Advertisement

Non-rigid Shape Registration: A Single Linear Least Squares Framework

  • Mohammad Rouhani
  • Angel D. Sappa
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7578)

Abstract

This paper proposes a non-rigid registration formulation capturing both global and local deformations in a single framework. This formulation is based on a quadratic estimation of the registration distance together with a quadratic regularization term. Hence, the optimal transformation parameters are easily obtained by solving a liner system of equations, which guarantee a fast convergence. Experimental results with challenging 2D and 3D shapes are presented to show the validity of the proposed framework. Furthermore, comparisons with the most relevant approaches are provided.

Keywords

Regularization Term Iterative Close Point Registration Error Thin Plate Spline Control Lattice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Huang, X., Paragios, N., Metaxas, D.: Shape registration in implicit spaces using information theory and free form deformations. IEEE Trans. on Pattern Analysis and Machine Intelligence 28, 1303–1318 (2006)CrossRefGoogle Scholar
  2. 2.
    Brown, B., Rusinkiewicz, S.: Global non-rigid alignment of 3-D scans. ACM Trans. Graph. 26, 21 (2007)CrossRefGoogle Scholar
  3. 3.
    El Munim, H., Farag, A.: Shape representation and registration using vector distance functions. In: Proc. IEEE International Conference on Computer Vision and Pattern Recognition, Minneapolis, Minnesota, USA (2007)Google Scholar
  4. 4.
    Fujiwara, K., Nishino, K., Takamatsu, J., Zheng, B., Ikeuchi, K.: Locally rigid globally non-rigid surface registration. In: Proc. IEEE International Conference on Computer Vision, Barcelona, Spain, pp. 1527–1534 (2011)Google Scholar
  5. 5.
    Taron, M., Paragios, N., Jolly, M.: Registration with uncertainties and statistical modeling of shapes with variable metric kernels. IEEE Trans. on Pattern Analysis and Machine Intelligence 31, 99–113 (2009)CrossRefGoogle Scholar
  6. 6.
    Wang, F., Vemuri, B.C., Rangarajan, A., Eisenschek, S.: Simultaneous nonrigid registration of multiple point sets and atlas construction. IEEE Trans. on Pattern Analysis and Machine Intelligence 30, 2011–2022 (2008)CrossRefGoogle Scholar
  7. 7.
    Wang, J., Chan, K.: Shape evolution for rigid and nonrigid shape registration and recovery. In: Proc. IEEE International Conference on Computer Vision and Pattern Recognition, Miami, USA, pp. 164–171 (2009)Google Scholar
  8. 8.
    Li, H., Shen, T., Huang, X.: Global optimization for alignment of generalized shapes. In: Proc. IEEE International Conference on Computer Vision and Pattern Recognition, Miami, USA, pp. 856–863 (2009)Google Scholar
  9. 9.
    Schmidt, F., Farin, D., Cremers, D.: Fast matching of planar shapes in sub-cubic runtime. In: Proc. IEEE International Conference on Computer Vision, Rio de Janeiro, Brazil, pp. 1–6 (2007)Google Scholar
  10. 10.
    Chen, Y., Medioni, G.: Object modelling by registration of multiple range images. Image Vision Computing 10, 145–155 (1992)CrossRefGoogle Scholar
  11. 11.
    Chui, H., Rangarajan, A.: A new point matching algorithm for non-rigid registration. Computer Vision and Image Understanding 89, 114–141 (2003)zbMATHCrossRefGoogle Scholar
  12. 12.
    Sorkine, O.: Differential representations for mesh processing. Comput. Graph. Forum 25, 789–807 (2006)CrossRefGoogle Scholar
  13. 13.
    Besl, P., McKay, N.: A method for registration of 3-d shapes. IEEE Trans. on Pattern Analysis and Machine Intelligence 14, 239–256 (1992)CrossRefGoogle Scholar
  14. 14.
    Jian, B., Vemuri, B.: A robust algorithm for point set registration using mixture of Gaussians. In: Proc. IEEE International Conference on Computer Vision, Beijing, China, pp. 1246–1251 (2005)Google Scholar
  15. 15.
    Rusinkiewicz, S., Levoy, M.: Efficient variants of the ICP algorithm. In: Proc. IEEE International Conference on on 3-D Digital Imaging and Modeling, Quebec, Canada (2001)Google Scholar
  16. 16.
    Pottmann, H., Leopoldseder, S., Hofer, M.: Registration without ICP. Computer Vision and Image Understanding 95, 54–71 (2004)CrossRefGoogle Scholar
  17. 17.
    Fitzgibbon, A.: Robust registration of 2d and 3d point sets. Image and Vision Computing 21, 1145–1153 (2001)CrossRefGoogle Scholar
  18. 18.
    Aigner, M., Juttler, B.: Gauss-Newton-type technique for robustly fitting implicit defined curves and surfaces to unorganized data points. In: Proc. IEEE International Conference on Shape Modeling and Applications, New York, USA, pp. 121–130 (2008)Google Scholar
  19. 19.
    http://shapes.aimatshape.net/ (AIM@SHAPE, Digital Shape WorkBench)
  20. 20.
    Sharvit, D., Chan, J., Tek, H., Kimia, B.: Symmetry-based indexing of image databases. Journal of Visual Communication and Image Representation 9, 366–380 (1998)CrossRefGoogle Scholar
  21. 21.
    http://graphics.stanford.edu/data/3Dscanrep/ (The Stanford 3D Scanning Repository)

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Mohammad Rouhani
    • 1
  • Angel D. Sappa
    • 1
  1. 1.Computer Vision CenterEdifici O, Campus UABBellaterra, BarcelonaSpain

Personalised recommendations