V., Hart, J.C.: Spectral surface quadrangulation. ACM Trans. Graph. 25(3), 1057–1066 (2006)

    Article  Google Scholar 

  7. Gal, R., Cohen-Or, D.: Salient geometric features for partial shape matching and similarity. ACM Trans. Graph. 25(1), 130–150 (2006)

    Google Scholar 

  8. Gelfand, N., Mitra, N.J., Guibas, L.J., Pottmann, H.: Robust Global Registration. In: Symposium on geometry processing, pp. 197–206 (2005)

  9. Gokberk, B., Dutagaci, H., Ulas, A., Akarun, L., Sankur, B.: Representation plurality and fusion for 3-D face recognition. IEEE Trans. Syst. Man Cybernet. Part B 38(1), 155–173 (2008)

    Google Scholar 

  10. Huang, Q.X., Adams, B., Wicke, M., Guibas, L.J.: Non-rigid registration under isometric deformations. Comput. Graph. Forum 27(5), 1449–1457 (2008)

    Article  Google Scholar 

  11. Huang, Q.X., Flory, S., Gelfand, N., Hofer, M., Pottmann, H.: Reassembling fractured objects by geometric matching. ACM Trans. Graph. 25(3), 569–578 (2006)

    Article  Google Scholar 

  12. Kang, U., Hebert, M., Park, S.: Fast and scalable approximate spectral graph matching for correspondence problems. Info. Sci. 220, 306–318 (2013)

    Article  MathSciNet  Google Scholar 

  13. Katchalski-Katzir, E., Shariv, I., Eisenstein, M., Friesem, A.A., Aflalo, C., Vakser, I.A.: Molecular surface recognition: determination of geometric fit between proteins and their ligands by correlation techniques. Proc. Natl. Acad. Sci. 89(6), 2195–2199 (1992)

    Article  Google Scholar 

  14. Koller, D., Levoy, M.: Computer-aided Reconstruction and new Matches in the Forma Urbis Romae. Bullettino Della Commissione Archeologica Comunale di Roma Supplementi 15, pp. 103–125 (2006)

  15. Kong, W., Kimia, B.B.: On solving 2D and 3D puzzles using curve matching. Computer Vision and Pattern Recognition. CVPR 2001. In: Proceedings of the 2001 IEEE Computer Society Conference, pp. 583–590 (2001)

  16. Leordeanu, M., Hebert, M.: A spectral technique for correspondence problems using pairwise constraints. In: Computer Vision, Tenth IEEE International Conference, pp. 1482–1489 (2005)

  17. Li, Q., Zhou, M., Geng, G.: Fractured surfaces matching for reassembling broken solids. In: Computational Intelligence and Design, Fifth International Symposium, pp. 511–514 (2012)

  18. Li, X., Guskov, I.: Multiscale features for approximate alignment of point-based surfaces. In: Symposium on geometry processing (2005)

  19. Lucchese, L., Doretto, G., Cortelazzo, G.M.: A frequency domain technique for range data registration. IEEE Trans. Patt. Anal. Mach. Intell. 24(11), 1468–1484 (2002)

    Article  Google Scholar 

  20. Mcbride, J.C., Kimia, B.B.: Archaeological fragment reconstruction using curve-matching. In: Proceedings of the 2003 Conference on Computer Vision and Pattern Recognition, Workshop, pp. 1–8 (2003)

  21. Oxholm, G., Nishino, K.: A flexible approach to reassembling thin artifacts of unknown geometry. J. Cultural Heritage 14(1), 51–61 (2013)

    Google Scholar 

  22. Papaioannou, G., Karabassi, E.A., Theoharis, T.: Reconstruction of three-dimensional objects through matching of their parts. IEEE Trans. Patt. Anal. Mach. Intell. 24(1), 114–124 (2002)

    Article  Google Scholar 

  23. Papaioannou, G., Karabassi, E.A.: On the automatic assemblage of arbitrary broken solid artefacts. Image Vis. Comput. 21(5), 401–412 (2003)

    Article  Google Scholar 

  24. Papaodysseus, C., Arabadjis, D., Exarhos, M., Rousopoulos, P., Zannos, S., Panagopoulos, M., Papazoglou-Manioudaki, L.: Efficient solution to the 3D problem of automatic wall paintings reassembly. Comput. Math. Appl. 64(8), 2712–2734 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  25. Parikh, D., Sukthankar, R., Chen, T., Chen, M.: Feature-based part retrieval for interactive 3D reassembly. In: Proceedings of the IEEE Workshop on Applications of Computer Vision (2007)

  26. Pauly, M., Gross, M.: Spectral processing of point-sampled geometry. SIGGRAPH 01, 379–386 (2001)

    Google Scholar 

  27. Peitgen, H.-O., Saupe, D.: The Science of Fractal Images. Springer-Verlag, New York (1988)

    MATH  Google Scholar 

  28. Toler-Franklin, C., Brown, B., Weyrich, T., Funkhouser, T., Rusinkiewicz, S.: Multi-feature matching of fresco fragments. ACM Trans. Graph. 29, 6 (2010)

    Article  Google Scholar 

  29. Willis, A.R., Cooper, D.B.: Alignment of multiple non-overlapping axially symmetric 3d datasets. In: Pattern Recognition, 2004. ICPR 2004. Proceedings of the 17th International Conference, pp. 96–99 (2004)

  30. Willis, A.R., Cooper, D.B.: Computational reconstruction of ancient artifacts. IEEE Signal Proces. Mag. 25(4), 65–83 (2008)

    Article  Google Scholar 

  31. Winkelbach, S., Wahl, F.M.: Pairwise matching of 3D fragments using cluster trees. Intern. J. Comput. Vis. 78(1), 1–13 (2008)

    Article  Google Scholar 

  32. Zheng, Q., Sharf, A., Tagliasacchi, A., Chen, B., Zhang, H., Sheffer, A., Cohen-Or, D.: Consensus skeleton for non-rigid space–time registration. Comput. Graph. Forum 29(2), 635–644 (2010)

    Google Scholar 

Download references

Acknowledgments

3D brick models are courtesy by Vienna University of Technology. This work was supported by JSPS KAKENHI Grant Number 24501253.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Enkhbayar Altantsetseg.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Altantsetseg, E., Matsuyama, K. & Konno, K. Pairwise matching of 3D fragments using fast fourier transform. Vis Comput 30, 929–938 (2014). https://doi.org/10.1007/s00371-014-0959-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00371-014-0959-9

Keywords

Navigation