A Hierarchical Voxel Hash for Fast 3D Nearest Neighbor Lookup

  • Bertram Drost
  • Slobodan Ilic
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8142)


We propose a data structure for finding the exact nearest neighbors in 3D in approximately O(log(log(N)) time. In contrast to standard approaches such as k-d-trees, the query time is independent of the location of the query point and the distribution of the data set. The method uses a hierarchical voxel approximation of the data point’s Voronoi cells. This avoids backtracking during the query phase, which is a typical action for tree-based methods such as k-d-trees. In addition, voxels are stored in a hash table and a bisection on the voxel level is used to find the leaf voxel containing the query point. This is asymptotically faster than letting the query point fall down the tree. The experiments show the method’s high performance compared to state-of-the-art approaches even for large point sets, independent of data and query set distributions, and illustrates its advantage in real-world applications.


Leaf Node Voronoi Diagram Hash Table Synthetic Dataset Query Point 
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  1. 1.
    Arya, S., Mount, D.M., Netanyahu, N.S., Silverman, R., Wu, A.Y.: An optimal algorithm for approximate nearest neighbor searching fixed dimensions. JACM 45(6), 891–923 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Bentley, J.L.: Multidimensional binary search trees used for associative searching. Communications of the ACM 18(9), 509–517 (1975)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Birn, M., Holtgrewe, M., Sanders, P., Singler, J.: Simple and fast nearest neighbor search. In: 11th Workshop on Algorithm Engineering and Experiments (2010)Google Scholar
  4. 4.
    Boada, I., Coll, N., Madern, N., Sellares, J.A.: Approximations of 3D generalized voronoi diagrams. In: 21st Europ. Workshop on Comp. Geometry (2005)Google Scholar
  5. 5.
    Boada, I., Coll, N., Madern, N., Sellares, J.A.: Approximations of 2D and 3D generalized voronoi diagrams. Int. Journal of Computer Mathematics 85(7) (2008)Google Scholar
  6. 6.
    Choi, W.S., Oh, S.Y.: Fast nearest neighbor search using approximate cached kd tree. In: IROS (2012)Google Scholar
  7. 7.
    Drost, B., Ulrich, M., Navab, N., Ilic, S.: Model globally, match locally: Efficient and robust 3D object recognition. In: CVPR (2010)Google Scholar
  8. 8.
    Elseberg, J., Magnenat, S., Siegwart, R., Nuechter, A.: Comparison of nearest-neighbor-search strategies and implementations for efficient shape registration. Journal of Software Engineering for Robotics 3(1), 2–12 (2012)Google Scholar
  9. 9.
    Glassner, A.S.: Space subdivision for fast ray tracing. IEEE Computer Graphics and Applications 4(10), 15–24 (1984)CrossRefGoogle Scholar
  10. 10.
    Greenspan, M., Godin, G.: A nearest neighbor method for efficient ICP. In: 3-D Digital Imaging and Modeling. IEEE (2001)Google Scholar
  11. 11.
    Greenspan, M., Yurick, M.: Approximate kd tree search for efficient ICP. In: 3DIM 2003. IEEE (2003)Google Scholar
  12. 12.
    Har-Peled, S.: A replacement for voronoi diagrams of near linear size. In: Proc. on Foundations of Computer Science, pp. 94–103 (2001)Google Scholar
  13. 13.
    Hwang, Y., Han, B., Ahn, H.K.: A fast nearest neighbor search algorithm by nonlinear embedding. In: CVPR (2012)Google Scholar
  14. 14.
    Meagher, D.: Geometric modeling using octree encoding. Computer Graphics and Image Processing 19(2), 129–147 (1982)CrossRefGoogle Scholar
  15. 15.
    Mount, D.M., Arya, S.: ANN: A library for approximate nearest neighbor searching,
  16. 16.
    Nuchter, A., Lingemann, K., Hertzberg, J.: Cached kd tree search for ICP algorithms. In: 3DIM 2007. IEEE (2007)Google Scholar
  17. 17.
    Samet, H.: Foundations of Multidimensional And Metric Data Structures. Morgan Kaufmann (2006)Google Scholar
  18. 18.
    Yan, P., Bowyer, K.W.: A fast algorithm for ICP-based 3D shape biometrics. Computer Vision and Image Understanding 107(3) (2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Bertram Drost
    • 1
  • Slobodan Ilic
    • 2
  1. 1.MVTec Software GmbHGermany
  2. 2.Technische Universität MünchenGermany

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