• No results found

I like to thank to LIA Research Group for supporting this work.

I owe many thanks to David Reboiro Jato and Pedro Silva Calveiro for pro- viding the code of Shaprox and Sharec.

I am heartedly thankful to my Master’s thesis advisor, Arno Formella, whose encouragement, guidance and support from the initial to the final level enabled me to develop an understanding of the subject.

6. A. Cantoni. Optimal curve fitting with piecewise linear functions. IEEE Transac- tions on Computers, pages 59–67, 1971.

7. J.C. Perez and E. Vidal. Optimum polygonal approximation of digitized curves. Pattern Recognition Letters, 15(8):743–750, 1994.

8. J.M. Chen, J.A. Ventura, and C.H. Wu. Segmentation of planar curves into circular arcs and line segments. Image and Vision Computing, 14(1):71–83, 1996. 9. P.S. Heckbert and M. Garland. Survey of polygonal surface simplification algo-

rithms, 1997.

10. C.C. Tseng, C.J. Juan, H.C. Chang, and J.F. Lin. An optimal line segment extrac- tion algorithm for online Chinese character recognition using dynamic program- ming. Pattern Recognition Letters, 19(10):953–961, 1998.

11. K. Mori, K. Wada, and K. Toraichi. Function Approximated Shape Representation using Dynamic Programing with Multi-Resolution Analysis. ICSPAT’99, 1999. 12. M. Salotti. Improvement of Perez and Vidal algorithm for the decomposition

ofdigitized curves into line segments. In 15th International Conference on Pattern Recognition, 2000. Proceedings, volume 2, 2000.

13. A. Kolesnikov and P. Fr¨anti. A fast near-optimal algorithm for approximation of polygonal curves. 16:335–338, 2002.

14. A. Kolesnikov and P. Fr¨anti. Reduced-search dynamic programming for approxi- mation of polygonal curves. Pattern Recognition Letters, 24(14):2243–2254, 2003. 15. A. Kolesnikov and P. Fr¨anti. Polygonal approximation of closed contours. Image

Analysis, 2749:409–417, 2003.

16. F. Attneave. Some informational aspects of visual perception. Psychological review, 61(3):183–193, 1954.

17. Jack Sklansky and Victor Gonzalez. Fast polygonal approximation of digitized curves. Pattern Recognition, 12(5):327 – 331, 1980.

18. D.H. Douglas and T.K. Peucker. Algorithms for the reduction of the number of points required to represent a digitized line or its caricature. Cartographica: The International Journal for Geographic Information and Geovisualization, 10(2):112– 122, 1973.

19. T. Pavlidis and S.L. Horowitz. Segmentation of plane curves. IEEE transactions on Computers, 100(23):860–870, 1974.

20. L.S. Davis and A. Rosenfeld. Curve segmentation by relaxation labeling. IEEE Transactions on Computers, pages 1053–1057, 1977.

21. J. Hershberger and J. Snoeyink. Speeding up the Douglas-Peucker line simplifica- tion algorithm. 1:134–143, 1992.

22. A. Pikaz and I. Dinstein. Optimal polygonal approximation of digital curves* 1. Pattern Recognition, 28(3):373–379, 1995.

23. T.Y. Phillips and A. Rosenfeld. An ISODATA algorithm for straight line fitting. Pattern Recognition Letters, 7(5):291–297, 1988.

24. F. Glover and M. Laguna. Tabu search, Modern heuristic techniques for combina- torial problems, 1993.

25. P.Y. Yin. A new method for polygonal approximation using genetic algorithms. Pattern Recognition Letters, 19(11):1017–1026, 1998.

26. U. Vallone. Bidimensional shapes polygonalization by ACO. Ant Algorithms, pages 79–101, 2002.

27. P.Y. Yin. Ant colony search algorithms for optimal polygonal approximation of plane curves. Pattern Recognition, 36(8):1783–1797, 2003.

28. David Reboiro Jato. C´alculo de un pol´ıgono para que represente a un conjunto de puntos de forma ´optima y extensi´on del algoritmo para optimizar segmenta- ciones de im´agenes. proyecto fin de carreira, inx-117, escuela superior de ingenier´ıa inform´atica, universidade de vigo, biblioteca, september 2005.

29. Pedro Silva Calveiro. Reconocimiento de formas a partir de una nube de pun- tos. proyecto fin de carreira, eni-143, escuela superior de ingenier´ıa inform´atica, universidade de vigo, biblioteca, june 2007.

30. http://www.cse.ohio-state.edu/ tamaldey/curverecon.htm.

31. P.J. Schneider and D.H. Eberly. Geometric tools for computer graphics. Morgan Kaufmann Pub, 2003.

32. J.E. Goodman and J. O’Rourke. Handbook of discrete and computational geometry. Chapman & Hall, 2004.

33. TH Cormen, CE Leiserson, RL Rivest, and C. Stein. Introduction to Algorithms. MIT Press, McGraw-Hill, second edition edition, 2001.

34. D.R. Chand and S.S. Kapur. An algorithm for convex polytopes. Journal of the ACM (JACM), 17(1):78–86, 1970.

35. RL Graham. An efficient algorith for determining the convex hull of a finite planar set. Information Processing Letters, 1(4):132–133, 1972.

36. RA Jarvis. On the identification of the convex hull of a finite set of points in the plane. Information Processing Letters, 2(1):18–21, 1973.

37. W.F. Eddy. A new convex hull algorithm for planar sets. ACM Transactions on Mathematical Software (TOMS), 3(4):398–403, 1977.

38. A. Bykat. Convex hull of a finite set of points in two dimensions. Information Processing Letters, 7(6):296–298, 1978.

39. FP Preparata and SJ Hong. Convex hulls of finite sets of points in two and three dimensions. Comm. ACM, 20:87–93, 1977.

40. AM Andrew. Another efficient algorithm for convex hulls in two dimensions. In- formation Processing Letters, 9(5):216–219, 1979.

41. M. Kallay. The complexity of incremental convex hull algorithms in Rd. Informa- tion Processing Letters, 19(4):197, 1984.

42. G. Voronoi. Nouvelles applications des param`etres continus `a la th´eorie des formes quadratiques. Premier m´emoire. Sur quelques propri´et´es des formes quadratiques positives parfaites. Journal f¨ur die reine und angewandte Mathematik (Crelle’s Journal), 1908(133):97–102, 1908.

43. A. Bowyer. Computing dirichlet tessellations. The Computer Journal, 24(2):162, 1981.

44. DF Watson. Computing the n-dimensional Delaunay tessellation with application to Voronoi polytopes. The computer journal, 24(2):167, 1981.

45. S. Fortune. A sweepline algorithm for Voronoi diagrams. Algorithmica, 2(1):153– 174, 1987.

53. Godfried T. Toussaint. The relative neighbourhood graph of a finite planar set. Pattern Recognition, 12(4):261 – 268, 1980.

54. Kenneth J. Supowit. The relative neighborhood graph, with an application to minimum spanning trees. J. ACM, 30(3):428–448, 1983.

55. J. Katajainen, O. Nevalainen, and J. Teuhola. A linear expected-time algorithm for computing planar relative neighbourhood graphs. Information Processing Letters, 25(2):77–86, 1987.

56. JW Jaromczyk and GT Toussaint. Relative neighborhood graphs and their rela- tives. Proceedings of the IEEE, 80(9):1502–1517, 1992.

57. A. Lingas. A linear-time construction of the relative neighborhood graph from the Delaunay triangulation. Computational Geometry, 4(4):199–208, 1994.

58. N. Amenta, M. Bern, and D. Eppstein. The crust and the beta-skeleton: combina- torial curve reconstruction. Graphical Models and Image Processing, 60(2):125–135, 1998.

59. H. Edelsbrunner, D. Kirkpatrick, and R. Seidel. On the shape of a set of points in the plane. IEEE Transactions on Information Theory, 29(4):551–559, 1983. 60. http://cgm.cs.mcgill.ca/ godfried/teaching/projects97/belair/alpha.html. 61. H. Edelsbrunner. Alpha Shapes—a Survey.

62. D.G. Kirkpatrick and J.D. Radke. A framework for computational morphology. Computational geometry, 85:217–248, 1985.

63. T.K. Dey and R. Wenger. Reconstruction curves with sharp corners. page 241, 2000.

64. T.K. Dey and R. Wenger. Fast reconstruction of curves with sharp corners. In- ternational Journal of Computational Geometry and Applications, 12(5):353–400, 2002.

65. T.K. Dey and P. Kumar. A simple provable algorithm for curve reconstruction. page 894, 1999.

66. N. Amenta, M. Bern, and M. Kamvysselis. A new Voronoi-based surface recon- struction algorithm. page 421, 1998.

67. O. Boruvka. On a minimal problem. Prace Morask´e Pridovedeck´e Spolecnosti, 3, 1926.

68. R.C. Prim. Shortest connection networks and some generalizations. Bell system technical journal, 36(6):1389–1401, 1957.

69. J.B. Kruskal Jr. On the shortest spanning subtree of a graph and the traveling salesman problem. Proceedings of the American Mathematical society, 7(1):48–50, 1956.

70. S. Arora. Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems. Journal of the ACM (JACM), 45(5):782, 1998.

71. G. Robins and A. Zelikovsky. Improved Steiner tree approximation in graphs. In Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms, page 779. Society for Industrial and Applied Mathematics, 2000.

72. P. Crescenzi and V. Kann. A compendium of NP optimization problems, 1998. 73. J. Giesen. Curve reconstruction, the traveling salesman problem, and Menger’s

theorem on length. Discrete and Computational Geometry, 24(4):577–603, 2000. 74. E. Althaus and K. Mehlhorn. TSP-based curve reconstruction in polynomial time.

pages 686–695, 2000.

75. H. Imai and M. Iri. Computational-geometric methods for polygonal approxima- tions of a curve. Computer Vision, Graphics, and Image Processing, 36(1):31–41, 1986.

76. A. KOLESNIKOV. Efficient algorithms for vectorization and polygonal approxi- mation. 2003.

77. P.L. Rosin. Techniques for Assessing Polygonal Approximationsof Curves. IEEE Transactions on Pattern Analysis and Machine Intelligence, 19(6):659–666, 1997. 78. U.M. Garc´ıa-Palomares and J.F. Rodr´ıguez. New sequential and parallel

derivative-free algorithms for unconstrained minimization. SIAM Journal on op- timization, 13:79, 2002.

79. http://www.algorithmic-solutions.com/leda/ledak/index.htm. 80. http://www.cgal.org/, June 2010.

81. http://www.boost.org/.

Related documents