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Mathematical Problems in Engineering
Volume 2018, Article ID 7090186, 9 pages
https://doi.org/10.1155/2018/7090186
Research Article

Efficient 3D Volume Reconstruction from a Point Cloud Using a Phase-Field Method

1Department of Mathematics, Korea University, Seoul 02841, Republic of Korea
2School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China
3ROKIT Inc., Seoul 08512, Republic of Korea

Correspondence should be addressed to Junseok Kim; rk.ca.aerok@mikdfc

Received 22 November 2017; Accepted 1 January 2018; Published 6 February 2018

Academic Editor: Costică Moroșanu

Copyright © 2018 Darae Jeong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. F. Remondino, “From point cloud to surface: the modeling and visualization problem,” in Proceedings of the International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, vol. XXXIV-5/W10, 2003.
  2. H. Hoppe, T. DeRose, T. Duchamp, J. McDonald, and W. Stuetzle, “Surface reconstruction from unorganized points,” Computer Graphics, vol. 26, no. 2, pp. 71–78, 1992. View at Publisher · View at Google Scholar · View at Scopus
  3. M. Kazhdan, “Reconstruction of solid models from oriented point sets,” in Proceedings of the third Eurographics Symposium on Geometry Processing, pp. 73–82, 2005.
  4. Y. Li, D. Lee, C. Lee et al., “Surface embedding narrow volume reconstruction from unorganized points,” Computer Vision and Image Understanding, vol. 121, pp. 100–107, 2014. View at Publisher · View at Google Scholar · View at Scopus
  5. Y. Li and J. Kim, “Fast and efficient narrow volume reconstruction from scattered data,” Pattern Recognition, vol. 48, no. 12, article no. 5459, pp. 4057–4069, 2015. View at Publisher · View at Google Scholar · View at Scopus
  6. J. Yang, R. Li, Y. Xiao, and Z. Cao, “3D reconstruction from non-uniform point clouds via local hierarchical clustering,” in Proceedings of the 9th International Conference on Digital Image Processing, ICDIP 2017, China, May 2017. View at Publisher · View at Google Scholar · View at Scopus
  7. H.-K. Zhao, S. Osher, and R. Fedkiw, “Fast surface reconstruction using the level set method,” in Proceedings of the IEEE Workshop on Variational and Level Set Methods in Computer Vision, VLSM 2001, pp. 194–199, can. View at Publisher · View at Google Scholar · View at Scopus
  8. A. Yezzi Jr., S. Kichenassamy, A. Kumar, P. Olver, and A. Tannenbaum, “A geometric snake model for segmentation of medical imagery,” IEEE Transactions on Medical Imaging, vol. 16, no. 2, pp. 199–209, 1997. View at Publisher · View at Google Scholar · View at Scopus
  9. M. Beneš, V. r. Chalupecky, and K. Mikula, “Geometrical image segmentation by the Allen-Cahn equation,” Applied Numerical Mathematics, vol. 51, no. 2-3, pp. 187–205, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  10. V. Caselles, F. Catte, T. Coll, and F. Dibos, “A geometric model for active contours in image processing,” Numerische Mathematik, vol. 66, no. 1, pp. 1–31, 1993. View at Publisher · View at Google Scholar · View at MathSciNet
  11. V. Caselles, R. Kimmel, and G. Sapiro, “Geodesic active contours,” International Journal of Computer Vision, vol. 22, no. 1, pp. 61–79, 1997. View at Publisher · View at Google Scholar · View at Scopus
  12. T. F. Chan and L. A. Vese, “Active contours without edges,” IEEE Transactions on Image Processing, vol. 10, no. 2, pp. 266–277, 2001. View at Publisher · View at Google Scholar · View at Scopus
  13. J. Hahn and C.-O. Lee, “Geometric attraction-driven flow for image segmentation and boundary detection,” Journal of Visual Communication and Image Representation, vol. 21, no. 1, pp. 56–66, 2010. View at Publisher · View at Google Scholar · View at Scopus
  14. S. Kichenassamy, A. Kumar, P. Olver, A. Tannenbaum, and J. Yezzi, “Conformal curvature flows: from phase transitions to active vision,” Archive for Rational Mechanics and Analysis, vol. 134, no. 3, pp. 275–301, 1996. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. B. Zhang, W. Wang, and X. Feng, “Subspace Clustering with Sparsity and Grouping Effect,” Mathematical Problems in Engineering, vol. 2017, Article ID 4787039, 9 pages, 2017. View at Publisher · View at Google Scholar · View at Scopus
  16. Y.-T. Chen, “Medical Image Segmentation Using Independent Component Analysis-Based Kernelized Fuzzy c-Means Clustering,” Mathematical Problems in Engineering, vol. 2017, Article ID 5892039, 21 pages, 2017. View at Publisher · View at Google Scholar · View at Scopus
  17. Y. Zhang, J. Xu, and H. D. Cheng, “A Novel Fuzzy Level Set Approach for Image Contour Detection,” Mathematical Problems in Engineering, vol. 2016, Article ID 2602647, 12 pages, 2016. View at Publisher · View at Google Scholar · View at Scopus
  18. C. Li, C. Xu, C. Gui, and M. D. Fox, “Level set evolution without re-initialization: a new variational formulation,” in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR '05), pp. 430–436, June 2005. View at Publisher · View at Google Scholar · View at Scopus
  19. L. A. Vese and T. F. Chan, “A multiphase level set framework for image segmentation using the Mumford and Shah model,” International Journal of Computer Vision, vol. 50, no. 3, pp. 271–293, 2002. View at Publisher · View at Google Scholar · View at Scopus
  20. Y. Li and J. Kim, “A fast and accurate numerical method for medical image segmentation,” Journal of the Korean Society for Industrial and Applied Mathematics, vol. 14, no. 4, pp. 201–210, 2010. View at Google Scholar · View at MathSciNet
  21. A. M. Stuart and A. R. Humphries, Dynamical Systems and Numerical Analysis, vol. 2, Cambridge University Press, New York, NY, USA, 1998. View at MathSciNet
  22. Y. Li, H. G. Lee, D. Jeong, and J. Kim, “An unconditionally stable hybrid numerical method for solving the Allen-Cahn equation,” Computers & Mathematics with Applications. An International Journal, vol. 60, no. 6, pp. 1591–1606, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  23. S. M. Allen and J. W. Cahn, “A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening,” Acta Metallurgica et Materialia, vol. 27, no. 6, pp. 1085–1095, 1979. View at Publisher · View at Google Scholar · View at Scopus
  24. B. Appleton and H. Talbot, “Globally optimal geodesic active contours,” Journal of Mathematical Imaging and Vision, vol. 23, no. 1, pp. 67–86, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  25. Stanford university computer graphics laboratory, http://lightfield.stanford.edu/acq.html.