A Novel Algorithm for Triangulating 2d Point Clouds Using Multi-Dimensional Data Structures and Nearest Neighbour Approach

  • Sundeep Joshi
  • Shriram K. VasudevanEmail author
Conference paper
Part of the Lecture Notes in Computational Vision and Biomechanics book series (LNCVB, volume 28)


Generating a mesh from a point cloud has always been a complex and tedious task. It requires many guidelines to be followed and geometry specific boundary condition to be taken care of. Mostly we end up writing a new algorithm for each scenario. The existing algorithms like Delaunay triangulation end up taking a lot of time without taking care of the internal holes properly. Also the convergence is not guaranteed. In this paper, we present a recursion free algorithm for triangulating a structured surface with n-vertices with or without holes using Ball trees. The algorithm takes the input in the form of an image, creates a mask for the object to be triangulated and then creates a mesh for it with respect to computed vertices.


Image segmentation Point cloud Triangulation Ball trees 


  1. 1.
    Delaunay, B.: Sur la sphere vide. A lamemoirede Georges Voronoi, Bulletin de Academie des Sciences de l’URSS. Classe des sciences math ́ematiques et na 6, 793–800 (1934)Google Scholar
  2. 2.
    Bowyer, A.: Computing Dirichlet tessellations. Comput. J. 24(2), 162–166 (1981)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Woerdenweber, B.: Finite element mesh generation. Comput. Aided Des. 16(5), 285–291 (1984)Google Scholar
  4. 4.
    Ho-Le, K.: Finite element mesh generation methods. Rev. Classif. 20(1), 27–38 (1988)Google Scholar
  5. 5.
    Baumgart, B.G.: Geometric modeling for computer vision. Report No. C5-463 Stanford Artificial Intelligence Laboratory, Computer Science Dept, Stanford, USA (October 1974)Google Scholar
  6. 6.
    Cavendish, J.C.: Automatic triangulation of arbitrary planar domains for the finite element method. Int. J. Numer. Meth. Eng. 8, pp. 679–696 (1974)Google Scholar
  7. 7.
    Rother, C., Kolmogorov, V., Blake, A.: “GrabCut”: interactive foreground extraction using iterated graph cuts, SIGGRAPH ‘04 ACM SIGGRAPH, pp. 309–314 (2004)Google Scholar
  8. 8.
    Simonyan, K., Zisserman, A.: Very deep convolutional networks for large-scale image recognition. Computer Vision and Pattern Recognition, arXiv:1409.1556
  9. 9.
    Chen, L.C., Papandreou, G., Kokkinos, I., Murphy, K., Yuille, A.L.: Semantic image segmentation with deep convolutional nets and fully connected CRFs. Computer Vision and Pattern Recognition. arXiv:1412.7062
  10. 10.
    Sundaram, V.M., Vasudevan, S.K., Santhosh, C., Barath Kumar, R.G.K., Kumar, G.D.: An augmented reality application with leap and android. Indian J. Sci. Technol. 8(7), 678–682 (2015)Google Scholar
  11. 11.
    Vasudevan, S.K., Ritesh, A., Santhosh, C.: An innovative app with for location finding with augmented reality using CLOUD. Proc. Comp. Sci. 50, 585–589 (2015)Google Scholar
  12. 12.
    Geethan, P., Jithin, P., Naveen, T., Padminy, K.V., Krithika, J.S., Vasudevan, S.K.: Augmented reality x-ray vision with gesture interaction. Indian J. Sci. Technol. 8(S7), 43–47 (2015)Google Scholar

Copyright information

© Springer International Publishing AG  2018

Authors and Affiliations

  1. 1.Department of Computer Science and Engineering, Amrita School of EngineeringAmrita Vishwa Vidyapeetham, Amrita UniversityCoimbatoreIndia

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