Coding 3D Connected Regions with F26 Chain Code

  • Osvaldo A. Tapia-Dueñas
  • Hermilo Sánchez-CruzEmail author
  • Hiram H. López
  • Humberto Sossa
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11289)


There are many applications in different fields, as diverse as computer graphics, medical imaging or pattern recognition for industries, where the use of three dimensional objects is needed. By the nature of these objects, it is very important to develop thrifty methods to represent, study and store them. In this paper, a new method to encode surfaces of three-dimensional objects that are not isomorphic to the plane is developed. In the proposed method, a helical path that covers the contour is obtained and then, the Freeman F26 chain code is used to encode the helical path. In order to solve geometric problems to find optimal paths between adjacent slices, a modification of the A star algorithm was carried out. Finally, our proposed method is applied to three-dimensional objects obtained from real data.


Voxel-based objects Chain code Three-dimensional objects Helical path 



Osvaldo A. Tapia-Dueñas was partially supported by CONACyT. H. Sánchez-Cruz thanks Universidad Autónoma de Aguascalientes, under Grant PII18-8 for the support. Hiram H. López was partially supported by CONACyT, CVU no. 268999, project “Network Codes”, and by Universidad Autónoma de Aguascalientes. H. Sossa thanks the Instituto Politécnico Nacional and CONACyT for the economical support under funds: SIP 20180730 and 65 (Fronteras de la Ciencia), respectively to undertake this research.


  1. 1.
    Cornea, N.D., Silver, D., Min, P.: Curve-skeleton properties, applications, and algorithms. IEEE Trans. Vis. Comput. Graph. 13(3), 530–548 (2007)CrossRefGoogle Scholar
  2. 2.
    Punam, K., Borgefors, S., Borgefors, G., di Baja, G.S.: A survey on skeletonization algorithms and their applications. Pattern Recogn. Lett. 76, 3–12 (2016). Special Issue on Skeletonization and its ApplicationCrossRefGoogle Scholar
  3. 3.
    Jin, D., Iyer, K.S., Chen, C., Hoffman, E.A., Saha, P.K.: A robust and efficient curve skeletonization algorithm for tree-like objects using minimum cost paths. Pattern Recogn. Lett. 76(C), 32–40 (2016)CrossRefGoogle Scholar
  4. 4.
    Svensson, S., Nystróm, I., di Baja, G.S.: Curve skeletonization of surface-like objects in 3D images guided by voxel classification. Pattern Recogn. Lett. 23(12), 1419–1426 (2002)CrossRefGoogle Scholar
  5. 5.
    Arcelli, C., di Baja, G.S., Serino, L.: Distance-driven skeletonization in voxel images. IEEE Trans. Pattern Anal. Mach. Intell. 33(4), 709–720 (2011)CrossRefGoogle Scholar
  6. 6.
    Sánchez-Cruz, H., Rodríguez-Dagnino, R.M.: Compressing bilevel images by means of a three-bit chain code. Opt. Eng. 44, 44–44–8 (2005)Google Scholar
  7. 7.
    Yong, K.L., Alik, B.: An efficient chain code with Huffman coding. Pattern Recogn. 38(4), 553–557 (2005)CrossRefGoogle Scholar
  8. 8.
    Echávarri, L., Aguinaga, R., Neri-Calderón, A., Rodriguez-Dagnino, R.M.: Compression rates comparison of entropy coding for three-bit chain codes of bilevel images. Opt. Eng. 46, 46–46–7 (2007)Google Scholar
  9. 9.
    Yong, K.L., Wei, W., Peng, J.W., Alik, B.: Compressed vertex chain codes. Pattern Recogn. 40(11), 2908–2913 (2007)CrossRefGoogle Scholar
  10. 10.
    Freeman, H.: Computer processing of line-drawing images. ACM Comput. Surv. 6(1), 57–97 (1974)CrossRefGoogle Scholar
  11. 11.
    Bribiesca, E.: A chain code for representing 3D curves. Pattern Recogn. 33(5), 755–765 (2000)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Sánchez-Cruz, H., López-Valdez, H., Cuevas, F.J.: A new relative chain code in 3D. Pattern Recogn. 47(2), 769–788 (2014)CrossRefGoogle Scholar
  13. 13.
    Salazar, J.M., Bribiesca, E.: Compression of three-dimensional surfaces by means of chain coding. Opt. Eng. 54, 54–54–12 (2015)CrossRefGoogle Scholar
  14. 14.
    Cui, S.G., Wang, H., Yang, L.: A simulation study of A-star algorithm for robot path planning, pp. 506–509, January 2012Google Scholar
  15. 15.
    Duchó, F., et al.: Path planning with modified a star algorithm for a mobile robot. Proc. Eng. 96, 59–69 (2014). Modelling of Mechanical and Mechatronic SystemsCrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Osvaldo A. Tapia-Dueñas
    • 1
  • Hermilo Sánchez-Cruz
    • 1
    Email author
  • Hiram H. López
    • 2
  • Humberto Sossa
    • 3
    • 4
  1. 1.Universidad Autónoma de Aguascalientes, Centro de Ciencias BásicasAguascalientesMexico
  2. 2.Department of Mathematical SciencesClemson UniversityClemsonUSA
  3. 3.Instituto Politécnico Nacional-CICMexico CityMexico
  4. 4.Tecnológico de Monterrey, Campus GuadalajaraZapopanMexico

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