Local Regression Based Statistical Model Fitting

  • Matthias Amberg
  • Marcel Lüthi
  • Thomas Vetter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6376)


Fitting statistical models is a widely employed technique for the segmentation of medical images. While this approach gives impressive results for simple structures, shape models are often not flexible enough to accurately represent complex shapes. We present a fitting approach, which increases the model fitting accuracy without requiring a larger training data-set. Inspired by a local regression approach known from statistics, our method fits the full model to a neighborhood around each point of the domain. This increases the model’s flexibility considerably without the need to introduce an artificial segmentation of the structure. By adapting the size of the neighborhood from small to large, we can smoothly interpolate between localized fits, which accurately map the data but are more prone to noise, and global fits, which are less flexible but constrained to valid shapes only. We applied our method for the segmentation of teeth from 3D cone-beam ct-scans. Our experiments confirm that our method consistently increases the precision of the segmentation result compared to a standard global fitting approach.


Segmentation Result Shape Model Target Shape Active Shape Model Hand Shape 
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.


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  1. 1.
    Cootes, T.F., Taylor, C.J.: Combining point distribution models with shape models based on finite element analysis. Image Vision Comput. 13(5), 403–409 (1995)CrossRefGoogle Scholar
  2. 2.
    Cootes, T.F., Taylor, C.J.: Data driven refinement of active shape model search. In: BMVC, British Machine Vision Association (1996)Google Scholar
  3. 3.
    Loog, M.: Localized maximum entropy shape modelling. In: Karssemeijer, N., Lelieveldt, B. (eds.) IPMI 2007. LNCS, vol. 4584, pp. 619–629. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  4. 4.
    Pekar, V., Kaus, M., Lorenz, C., Lobregt, S., Truyen, R., Weese, J.: Shape-model-based adaptation of 3D deformable meshes for segmentation of medical images. In: Proceedings of SPIE, vol. 4322, p. 281 (2001)Google Scholar
  5. 5.
    Shang, Y., Dossel, O.: Statistical 3D shape-model guided segmentation of cardiac images. Computers in Cardiology 31, 553 (2004)CrossRefGoogle Scholar
  6. 6.
    Weese, J., Kaus, M., Lorenz, C., Lobregt, S., Truyen, R., Pekar, V.: Shape constrained deformable models for 3D medical image segmentation. LNCS, pp. 380–387. Springer, Heidelberg (2001)Google Scholar
  7. 7.
    Shen, D., Herskovits, E.H., Davatzikos, C.: An adaptive-focus statistical shape model for segmentation and shape modeling of 3-d brain structures. IEEE Trans. Med. Imaging 20(4), 257–270 (2001)CrossRefGoogle Scholar
  8. 8.
    de Bruijne, M., van Ginneken, B., Viergever, M.A., Niessen, W.J.: Adapting active shape models for 3d segmentation of tubular structures in medical images. Inf. Process. Med. Imaging 18 (July 2003)Google Scholar
  9. 9.
    Zhao, Z., Aylward, S., Teoh, E.: A novel 3D partitioned active shape model for segmentation of brain MR images. In: Duncan, J.S., Gerig, G. (eds.) MICCAI 2005. LNCS, vol. 3749, pp. 221–228. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  10. 10.
    Blanz, V., Vetter, T.: A morphable model for the synthesis of 3d faces. In: SIGGRAPH 1999: Proceedings of the 26th annual conference on Computer graphics and interactive techniques, pp. 187–194. ACM Press, New York (1999)CrossRefGoogle Scholar
  11. 11.
    Davatzikos, C., Tao, X., Shen, D.: Hierarchical active shape models, using the wavelet transform. IEEE Trans. Med. Imaging 22(3), 414–423 (2003)CrossRefGoogle Scholar
  12. 12.
    Nain, D., Haker, S., Bobick, A., Tannenbaum, A.: Multiscale 3-d shape representation and segmentation using spherical wavelets. IEEE Trans. Med. Imaging 26(4), 598–618 (2007)CrossRefGoogle Scholar
  13. 13.
    Knothe, R.: A Global-to-local model for the representation of human faces. PhD thesis, Computer Science Department, University of Basel (2009)Google Scholar
  14. 14.
    Hastie, T., Tibshirani, R., Friedman, J.: Kernel Smoothing Methods. In: The Elements of Statistical Learning. Springer Series in Statistics. Springer, New York (2001)Google Scholar
  15. 15.
    Heimann, T., Meinzer, H.: Statistical shape models for 3D medical image segmentation: A review. In: Medical Image Analysis (2009)Google Scholar
  16. 16.
    Cootes, T., Taylor, C., Cooper, D., Graham, J., et al.: Active shape models-their training and application. Computer Vision and Image Understanding 61(1), 38–59 (1995)CrossRefGoogle Scholar
  17. 17.
    Rueckert, D., Frangi, A.F., Schnabel, J.A.: Automatic construction of 3d statistical deformation models using non-rigid registration. In: Niessen, W.J., Viergever, M.A. (eds.) MICCAI 2001. LNCS, vol. 2208, pp. 77–84. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  18. 18.
    Tipping, M.E., Bishop, C.M.: Probabilistic principal component analysis. Journal of the Royal Statistical Society 61, 611–622 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Dryden, I., Mardia, K.: Statistical shape analysis. Wiley, New York (1998)zbMATHGoogle Scholar
  20. 20.
    Cleveland, W.S., Devlin, S.J.: Locally-Weighted regression: An approach to regression analysis by local fitting. Journal of the American Statistical Association 83(403), 596–610 (1988)CrossRefGoogle Scholar
  21. 21.
    Zhu, C., Byrd, R., Lu, P., Nocedal, J.: Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization. ACM Transactions on Mathematical Software (TOMS) 23(4), 550–560 (1997)zbMATHCrossRefMathSciNetGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Matthias Amberg
    • 1
  • Marcel Lüthi
    • 1
  • Thomas Vetter
    • 1
  1. 1.Computer Science DepartmentUniversity of BaselSwitzerland

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