Pattern Analysis and Applications

, Volume 17, Issue 3, pp 481–496 | Cite as

Geometric algorithm for dominant point extraction from shape contour

  • Maedeh S. Tahaei
  • Seyed Naser Hashemi
  • Ali Mohades
  • Amin Gheibi
Theoretical Advances


In this paper we propose a new algorithm for extracting dominant points from the real contour of a digital shape. A polygonal approximation of the shape can be obtained by the set of dominant points. In the proposed algorithm, in the first step before searching for dominant points, the real contour is made sparse using a geometric concept, named convex deficiency tree. This helps to select a set of candidate points from real contour. In comparison with break points (which are initial points in many algorithms), the set of candidate points is more heuristic and the ratio of them to the all points of the contour is lower. In the second step of the proposed algorithm, the less informative candidate points are removed in an iterative manner. After removing one candidate point, its adjacent positions are searched to find more stable position for its neighbors. The comparative result of the proposed algorithm with others shows its efficiency. The algorithm finds an effective polygonal approximation for digital shapes especially for the real contours, which makes the method more practical.


Dominant point Polygonal approximation Digital planner curve Shape representation Convex deficiency tree 



We want to thank A. A. Carmona-Poyato for kindly providing us the results of his method via mail to be compared with our proposed method.


  1. 1.
    Ruberto DC, Morgera A (2009) A new iterative approach for dominant points extraction in planar curves Source. WSEAS Trans Comput 8(3):482–493Google Scholar
  2. 2.
    Wu WY (2003) An adaptive method for detecting dominant points. Pattern Recognit 36:2231–2237CrossRefzbMATHGoogle Scholar
  3. 3.
    Attneave F (1954) Some informational aspects of visual perception. Psychol Rev 61:189–193CrossRefGoogle Scholar
  4. 4.
    Masood A, Haq SA (2007) A novel approach to polygonal approximation of digital curves. J Vis Commun Image Represent 18:264–274CrossRefGoogle Scholar
  5. 5.
    Hsin-Teng S, Wu-Chih H (1996) A rotationally invariant two-phase scheme for corner detection. Pattern Recognit 29:819–828CrossRefGoogle Scholar
  6. 6.
    Melkman A, O’Rourke J (1998) On polygonal chain approximation. In: Toussaint GT (ed) Computational morphology. North-Holland, Amsterdam, pp 87–95Google Scholar
  7. 7.
    Perez JC, Vidal E (1994) Optimum polygonal approximation of digitized curves. Pattern Recognit Lett 15:743–750CrossRefzbMATHGoogle Scholar
  8. 8.
    Pikaz A, Dinstein I (1995) Optimal polygonal approximation of digital curves. Pattern Recognit 28:373–379CrossRefGoogle Scholar
  9. 9.
    Salotti M (2001) An efficient algorithm for the optimal polygonal approximation of digitized curves. Pattern Recognit Lett 22:215–221CrossRefzbMATHGoogle Scholar
  10. 10.
    Teh CH, Chin RT (1989) On the detection of dominant points on digital curves. IEEE Trans Pattern Anal Mach Intell 11:859–872CrossRefGoogle Scholar
  11. 11.
    Ansari N, Huang KW (1991) Non-parametric dominant points detection. Pattern Recognit 24:849–862CrossRefGoogle Scholar
  12. 12.
    Ray BK, Ray KS (1992) Detection of significant points and polygonal approximation of digitized curves. Pattern Recognit Lett 22:443–452CrossRefGoogle Scholar
  13. 13.
    Ray BK, Ray KS (1992) An algorithm for detecting dominant points and polygonal approximation of digitized curves. Pattern Recognit Lett 13:849–856CrossRefGoogle Scholar
  14. 14.
    Zhu P, Chirlian PM (1995) On critical point detection of digital shapes. IEEE Trans Pattern Anal Mach Intell 17(8):737–748CrossRefGoogle Scholar
  15. 15.
    Marji M, Siy P (2003) A new algorithm for dominant point detection and polygonization of digital curves. Pattern Recognit 36:2239–2251CrossRefzbMATHGoogle Scholar
  16. 16.
    Wu WY (2003) Dominant point detection using adaptive bending value. Image Vis Comput 21:517–525CrossRefGoogle Scholar
  17. 17.
    Marji M, Siy P (2004) Polygonal representation of digital planar curves through dominant point detection—a nonparametric algorithm. Pattern Recognit 37:2113–2130CrossRefGoogle Scholar
  18. 18.
    Carmona-Poyato A, Fernandez-Garcia NL, Medina-Carnicer R, Madrid-Cuevas FJ (2005) Dominant point detection: a new proposal. Image Vis Comput 23:1226–1236CrossRefGoogle Scholar
  19. 19.
    Masood A (2008) Dominant point deletion by reverse polygonization of digital curves. Image Vis Comput 26:702–715CrossRefGoogle Scholar
  20. 20.
    Masood A (2008) Optimized polygonal approximation by dominant point deletion. Pattern Recognit 41:227–239CrossRefzbMATHGoogle Scholar
  21. 21.
    Garrido A, Perez N, Garcia-Silvente M (1998) Boundary simplification using a multiscale dominant-point detection algorithm. Pattern Recognit 31:791–804CrossRefGoogle Scholar
  22. 22.
    Ray BK, Pandyan R (2003) ACORD—an adaptive corner detector for planar curves. Pattern Recognit 36:703–708CrossRefzbMATHGoogle Scholar
  23. 23.
    Canny J (1986) A computational approach to edge detection. IEEE Trans Pattern Anal Mach Intell PAMI-8(6):679–698Google Scholar
  24. 24.
    Freeman H (1961) On the encoding of arbitrary geometric configurations. IEEE Trans Electron Comput 10:260–268CrossRefMathSciNetGoogle Scholar
  25. 25.
    Wu L (1982) On the chain code of a line. IEEE Trans Pattern Anal Mach Intell 4:347–353CrossRefzbMATHGoogle Scholar
  26. 26.
    Sarkar D (1993) A simple algorithm for detection of significant vertices for polygonal approximation of chain-coded curves. Pattern Recognit Lett 14:959–964CrossRefGoogle Scholar
  27. 27.
    Rosin PL (1997) Techniques for assessing polygonal approximation of curves. IEEE Trans Pattern Anal Mach Intell 19(6):659–666CrossRefGoogle Scholar
  28. 28.
    Batchelor BG (1980) Hierarchical shape description based upon convex hulls of concavities. J Cybern 10:205–210CrossRefGoogle Scholar
  29. 29.
    Carmona-Poyato A, Madrid-Cuevas FJ, Medina Carnicer R, Munoz-Salinas R (2010) Polygonal approximation of digital planar curves through break point suppression. Pattern Recognit 43(1):14–25CrossRefzbMATHMathSciNetGoogle Scholar
  30. 30.
    Carmona-Poyato A, Medina-Carnicer R, Muñoz-Salinas R, Yeguas-Bolivar E (2012) On stop conditions about methods to obtain polygonal approximations relied on breakpoint suppression. Image Vis Comput 30(8):513–523CrossRefGoogle Scholar
  31. 31.
    Hao S, Jiang J, Guo Y, Zhan S (2012) ϵ-Isometry based shape approximation for image content representation. Signal Process (in press)Google Scholar
  32. 32.
    Latecki LJ, Lakamper R (1999) Convexity rule for shape decomposition based on discrete contour evolution. Comput Vis Image Underst 73:441–454CrossRefGoogle Scholar
  33. 33.
    Cronin TM (1999) A boundary concavity code to support dominant points detection. Pattern Recognit Lett 20:617–634CrossRefGoogle Scholar
  34. 34.
    Dobkin D, Guibas L, Hershberger J, Snoeyink J (1988) An efficient algorithm for finding the CSG representation of a simple polygon. Comput Graph 22(4):31–40CrossRefGoogle Scholar
  35. 35.
    Shapiro V (2001) A convex deficiency tree algorithm for curved polygons. Int J Comput Geom Appl 11(2):215–238CrossRefzbMATHGoogle Scholar
  36. 36.
    Parvez MT, Mahmoud SA (2010) Polygonal approximation of digital planar curves through adaptive optimizations. Pattern Recognit Lett 31:1997–2005CrossRefGoogle Scholar
  37. 37.
    Nguyen TP, Rennesson ID (2011) A discrete geometry approach for dominant point detection. Pattern Recognit 44:32–44CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag London 2012

Authors and Affiliations

  • Maedeh S. Tahaei
    • 1
  • Seyed Naser Hashemi
    • 1
  • Ali Mohades
    • 1
  • Amin Gheibi
    • 2
  1. 1.Department of Mathematics and Computer ScienceAmirkabir University of TechnologyTehranIran
  2. 2.Department of Computer ScienceCarleton UniversityOttawaCanada

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