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Linear Capture of Digital Curves

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Interactive Curve Modeling

This chapter is devoted to the detailed study of linear or polygonal approximation needed in various applications, including shape recognition, point-based motion estimation, coding methods, and so on., in the areas of computer graphics, imaging and vision. Some important aspects related to capturing with linear approximation have been addressed. A detailed survey of many methods, in the current literature has been made. Some commonly referred algorithms have been explained and their results are demonstrated and compared.

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References

  1. Attneave, F. (1954), Some information aspects of visual perception. Psychol Rev 61:183-193.

    Article  Google Scholar 

  2. Ansari, N., and Huang, K.W. (1991), Nonparametric dominant points detection. Pat-tern Recognition 24:849-862.

    Article  Google Scholar 

  3. Arcelli, C., and Ramella, G. (1993), Finding contour-based abstractions of planner patterns. Pattern Recognition 26(10):1563-1577.

    Article  Google Scholar 

  4. Cronin, T.M. (1999), A boundary concavity code to support dominant points detection, Pattern Recognition Lett 20, 617-634.

    Article  Google Scholar 

  5. Dunham, J.G. (1986), Optimum uniform piecewise linear approximation of planner curves. IEEE Trans Anal Mach Intell 8:67-75.

    Article  Google Scholar 

  6. Freeman, H. (1061), On the encoding of arbitrary geometric configurations. IRE Trans Elec Comp 10:260-268.

    Article  MathSciNet  Google Scholar 

  7. Kurozumi, Y., and Davis, W.A. (1982), Polygonal approximation by minimax method. Comput Graphics Image Process 19:248-264.

    Article  MATH  Google Scholar 

  8. Lowe, D.G. (1987), Three-dimensional object recognition from single two- dimensional images. AI 31:355-395.

    Google Scholar 

  9. Marji, M., and Siy, P. (2003), A new algorithm for dominant points detection and polygonization of digital curves, Pattern Recognition 36, 2239-2251.

    Article  MATH  Google Scholar 

  10. Ramer, U. (1972), An iterative procedure for the polygonal approximation of plane curves. Comput Graphics Image Process 1:244-256.

    Article  Google Scholar 

  11. Ray, B.K., and Ray, K.S. (1992), Detection of significant points and polygonal approx-imation of digitized curves, Pattern Recognition Lett 13, 443-452.

    Article  Google Scholar 

  12. Rosin, P.L. (1998), Assessing the behavior of polygonal approximation algorithms. Ninth British Machine Vision Conference, Southampton, UK.

    Google Scholar 

  13. Rosin, P.L. (1997), Techniques for assessing polygonal approximations of curves. IEEE Trans PAMI 19(6):659-666.

    Google Scholar 

  14. Sarfraz, M., Asim, M.R., and Masood, A. (2004), Piecewise polygonal approximation of digital curves, The Proceedings of IEEE International Conference on Information Visualisation (IV’2004)-UK, IEEE Computer Society Press, pp. 991-996.

    Google Scholar 

  15. Sarkar, D. (1993), A simple algorithm for detection of significant vertices for polygo-nal approximation of chain-coded curves, Pattern Recognition Lett 14, 959-964.

    Article  Google Scholar 

  16. Sato, Y. (1992), Piecewise linear approximation of plane curves by perimeter opti-mization. Pattern Recognition 25:1535-1543.

    Article  Google Scholar 

  17. Slansky, J., and Gonazlez, V. (1980), Fast polygonal approximation of digitized curves. Pattern Recognition 12:327-331.

    Article  Google Scholar 

  18. The, C., and Chin, R. (1989), On the detection of dominant points on digital curves, IEEE Trans PAMI 8, 859-873.

    Google Scholar 

  19. Wang, M.J., Wu, W.Y., Huang, L.K., and Wang, D.M. (1995), Corner detection using bending value. Pattern Recognition Lett 16:575-583.

    Article  Google Scholar 

  20. Wu, W.Y. (2003), An adaptive method for detecting dominant points, Pattern Recog- nition 36, 2231-2237.

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  22. Melkman, A., and Rourke, J.O. (1988), On polygonal chain approximation. Proceed-ings of Computational Morphology, North-Holland, Amsterdam, pp. 87-95.

    Google Scholar 

  23. Sklansky, J., and Gonzalez, V. (1980), Fast polygonal approximation of digitized curves, Pattern Recognition 12, 327-331.

    Article  Google Scholar 

  24. Held, A., Abe, K., and Arcelli, C. (1994), Towards a hierarchical contour description via dominant point detection, IEEE Trans Sys Man Cybernetics 24, 942-949.

    Article  Google Scholar 

  25. Dunham, J.G. (1986), Optimum uniform piecewise linear approximation of planar curves, IEEE Trans PAMI 8, 67-75.

    Google Scholar 

  26. Sato, Y. (1992), Piecewise linear approximation of plane curves by perimeter opti- mization, Pattern Recognition 25, 1535-1543.

    Article  Google Scholar 

  27. Goldberg, D.E. (1989), Genetic Algorithms in Search Optimization and Machine Learning, Addison-Wesley, Reading, MA.

    MATH  Google Scholar 

  28. Huang, S.C., and Sun, Y.N. (1999), Polygonal approximation using genetic algorithms, Pattern Recognition 32, 1409-1420.

    Article  Google Scholar 

  29. Pal, N.R., Nandi, S., and Kundu, M.K. (1998), Self-crossover: a new genetic operator and its application to feature selection. Int J Systems Sci 2, 207-212.

    Article  Google Scholar 

  30. Yin, P.Y. (1999), Genetic algorithms for polygonal approximation of digital curves, Int J Pattern Recognition Artif Intell 13, 1-22.

    Article  Google Scholar 

  31. Yin, P.Y. (2000), A tabu search approach to the polygonal approximation of digital curves, Int J Pattern Recognition Artif Intell 14, 243-255.

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  33. Davis, L.S. (1977), Understanding shape angles and sides, IEEE Trans Comput 26, 236-242.

    Article  MATH  Google Scholar 

  34. Sankar, P.V., and Sharma, C.V. (1978), A parallel procedure for the detection of dom-inant points on digital curve, Comput Graphics Image Process 7, 403-412.

    Article  Google Scholar 

  35. Latecki, L.J., and Lak ämper, R. (1999), Convexity rule for shape decomposition based on discrete contour evolution, Comput Vision Image Understanding 73, 441-454.

    Article  Google Scholar 

  36. Latecki, L.J., Ghadially, R.R., Lak ämper, R., and Eckhardt, U. (2000), Continuity of the discrete curve evolution, J Electronic Imaging 9, 317-326.

    Article  Google Scholar 

  37. Sankar, P.V., and Sharma, C.V. (1978), A parallel procedure for the detection of dom-inant points on digital curve, Comput Graphics Image Process 7, 403-412.

    Article  Google Scholar 

  38. Latecki, L.J., and Lak ämper, R. (1999), Convexity rule for shape decomposition based on discrete contour evolution, Comput Vision Image Understanding 73, 441-454.

    Article  Google Scholar 

  39. Latecki, L.J., Ghadially, R.R., Lak ämper, R., and Eckhardt, U. (2000), Continuity of the discrete curve evolution, J Electronic Imaging 9, 317-326.

    Article  Google Scholar 

  40. Rosenfeld, A., and Weszka, J.S. (1975), An improved method of angle detection on digital curves, IEEE Trans Comput 24, 940-941.

    Article  Google Scholar 

  41. Rosenfeld, A., Johnston, E. (1973), Angle detection on digital curves, IEEE Trans Comput 22, 875-878.

    Article  Google Scholar 

  42. Freeman, H., and Davis, L.S. (1977), A corner-finding algorithm for chain-coded curves, IEEE Trans Comput 26, 297-303.

    Article  Google Scholar 

  43. Neumann, R., and Teisseron, G. (2002), Extraction of dominant points by estimation of the contour fluctuations, Pattern Recognition 35, 1447-1462.

    Article  MATH  Google Scholar 

  44. Lowe, D.G. (1987), Three-dimensional object recognition from single two- dimensional images, Artific Intell 31, 355-395.

    Article  Google Scholar 

  45. Perez, J.C., and Vidal, E. (1994), Optimum polygonal approximation of digitized curves, Pattern Recognition Lett 15, 743-750.

    Article  MATH  Google Scholar 

  46. Chan, W.S., and Chin, F. (1996), On approximation of polygonal curves with minimum number of line segments or minimum error, Int J Comput Geom Appl 6, 59-77.

    Article  MATH  MathSciNet  Google Scholar 

  47. Saghri, J., and Freeman, H. (1981), Analysis of the precision of generalized chain codes for the representation of planar curves, IEEE Trans PAMI 3, 533-539.

    Google Scholar 

  48. Koplowitz, J. (1981), On the performance of chain codes for quantization of the line drawings. IEEE Trans PAMI 3, 180-185.

    MATH  Google Scholar 

  49. Li, L. Chen, W. (1999), Corner detection and interpretation on planar curves using fuzzy reasoning, IEEE Trans PAMI, 21, 1204-1210.

    Google Scholar 

  50. Kaneko, T., and Okudaira, M. (1985), Encoding of arbitrary curves based on the chain code representation, IEEE Trans Comm 33, 697-707.

    Article  Google Scholar 

  51. Kurozumi, Y., and Davis, W.A. (1982), Polygonal approximation by the minimax method, Comput Graphics Image Process 19, 248-264.

    Article  MATH  Google Scholar 

  52. Pikaz, A., and Dinstein, I. (1995), An algorithm for polygonal approximation of digital curves based on iterative points elimination, Pattern Recognition Lett 16, 557-563.

    Article  Google Scholar 

  53. Leu, J.G., and Chen, L. (1988), Polygonal approximation of 2-D shapes through boundary merging, Pattern Recognition, 28, 571-579.

    Google Scholar 

  54. Ray, B.K., and Ray, K.S. (1995), A new split-and-merge technique for polygonal approximation of chain coded curves, Pattern Recognition Lett 16, 161-169.

    Article  Google Scholar 

  55. Inesta, J.M., Buendia, M., and Sarti, M.A. (1988), Reliable polygonal approxima-tions of imaged real objects through dominant point detection, Pattern Recognition 31, 685-697.

    Article  Google Scholar 

  56. Yin, P.Y. (1998), Algorithms for straight-line fitting using K -means, Pattern Recogni- tion Lett 19, 31-41.

    Article  MATH  Google Scholar 

  57. Yukio, S. (1992), Piecewise linear approximation of plane curves by perimeter opti-mization, Pattern Recognition, 25, 1535-1543.

    Article  Google Scholar 

  58. Imai, H., and Iri, M. (1986), Computational-geometric methods for polygonal approx-imations of a curve, Comp Vis Image Proc 36, 31-41.

    Article  Google Scholar 

  59. Leymarie, F., and Levine, M.D. (1988), Curvature Morphology, Center of Intelligent Machines, TR-CIM-88-26, McGill University, Montreal.

    Google Scholar 

  60. Ray, B.K., and Ray, K.S. (1992), An algorithm for detecting dominant points and polygonal approximation of digitized curves, Pattern Recognition Lett 13, 849-856.

    Article  Google Scholar 

  61. Zhang, X., and Zhao, D. (1997), A parallel algorithm for detecting dominant points on multiple digital curves, Pattern Recognition, 30, 239-244.

    Article  Google Scholar 

  62. Cheng, K.H., and Hsu W.H., (1988), Parallel algorithms for corner following on digital curves, Pattern Recognition Lett 8, 47-53.

    Article  MATH  Google Scholar 

  63. Phillips, T.Y., and Rosenfeld, A. (1987), A method for curve partitioning using arc- chord distance, Pattern Recognition Lett 5, 285-288.

    Article  Google Scholar 

  64. Fischler, M.A., and Wolf, H.C. (1994), Locating perceptually salient points on planar curves, IEEE Trans. PAMI 16, 113-129.

    Google Scholar 

  65. Han, J.H., and Poston, T. (2001), Chord-to-point distance accumulation and planar curvature: a new approach to discrete curvature, Pattern Recognition Lett 22, 1133-1144.

    Article  MATH  Google Scholar 

  66. Ogawa, H. (1989), Corner detection on digital curves based on local symmetry of the shape, Pattern Recognition, 22, 351-357.

    Article  Google Scholar 

  67. Ansari, N., and Huang, K.W. (1991), Nonparametric dominant point detection, Pattern Recognition, 24, 849-862.

    Article  Google Scholar 

  68. Koplowitz, J., and Plante, S. (1995), Corner detection for chain coded curves, Pattern Recognition 28, 843-852.

    Article  Google Scholar 

  69. Tsai, D.M. (1997), Boundary-based corner detection using neural networks, Pattern Recognition 30, 85-97.

    Article  MATH  Google Scholar 

  70. Lee, J.S., Sun, Y.N., Chen, C.H., and Tsai, C.T. (1993), Wavelet-based corner detec- tion, Pattern Recognition, 26, 853-865.

    Article  Google Scholar 

  71. Quddus, A., and Fahmy, M.M. (1999), Fast wavelet-based corner detection technique, Electron Lett 35, 287-288.

    Article  Google Scholar 

  72. Pikaz, A., and Dinstein, I. (1995), Optimal polygonal approximation of digital curves, Pattern Recognition 28, 373-279.

    Article  Google Scholar 

  73. Horng, J.H., and Li, J.T. (2002), An automatic and efficient dynamic programming algorithm for polygonal approximation of digital curves, Pattern Recognition Lett 23, 171-182.

    Article  MATH  Google Scholar 

  74. Kolesnikov, A., and Fr änti, P. (2003), Reduced search dynamic programming for approximation of polygonal curves, Pattern Recognition Lett 24, pp. 2243-2254.

    Article  MATH  Google Scholar 

  75. Salotti, M. (2000), Improvement of Perez and Vidal algorithm for the decomposition of digitized curves into line segments, 15th International Conference on Pattern Recog-nition, Vol. 2, pp. 878-882.

    Google Scholar 

  76. Zhu, Y., and Seneviratne, L.D (1997), Optimal polygonal approximation of digitized curves. IEE Proc. of Vision, Image and Signal Processing, Vol. 144, pp. 8-14.

    Article  Google Scholar 

  77. Chan, W.S., and Chin, F. (1996), On approximation of polygonal curves with minimum number of line segments or minimum error, Int J Comput Geom Appl 6, 59-77.

    Article  MATH  MathSciNet  Google Scholar 

  78. Kolesnikov, A., and Franti, P. (2005), Min-# polygonal approximation of closed curves, IEEE International Conference on Image Processing, Vol. 2, pp. 522-525.

    Google Scholar 

  79. Horng, J.H. (2002), Improving fitting quality of polygonal approximation by using the dynamic programming technique, Pattern Recognition Lett 23, 1657-1673.

    Article  MATH  Google Scholar 

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(2008). Linear Capture of Digital Curves. In: Interactive Curve Modeling. Springer, London. https://doi.org/10.1007/978-1-84628-871-5_12

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  • DOI: https://doi.org/10.1007/978-1-84628-871-5_12

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-84628-870-8

  • Online ISBN: 978-1-84628-871-5

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