Journal of KIISE:Computer Systems and Theory (한국정보과학회논문지:시스템및이론)

Korean Institute of Information Scientists and Engineers (한국정보과학회)
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An Efficient Algorithm for Hausdorff Distance Computation of 2D Convex Polygons using k-DOPs

k-DOP을 이용하여 2차원 볼록 다각형간의 Hausdorff 거리를 계산하는 효율적인 알고리즘

  • 이지은 (조선대학교 컴퓨터공학부) ;
  • 김용준 (서울대학교 컴퓨터공학부)
  • Published : 2009.04.15
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Abstract

We present an efficient algorithm for computing the Hausdorff distance between two 2D convex polygons. Two convex polygons are bounded by k-DOPs and the regions of interest are traced using the orientational and hierarchical properties of k-DOP. The algorithm runs in a logarithmic time in the average case, and the worst case time complexity is linear.

본 논문에서는 두 개의 이차원 볼록 다각형간의 Hausdorff 거리를 계산하는 효율적인 알고리즘을 제안한다. 볼록 다각형을 k-DOP으로 바운딩하고, k-DOP의 방향성과 계층적인 특성에 따라 관심영역만을 추적하는 방법으로, 본 논문에서 제안하는 알고리즘은 평균적으로 O(logn)시간에 수행되며, 최악의 경우에도 O(n)의 수행성능을 보인다.

Keywords

References

  1. J. T. Schwartz, "Finding the minimum distance between two onvex polgons," Information Processing Letters, Vol.13, pp. 168, 1981. https://doi.org/10.1016/0020-0190(81)90051-X
  2. F. Chin, and C. A. Wang, "Optimal algorithms for the intersection and the minimum distance problems between planar polygons," IEEE Trans. on Computers, Vol.32, No.12, pp. 1203-1207, 1983. https://doi.org/10.1109/TC.1983.1676186
  3. E. Gilbert, D. Johnson, and S. S. Keerthi, " A fast proedure for computing the istance between complex objects in three dimensional space," IEEE Journal of Robbtics and Automation, Vol.4, No. 2, pp. 193-203, 1998.
  4. G. Elber and T. Grandine, "Hausdorf and minimal Distances between parametric freeforms in R and R, " Lecture Notes in Computer Science: Advances in Geometric Modieling and Processing, Proc. of 5th Int. Conf. GMP 2008, Vol. 4975, pp 191-204, 2008.
  5. H. P. Moon, "Minkowski Pythagorean hodographs," Computer Aided Geometric Design, Vol.16, No. 8, pp. 739-753, 1999. https://doi.org/10.1016/S0167-8396(99)00016-3
  6. M. J. Atallah, "A linear time algorithm for the Hausdorff distance between convex polygons," Information Processing Letters, Vol.17, pp. 207-209, 1983. https://doi.org/10.1016/0020-0190(83)90042-X
  7. G. Rote, "Computing the minimum Hausdorff istance between two point sets on a line under translation," Information Processing Letters, Vol.38, pp. 123-127, 1991. https://doi.org/10.1016/0020-0190(91)90233-8
  8. H. Alt and L. Scharf, "Computing the Hausdorff distance between sets of curves," Proc. of the 20th European Workshop on Computational Geometry, pp. 233-236, 2004.
  9. B. Lianas, "Eficient computation of the Gausdorff distance between polytopes by exterior random covering," Computational Optimization and Applications, Vol.30, pp. 161-194, 2005. https://doi.org/10.1007/s10589-005-4560-z
  10. J.-M. Morvan, Generalized curvatures, Springer, 2008.
  11. M. P. Do Carmo, Differential geometry of curves and surfaces, Prentice-Hall, 1976.
  12. H. Alt, B. Behrends, and J. Blomer, "Approximate matching of polygonal shapes," Technical report B 93-10, Institut fur Informatik, Freie Universitat Berlin, 1992.
  13. M. P. Dubuisson, and A. K. Jain, "Modified Hausorf distance for object matching," Proc. of 12th Int. Conf. on Pattern Recognition, pp. 566-568, 1994.
  14. D. P. Huttenlocher, G. A. Klanderman, and W. J. Rucklidge, "Comparing images using the Hausdorff istance," IEEE Trans. on Pattern Analysis and Machine Inteligence, Vol.15, No.9, pp. 850-863, 1993. https://doi.org/10.1109/34.232073
  15. W. J. Ruckldge, Lecture Notes in Computer Science: Eficient visual recognition using the Hausdorff dstance, Vol.1173, Springer-Verlag, NewYork, 1996.
  16. N. K. Govindaraju, S. Redon, M. C. Lin, and D. Manocha, "CULLIDE: Interactive collision detection between complex models in large environments using graphics hardware," In Graphics Hardware 2003, pp. 25-32, July 2003.
  17. A. Gress and G. Zachmann, "Object-space interference detection on programmable graphics hardware," In SIAM Conf. on Geometric Design and Computing, 2003.
  18. T. Klein, S. Stegmaier, and T. Eri, "Hardware-accelerated reconstruction of polygonal isosurface representations on unstructured grids," Pacific Conf. on Computer Graphics and Applications, pp. 186-195, 2004.
  19. M. Guthe, A. Balazs, and R. Klein, "GPU-based trimming and tessellation of NURBS and T-Spline surfaces," ACM Trasn. on Graphics, Vol.24, No.3, pp. 1016-1023, 2005.
  20. C. Loop and J. Blinn, "Real-time GPU Rendering of piecewise algebraic surfaces," ACM Trans. on Graphics, Vol.25, No. 3, pp. 664-670, 2006. https://doi.org/10.1145/1141911.1141939
  21. J. T. Klosowski, M. Held, J. S. B. Mithell, H. Sowizral, and K. Zikan, "Eficient collision detection using bounding volume hierarchies of-DOPs," IEEE Trans. on Visualization and Computer Graphics, Vol.4, No.1, pp. 21-36, 1998. https://doi.org/10.1109/2945.675649
  22. G. Zachmann, "Rapid collision detection by dynamically allgned DOP-trees," Proc. of Virtual Reality Annual Int. Symp., pp. 90-97, 1998.
  23. A. Raabe, B. Bartyzel, J. K. Anlau, and G. Zachmann, "Hardware acelerated collision detection - an archtecture and simulation results," Proc. of Design, Automation and Test in Europe, Vol.3, pp. 130-135, 2005.
  24. E. Belogay, C. Cabrelli, U. Molter, and R. Shonkwiler, "Calculating the Hausdorff distance between curves," Information Processing Letters, Vol.64, pp. 17-22, 1997. https://doi.org/10.1016/S0020-0190(97)00140-3
  25. N. Gregoire, and M. Bouilot, "Hausdorf distance between convex polygons," http://cgm.cs.mcgill.ca/~godfriend/teaching/cg-projects/98/normand/main.html.