GridDS: a hybrid data structure for residue computation in point set matching

Abstract

Registration of 3D point clouds is a problem that arises in a variety of research areas such as computer vision, computer graphics and computational geometry. This situation causes most papers in the area to focus on solving practical problems by using data structures often developed in theoretical contexts. Consequently, discrepancies arise between asymptotic cost and experimental performance. The point cloud registration or matching problem encompasses many different steps. Among them, the computation of the distance between two point sets (often refereed to as residue computation) is crucial and can be seen as an aggregate of range searching or nearest neighbor searching. In this paper, we aim at providing theoretical analysis and experimental performance of range searching and nearest neighbor data structures applied to 3D point cloud registration. Performance of widely used data structures such as compressed octrees, KDtrees, BDtrees and regular grids is reported. Additionally, we present a new hybrid data structure named GridDS, which combines a regular grid with some preexisting “inner” data structure in order to meet the best asymptotic bounds while also obtaining the best performance. The experimental evaluation in both synthetic and real data demonstrates that the hybrid data structures built using GridDS improve the running times of the single data structures. Thus, as we have studied the performances of the state-of-the-art techniques managing to improve their respective running times thanks to GridDS, this paper presents the best running time for point cloud residue computation up to date.

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Notes

  1. 1.

    Holding \(d(a_i,b_j)=d(\mu (a_i),\mu (b_j) ) \forall a_i,b_j \in {\mathbb {R}}^3\), d() being the Euclidean distance.

  2. 2.

    http://geometry.cs.ucl.ac.uk/projects/2014/super4pcs/.

  3. 3.

    http://gfx.cs.princeton.edu/proj/trimesh2/.

  4. 4.

    https://www.cs.umd.edu/mount/ann/.

  5. 5.

    http://www.pointclouds.org.

  6. 6.

    https://gitlab.com/froure/pointcloudgenerator.

  7. 7.

    http://graphics.stanford.edu/data/3dscanrep.

  8. 8.

    http://www.vision.deis.unibo.it/research/80-shot.

  9. 9.

    https://github.com/ferranroure/gridds.

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Roure, F., Lladó, X., Salvi, J. et al. GridDS: a hybrid data structure for residue computation in point set matching. Machine Vision and Applications 30, 291–307 (2019). https://doi.org/10.1007/s00138-018-0985-0

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Keywords

  • Data structures
  • Residue computation
  • Point clouds
  • 3D registration