Abstract
Non-rigid registration and shape model fitting are the central problems in any shape modeling pipeline. Even though the goal is in both problems to establishing point-to-point correspondence between two objects, their algorithmic treatment is usually very different. In this paper we present an approach that allows us to treat both problems in a unified algorithmic framework. We use the well known formulation of non-rigid registration as the problem of fitting a Gaussian process model, whose covariance function favors smooth deformations. We compute a low rank approximation of the Gaussian process using the Nyström method, which allows us to formulate it as a parametric fitting problem of the same form as shape model fitting. Besides simplifying the modeling pipeline, our approach also lets us naturally combine shape model fitting and non-rigid registration, in order to reduce the bias in statistical model fitting, or to make registration more robust. As our experiments on 3D surfaces and 3D CT images show, the method leads to a registration accuracy that is comparable to standard registration methods.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
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 (1999)
Christensen, G.E., Miller, M.I., Vannier, M.W., Grenander, U.: Individualizing neuro-anatomical atlases using a massively parallel computer. Computer 29(1), 32–38 (1996)
Cootes, T.F., Taylor, C.J.: Combining point distribution models with shape models based on finite element analysis. Image and Vision Computing 13(5) (1995)
Grenander, U., Miller, M.I.: Computational anatomy: An emerging discipline. Quarterly of Applied Mathematics 56(4), 617–694 (1998)
Hein, M., Bousquet, O.: Kernels, associated structures and generalizations. Max-Planck-Institut fuer biologische Kybernetik, Technical Report (2004)
Klein, S., Staring, M., Pluim, J.P.: Evaluation of optimization methods for nonrigid medical image registration using mutual information and b-splines. IEEE Transactions on Image Processing 16(12), 2879–2890 (2007)
Lüthi, M., Jud, C., Vetter, T.: Using landmarks as a deformation prior for hybrid image registration. Pattern Recognition, 196–205 (2011)
Lüthi, M., Blanc, R., Albrecht, T., Gass, T., Goksel, O., Büchler, P., Kistler, M., Bousleiman, H., Reyes, M., Cattin, P.C., et al.: Statismo-a framework for pca based statistical models (2012)
Opfer, R.: Multiscale kernels. Advances in Computational Mathematics 25(4), 357–380 (2006)
Paysan, P., Knothe, R., Amberg, B., Romdhani, S., Vetter, T.: A 3D face model for pose and illumination invariant face recognition. In: Advanced Video and Signal Based Surveillance 2009, pp. 296–301 (2009)
Rasmussen, C.E., Williams, C.K.: Gaussian processes for machine learning. Springer (2006)
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)
Schölkopf, B., Steinke, F., Blanz, V.: Object correspondence as a machine learning problem. In: ICML 2005: Proceedings of the 22nd International Conference on Machine Learning, pp. 776–783. ACM Press, New York (2005)
Thirion, J.P.: Image matching as a diffusion process: an analogy with Maxwell’s demons. Medical Image Analysis 2(3), 243–260 (1998)
Wahba, G.: Spline models for observational data. Society for Industrial Mathematics (1990)
Wang, Y., Staib, L.H.: Boundary finding with prior shape and smoothness models. IEEE Transactions on Pattern Analysis and Machine Intelligence 22(7) (2000)
Wang, Y., Staib, L.H.: Physical model-based non-rigid registration incorporating statistical shape information. Medical Image Analysis 4(1), 7–20 (2000)
Xue, Z., Shen, D., Davatzikos, C.: Statistical representation of high-dimensional deformation fields with application to statistically constrained 3D warping. Medical Image Analysis 10(5), 740–751 (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer International Publishing Switzerland
About this paper
Cite this paper
Lüthi, M., Jud, C., Vetter, T. (2013). A Unified Approach to Shape Model Fitting and Non-rigid Registration. In: Wu, G., Zhang, D., Shen, D., Yan, P., Suzuki, K., Wang, F. (eds) Machine Learning in Medical Imaging. MLMI 2013. Lecture Notes in Computer Science, vol 8184. Springer, Cham. https://doi.org/10.1007/978-3-319-02267-3_9
Download citation
DOI: https://doi.org/10.1007/978-3-319-02267-3_9
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-02266-6
Online ISBN: 978-3-319-02267-3
eBook Packages: Computer ScienceComputer Science (R0)