Abstract
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.
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References
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)
Cootes, T.F., Taylor, C.J.: Data driven refinement of active shape model search. In: BMVC, British Machine Vision Association (1996)
Loog, M.: Localized maximum entropy shape modelling. In: Karssemeijer, N., Lelieveldt, B. (eds.) IPMI 2007. LNCS, vol. 4584, pp. 619–629. Springer, Heidelberg (2007)
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)
Shang, Y., Dossel, O.: Statistical 3D shape-model guided segmentation of cardiac images. Computers in Cardiology 31, 553 (2004)
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)
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)
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)
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)
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)
Davatzikos, C., Tao, X., Shen, D.: Hierarchical active shape models, using the wavelet transform. IEEE Trans. Med. Imaging 22(3), 414–423 (2003)
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)
Knothe, R.: A Global-to-local model for the representation of human faces. PhD thesis, Computer Science Department, University of Basel (2009)
Hastie, T., Tibshirani, R., Friedman, J.: Kernel Smoothing Methods. In: The Elements of Statistical Learning. Springer Series in Statistics. Springer, New York (2001)
Heimann, T., Meinzer, H.: Statistical shape models for 3D medical image segmentation: A review. In: Medical Image Analysis (2009)
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)
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)
Tipping, M.E., Bishop, C.M.: Probabilistic principal component analysis. Journal of the Royal Statistical Society 61, 611–622 (1999)
Dryden, I., Mardia, K.: Statistical shape analysis. Wiley, New York (1998)
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)
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)
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Amberg, M., Lüthi, M., Vetter, T. (2010). Local Regression Based Statistical Model Fitting. In: Goesele, M., Roth, S., Kuijper, A., Schiele, B., Schindler, K. (eds) Pattern Recognition. DAGM 2010. Lecture Notes in Computer Science, vol 6376. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15986-2_46
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DOI: https://doi.org/10.1007/978-3-642-15986-2_46
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