Polygonal Approximation Using a Multiresolution Method and a Context-free Grammar

  • Hermilo Sánchez-CruzEmail author
  • Osvaldo A. Tapia-Dueñas
  • Francisco Cuevas
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11524)


An new method to obtain polygonal approximation for object contours is presented. The method consists of coding the contour with the Angle Freeman chain code (AF8), obtaining strings of eight symbols, and looking for patterns of substrings that represent slope changes along the contour. Our strategy for detecting dominant points is to look for the ends of discrete straight lines through patterns of AF8 symbols, which can be produced by a context-free grammar. With a multiresolution method, we present the polygonal approximation for noisy contours. A set of N dominant points is obtained, the integral square error (ISE) is calculated and, finally, based on lost pixels (LP) in decoding process a new error criterion, that we call lost ratio (LR), is proposed. We found that our method produces the lowest ISE, LP and LR regarding the state-of-the-art.


Dominant points Polygonal approximation Angle Freeman chain code Contour shapes Context-free grammar 



H. Sánchez-Cruz was supported by CONACyT and Universidad Autónoma de Aguascalientes, under Grant PII18-8.


  1. 1.
    Arrebola, F., Sandoval, F.: Corner detection and curve segmentation by multiresolution chain-code linking. Pattern Recogn. 38(10), 1596–1614 (2005)CrossRefGoogle Scholar
  2. 2.
    Attneave, F.: Some informational aspects of visual perception. Psychol. Rev. 61(3), 183–193 (1954)CrossRefGoogle Scholar
  3. 3.
    Carmona-Poyato, A., Madrid-Cuevas, F., Medina-Carnicer, R., Munoz-Salinas, R.: Polygonal approximation of digital planar curves through break point suppression. Pattern Recogn. 43(1), 14–25 (2010)CrossRefGoogle Scholar
  4. 4.
    Cronin, T.M.: A boundary concavity code to support dominant point detection. Pattern Recogn. Lett. 20(6), 617–634 (1999)CrossRefGoogle Scholar
  5. 5.
    Freeman, H.: On the encoding of arbitrary geometric configurations. IRE Trans. Electron. Comput. 10(2), 260–268 (1961)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Liu, Y., Zalik, B.: An efficient chain code with huffman coding. Pattern Recogn. 38(4), 553–557 (2005)CrossRefGoogle Scholar
  7. 7.
    Madrid-Cuevas, F., Aguilera-Aguilera, E., Carmona-Poyato, A., Munoz-Salinas, R., Medina-Carnicer, R., Fernandez-Garcia, N.: An efficient unsupervised method for obtaining polygonal approximations of closed digital planar curves. J. Vis. Commu. Image Represent. 39, 152–163 (2016)CrossRefGoogle Scholar
  8. 8.
    Masood, A.: Dominant point detection by reverse polygonization of digital curves. Image Vis. Comput. 26(5), 702–715 (2008)CrossRefGoogle Scholar
  9. 9.
    Masood, A.: Optimized polygonal approximation by dominant point deletion. Pattern Recogn. 41(1), 227–239 (2008)CrossRefGoogle Scholar
  10. 10.
    Masood, A., Haq, S.A.: A novel approach to polygonal approximation of digital curves. J. Vis. Commun. Image Represent. 18(3), 264–274 (2007)CrossRefGoogle Scholar
  11. 11.
    Nasser, H., Ngo, P., Debled-Rennesson, I.: Dominant point detection based on discrete curve structure and applications. J. Comput. Syst. Sci. 95, 177–192 (2018)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Sarkar, D.: A simple algorithm for detection of significant vertices for polygonal approximation of chain-coded curves. Pattern Recogn. Lett. 14(12), 959–964 (1993)CrossRefGoogle Scholar
  13. 13.
    Teh, C., Chin, R.T.: On the detection of dominant points on digital curves. IEEE Transactions on Pattern Analysis and Machine Intelligence 11(8), 859–872 (1989)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Hermilo Sánchez-Cruz
    • 1
    Email author
  • Osvaldo A. Tapia-Dueñas
    • 1
  • Francisco Cuevas
    • 2
  1. 1.Centro de Ciencias BásicasUniversidad Autónoma de AguascalientesAguascalientesMexico
  2. 2.Departamento de Metrología ÓpticaCentro de Investigaciones en Óptica, A. C.LeónMexico

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