Abstract
For segmenting complex structures like vertebrae, a priori knowledge by means of statistical shape models (SSMs) is often incorporated. One of the main challenges using SSMs is the solution of the correspondence problem. In this work we present a generic automated approach for solving the correspondence problem for vertebrae. We determine two closed loops on a reference shape and propagate them consistently to the remaining shapes of the training set. Then every shape is cut along these loops and parameterized to a rectangle. There, we optimize a novel combined energy to establish the correspondences and to reduce the unavoidable area and angle distortion. Finally, we present an adaptive resampling method to achieve a good shape representation. A qualitative and quantitative evaluation shows that using our method we can generate SSMs of higher quality than the ICP approach.
Chapter PDF
References
Besl, P.J., Mckay, H.D.: A method for registration of 3-D shapes. IEEE Trans. Pattern Anal. Mach. Intell. 14(2), 239–256 (1992)
Brett, A., Taylor, C.: Construction of 3D shape models of femoral articular cartilage using harmonic maps. In: Delp, S., DiGoia, A., Jaramaz, B. (eds.) MICCAI 2000. LNCS, vol. 1935, pp. 1205–1214. Springer, Heidelberg (2000)
Cates, J.E., Fletcher, P.T., Styner, M.A., Shenton, M.E., Whitaker, R.T.: Shape modeling and analysis with entropy-based particle systems. In: Karssemeijer, N., Lelieveldt, B. (eds.) IPMI 2007. LNCS, vol. 4584, pp. 333–345. Springer, Heidelberg (2007)
Cootes, T.F., Taylor, C.J., Cooper, D.H., Graham, J.: Active shape models their training and application. Comput. Vis. Image Underst. 61, 38–59 (1995)
Davies, R.H., Twining, C.J., Taylor, C.J.: Statistical Models of Shape: Optimisation and Evaluation. Springer, London (2008)
Degener, P., Meseth, J., Klein, R.: An adaptable surface parameterization method. In: 12th International Meshing Roundtable 2003, Santa Fe, pp. 201–213 (2003)
Erickson, J., Whittlesey, K.: Greedy optimal homotopy and homology generators. In: 16th ACM-SIAM Symposium on Discrete Algorithms, pp. 1038–1046. SIAM, Vancouver (2005)
Fuhrmann, S., Ackermann, J., Kalbe, T., Goesele, M.: Direct resampling for isotropic surface remeshing. In: Vision, Modeling, and Visualization 2010, pp. 9–16. Eurographics Association, Siegen (2010)
Heimann, T., Wolf, I., Meinzer, H.P.: Automatic generation of 3D statistical shape models with optimal landmark distribution. Methods Inf. Med. 46(3), 275–281 (2007)
Heimann, T., Wolf, I., Meinzer, H.P.: Statistical shape models for 3D medical image segmentation: A review. Medical Image Analysis 13(4), 543–563 (2009)
Hormann, K., Lévy, B., Sheffer, A.: Mesh parameterization: Theory and practice. In: SIGGRAPH 2007 Course Notes, vol. 2. ACM Press, San Diego (2007)
Klinder, T., Ostermann, J., Ehm, M., Franz, A., Kneser, R., Lorenz, C.: Automated model-based vertebra detection, identification, and segmentation in CT images. Medical Image Analysis 13(3), 471–482 (2009)
Lamecker, H., Lange, T., Seebass, M.: A statistical shape model for the liver. In: Dohi, T., Kikinis, R. (eds.) MICCAI 2002. LNCS, vol. 2489, pp. 421–427. Springer, Heidelberg (2002)
Meier, D., Fisher, E.: Parameter space warping: shape-based correspondence between morphologically different objects. IEEE Trans. Med. Imaging 21(1), 31–47 (2002)
Munkres, J.R.: Topology. Prentice Hall, Upper Saddle River (2000)
Steiner, D., Fischer, A.: Planar parameterization for closed manifold genus-g meshes using any type of positive weights. J. Comput. Inf. Sci. Eng. 5, 118–125 (2005)
Tewari, G., Gotsman, C., Gortler, S.J.: Meshing genus-1 point clouds using discrete one-forms. Computers and Graphics 30(6), 917–926 (2006)
Tutte, W.T.: How to draw a graph. London Math. Soc. 13, 743–768 (1963)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Becker, M., Kirschner, M., Fuhrmann, S., Wesarg, S. (2011). Automatic Construction of Statistical Shape Models for Vertebrae. In: Fichtinger, G., Martel, A., Peters, T. (eds) Medical Image Computing and Computer-Assisted Intervention – MICCAI 2011. MICCAI 2011. Lecture Notes in Computer Science, vol 6892. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23629-7_61
Download citation
DOI: https://doi.org/10.1007/978-3-642-23629-7_61
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23628-0
Online ISBN: 978-3-642-23629-7
eBook Packages: Computer ScienceComputer Science (R0)