Non-rigid Surface Registration using Cover Tree based Clustering and Nearest Neighbor Search

Manal H. Alassaf, Yeny Yim, James K. Hahn

2014

Abstract

We propose a novel non-rigid registration method that computes the correspondences of two deformable surfaces using the cover tree. The aim is to find the correct correspondences without landmark selection and to reduce the computational complexity. The source surface S is initially aligned to the target surface T to generate a cover tree from the densely distributed surface points. The cover tree is constructed by taking into account the positions and normal vectors of the points and used for hierarchical clustering and nearest neighbor search. The cover tree based clustering divides the two surfaces into several clusters based on the geometric features, and each cluster on the source surface is transformed to its corresponding cluster on the target. The nearest neighbor search from the cover tree reduces the search space for correspondence computation, and the source surface is deformed to the target by optimizing the point pairs. The correct correspondence of a given source point is determined by choosing one target point with the best correspondence measure from the k nearest neighbors. The proposed energy function with Jacobian penalty allows deforming the surface accurately and with less deformation folding.

References

  1. Allen, B., Curless, B., & Popovic, Z., 2003. The space of human body shapes: reconstruction and parameterization from range scans. In ACM.
  2. Amberg, B., Romdhani, S., & Vetter, T., 2007. Optimal step nonrigid icp algorithms for surface registration. In IEEE.
  3. Anguelov, D., Srinivasan, P., Pang, H. C., Koller, D., Thrun, S., & Davis, J., 2005. The correlated correspondence algorithm for unsupervised registration of nonrigid surfaces. In Advances in neural information processing systems.
  4. Arthur, D., & Vassilvitskii, S., 2007. k-means++: The advantages of careful seeding. In Society for Industrial and Applied Mathematics.
  5. Bentley, J. L., 1975. Multidimensional binary search trees used for associative searching. In Communications of the ACM.
  6. Besl, P. J., & McKay, N. D., 1992. A method for registration of 3-D shapes. In IEEE Transactions on pattern analysis and machine intelligence.
  7. Beygelzimer, A., Kakade, S., & Langford, J., 2006. Cover trees for nearest neighbor. In ACM.
  8. Bookstein, F. L. 1989. Principal warps: Thin-plate splines and the decomposition of deformations. In IEEE Transactions on Pattern Analysis and Machine Intelligence.
  9. Chang, W., & Zwicker, M., 2009. Range scan registration using reduced deformable models. In Wiley Online Library.
  10. Greenspan, M., & Godin, G., 2001. A nearest neighbor method for efficient ICP. In IEEE.
  11. Huang, Q. X., Adams, B., Wicke, M., & Guibas, L. J., 2008. Non Rigid Registration Under Isometric Deformations. In Wiley Online Library.
  12. Kumar, N., Zhang, L., & Nayar, S., 2008. What is a good nearest neighbors algorithm for finding similar patches in images? In Computer Vision-ECCV.
  13. Li, H., Sumner, R. W., & Pauly, M., 2008. Global Correspondence Optimization for Non Rigid Registration of Depth Scans. In Wiley Online Library.
  14. Liu, Y., Li, L., Xie, X., & Wei, B., 2009. Range image registration using hierarchical segmentation and clustering. In IEEE.
  15. Lloyd, S., 1982. Least squares quantization in PCM. In IEEE Transactions on Information Theory.
  16. Lorensen, W. E., Cline, H. E. 1987. Marching cubes: A high resolution 3D surface construction algorithm. In ACM.
  17. Marquardt, D. W., 1963. An algorithm for least-squares estimation of nonlinear parameters. In Journal of the society for Industrial and Applied Mathematics.
  18. Pauly, M., Mitra, N. J., Giesen, J., Gross, M., & Guibas, L. J., 2005. Example-based 3D scan completion. In Eurographics Association.
  19. Rohlfing, T., & Maurer Jr, C. R., 2001. Intensity-based non-rigid registration using adaptive multilevel freeform deformation with an incompressibility constraint. In Medical Image Computing and Computer-Assisted Intervention-MICCAI.
  20. Rueckert, D., Aljabar, P., Heckemann, R. A., Hajnal, J. V., & Hammers, A., 2006. Diffeomorphic registration using B-splines. In Medical Image Computing and Computer-Assisted Intervention-MICCAI.
  21. Sumner, R. W., Schmid, J., & Pauly, M., 2007. Embedded deformation for shape manipulation. In ACM.
  22. Vercauteren, T., Pennec, X., Perchant, A., & Ayache, N., 2009. Diffeomorphic demons: Efficient nonparametric image registration. In NeuroImage.
  23. Zhang, Z., 1992. Iterative point matching for registration of free-form curves and surfaces. In International journal of computer vision.
  24. 13.8 19.98 6.68 9.22 10.97 5.07 8.21 11.16 4.61 Table 3: Processing Time Correspondence Computation.
Download


Paper Citation


in Harvard Style

H. Alassaf M., Yim Y. and K. Hahn J. (2014). Non-rigid Surface Registration using Cover Tree based Clustering and Nearest Neighbor Search . In Proceedings of the 9th International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2014) ISBN 978-989-758-003-1, pages 579-587. DOI: 10.5220/0004738405790587


in Bibtex Style

@conference{visapp14,
author={Manal H. Alassaf and Yeny Yim and James K. Hahn},
title={Non-rigid Surface Registration using Cover Tree based Clustering and Nearest Neighbor Search},
booktitle={Proceedings of the 9th International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2014)},
year={2014},
pages={579-587},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004738405790587},
isbn={978-989-758-003-1},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 9th International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2014)
TI - Non-rigid Surface Registration using Cover Tree based Clustering and Nearest Neighbor Search
SN - 978-989-758-003-1
AU - H. Alassaf M.
AU - Yim Y.
AU - K. Hahn J.
PY - 2014
SP - 579
EP - 587
DO - 10.5220/0004738405790587