Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2011, Article ID 937263, 29 pages
http://dx.doi.org/10.1155/2011/937263
Research Article

Efficient Boundary Extraction from Orthogonal Pseudo-Polytopes: An Approach Based on the 𝑛 D-EVM

Computer Engineering Institute, The Technological University of the Mixteca (UTM), Carretera Huajuapan-Acatlima Km. 2.5, Huajuapan de León, 69000 Oaxaca, Mexico

Received 9 December 2010; Accepted 9 March 2011

Academic Editor: Tak-Wah Lam

Copyright © 2011 Ricardo Pérez-Aguila. 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. A. Aguilera, Orthogonal polyhedra: study and application, Ph.D. thesis, Universitat Politècnica de Catalunya, 1998.
  2. A. Aguilera and D. Ayala, “Orthogonal polyhedra as geometric bounds in constructive solid geometry,” in Proceedings of the 4th ACM Siggraph Symposium on Solid Modeling and Applications (SM ’97), pp. 56–67, ACM, Atlanta, Ga, USA, 1997.
  3. R. Pérez-Aguila, Orthogonal polytopes: study and application, Ph.D. thesis, Universidad de las Américas-Puebla (UDLAP), 2006.
  4. R. Pérez-Aguila, “Modeling and manipulating 3D datasets through the extreme vertices model in the n-dimensional space (nD-EVM),” Research in Computer Science, vol. 31, pp. 15–24, 2007. View at Google Scholar
  5. R. Pérez-Aguila, “Computing the discrete compactness of orthogonal pseudo-polytopes via their n-EVM representation,” Mathematical Problems in Engineering, vol. 2010, Article ID 598910, 28 pages, 2010. View at Publisher · View at Google Scholar
  6. J. Rodríguez and D. Ayala, “Erosion and dilation on 2D and 3D digital images: a new size-independent approach,” Vision Modeling and Visualization, pp. 143–150, 2001. View at Google Scholar
  7. J. Rodríguez and D. Ayala, “Fast neighborhood operations for images and volume data sets,” Computers and Graphics, vol. 27, no. 6, pp. 931–942, 2003. View at Publisher · View at Google Scholar
  8. A. Rosenfeld and J. L. Pfaltz, “Sequential operations in digital picture processing,” Journal of the ACM, vol. 13, no. 4, pp. 471–494, 1966. View at Google Scholar
  9. S. Marchand-Maillet and Y. M. Sharaiha, Binary Digital Image Processing, Academic Press Inc., San Diego, Calif, USA, 2000. View at Zentralblatt MATH
  10. H. Samet and M. Tamminen, “efficient component labeling of images of arbitrary dimension represented by linear bintrees,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 10, no. 4, pp. 579–586, 1988. View at Publisher · View at Google Scholar
  11. K. Sandfort and J. Ohser, “Labeling of n-dimensional images with choosable adjacency of the pixels,” Image Analysis & Stereology, vol. 28, no. 1, pp. 45–61, 2009. View at Google Scholar
  12. K. Wu, E. Otoo, and A. Shoshani, “Optimizing connected component labeling algorithms,” in Progress in Biomedical Optics and Imaging, vol. 5747 of Proceedings of SPIE, no. 3, pp. 1965–1976, 2005. View at Publisher · View at Google Scholar
  13. K. Suzuki, I. Horiba, and N. Sugie, “Linear-time connected-component labeling based on sequential local operations,” Computer Vision and Image Understanding, vol. 89, no. 1, pp. 1–23, 2003. View at Publisher · View at Google Scholar
  14. H. Samet, “Connected component labeling using quadtrees,” Journal of the Association for Computing Machinery, vol. 28, no. 3, pp. 487–501, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. A. A. Requicha, “Representations for rigid solids: theory, methods, and systems,” Computing Surveys, vol. 12, no. 4, pp. 437–464, 1980. View at Google Scholar
  16. H. Hansen and N. Christensen, “A model for n-dimensional boundary topology,” in Proceedings of the 2th Symposium on Solid Modeling and Applications, pp. 65–73, Montreal, Canada, 1993.
  17. L. K. Putnam and P. A. Subrahmanyam, “Boolean operations on n-dimensional objects,” IEEE Computer Graphics and Applications, vol. 6, no. 6, pp. 43–51, 1986. View at Google Scholar
  18. M. Spivak, Calculus on Manifolds. A Modern Approach to Classical Theorems of Advanced Calculus, W. A. Benjamin, Inc., New York, NY, USA, 1965.
  19. G. McCarty and G. S. Yound, Topology, Dover Publications Inc., New York, NY, USA, 2nd edition, 1988. View at Zentralblatt MATH
  20. G. L. Naber, Topological Methods in Euclidean Spaces, Dover Publications Inc., Mineola, NY, USA, 2000. View at Zentralblatt MATH
  21. A. Kolcun, “Visibility criterion for planar faces in 4D,” in Proceedings of Spring Conference on Computer Graphics (SCCG '04), pp. 216–219, Budmerice, Slovakia, 2004.
  22. T. Takala, “A taxonomy on geometric and topological models,” Computer Graphics and Mathematics, pp. 146–171, 1992. View at Google Scholar
  23. R. Pérez-Aguila, “Representing and visualizing vectorized videos through the extreme vertices model in the n-dimensional Sspace (nD-EVM),” Journal Research in Computer Science, vol. 29, pp. 65–80, 2007. View at Google Scholar