Abstract
Active Shape Models are a popular method for segmenting three-dimensional medical images. To obtain the required landmark correspondences, various automatic approaches have been proposed. In this work, we present an improved version of minimizing the description length (MDL) of the model. To initialize the algorithm, we describe a method to distribute landmarks on the training shapes using a conformal parameterization function. Next, we introduce a novel procedure to modify landmark positions locally without disturbing established correspondences. We employ a gradient descent optimization to minimize the MDL cost function, speeding up automatic model building by several orders of magnitude when compared to the original MDL approach. The necessary gradient information is estimated from a singular value decomposition, a more accurate technique to calculate the PCA than the commonly used eigendecomposition of the covariance matrix. Finally, we present results for several synthetic and real-world datasets demonstrating that our procedure generates models of significantly better quality in a fraction of the time needed by previous approaches.
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References
Cootes, T.F., Taylor, C.J., Cooper, D.H., Graham, J.: Active shape models – their training and application. Computer Vision and Image Understanding 61, 38–59 (1995)
Brett, A.D., Taylor, C.J.: A method of automated landmark generation for automated 3D PDM construction. Image and Vision Computing 18, 739–748 (2000)
Shelton, C.R.: Morphable surface models. Int. Journal of Computer Vision 38, 75–91 (2000)
Paulsen, R.R., Hilger, K.B.: Shape modelling using markov random field restoration of point correspondences. In: Proc. IPMI, pp. 1–12 (2003)
Zhao, Z., Teoh, E.K.: A novel framework for automated 3D PDM construction using deformable models. In: Proc. SPIE Medical Imaging, vol. 5747 (2005)
Davies, R.H., Twining, C.J., Cootes, T.F., Waterton, J.C., Taylor, C.J.: 3D statistical shape models using direct optimisation of description length. In: Proc. European Conference on Computer Vision, Part III, pp. 3–20. Springer, Heidelberg (2002)
Styner, M., Rajamani, K.T., Nolte, L.-P., Zsemlye, G., Székely, G., Taylor, C.J., Davies, R.H.: Evaluation of 3D correspondence methods for model building. In: Proc. IPMI, pp. 63–75 (2003)
Kalman, D.: A singularly valuable decomposition: The SVD of a matrix. College Math Journal 27, 2–23 (1996)
Davies, R.H., Twining, C.J., Cootes, T.F., Waterton, J.C., Taylor, C.J.: A minimum description length approach to statistical shape modelling. IEEE trans. Medical Imaging 21, 525–537 (2002)
Thodberg, H.H.: Minimum description length shape and appearance models. In: Proc. IPMI, pp. 51–62 (2003)
Floater, M.S., Hormann, K.: Surface parameterization: a tutorial and survey. In: Dodgson, N.A., Floater, M.S., Sabin, M.A. (eds.) Advances in Multiresolution for Geometric Modelling. Mathematics and Visualization, pp. 157–186. Springer, Heidelberg (2005)
Brechbühler, C., Gerig, G., Kübler, O.: Parametrization of closed surfaces for 3-D shape description. Computer Vision and Image Understanding 61, 154–170 (1995)
Gu, X., Wang, Y., Chan, T.F., Thompson, P.M., Yau, S.-T.: Genus zero surface conformal mapping and its application to brain surface mapping. In: Proc. IPMI, pp. 172–184 (2003)
Gotsman, C., Gu, X., Sheffer, A.: Fundamentals of spherical parameterization for 3D meshes. ACM Trans. Graph. 22, 358–363 (2003)
Möller, T., Trumbore, B.: Fast, minimum storage ray-triangle intersection. Journal of Graphics Tools 2, 21–28 (1997)
Arvo, J.: Fast random rotation matrices. In: Kirk, D. (ed.) Graphics Gems III, pp. 117–120. Academic Press, London (1992)
Ericsson, A., Åström, K.: Minimizing the description length using steepest descent. In: Proc. British Machine Vision Conference, pp. 93–102 (2003)
Papadopoulo, T., Lourakis, M.I.A.: Estimating the Jacobian of the Singular Value Decomposition: Theory and Applications. In: Vernon, D. (ed.) ECCV 2000. LNCS, vol. 1842, pp. 554–570. Springer, Heidelberg (2000)
Davies, R.H.: Learning Shape: Optimal Models for Analysing Shape Variability. PhD thesis, University of Manchester, Manchester, UK (2002)
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Heimann, T., Wolf, I., Williams, T., Meinzer, HP. (2005). 3D Active Shape Models Using Gradient Descent Optimization of Description Length. In: Christensen, G.E., Sonka, M. (eds) Information Processing in Medical Imaging. IPMI 2005. Lecture Notes in Computer Science, vol 3565. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11505730_47
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DOI: https://doi.org/10.1007/11505730_47
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26545-0
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