Abstract
The Large Deformation Diffeomorphic Metric Mapping framework constitutes a widely used and mathematically well-founded setup for registration in medical imaging. At its heart lies the notion of the regularization kernel, and the choice of kernel greatly affects the results of registrations. This paper presents an extension of the LDDMM framework allowing multiple kernels at multiple scales to be incorporated in each registration while preserving many of the mathematical properties of standard LDDMM. On a dataset of landmarks from lung CT images, we show by example the influence of the kernel size in standard LDDMM, and we demonstrate how our framework, LDDKBM, automatically incorporates the advantages of each scale to reach the same accuracy as the standard method optimally tuned with respect to scale. The framework, which is not limited to landmark data, thus removes the need for classical scale selection. Moreover, by decoupling the momentum across scales, it promises to provide better interpolation properties, to allow sparse descriptions of the total deformation, to remove the trade-off between match quality and regularity, and to allow for momentum based statistics using scale information.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
References
Arsigny, V., Commowick, O., Pennec, X., Ayache, N.: A log-euclidean framework for statistics on diffeomorphisms. In: Larsen, R., Nielsen, M., Sporring, J. (eds.) MICCAI 2006. LNCS, vol. 4190, pp. 924–931. Springer, Heidelberg (2006)
Beg, M.F., Miller, M.I., Trouvé, A., Younes, L.: Computing large deformation metric mappings via geodesic flows of diffeomorphisms. IJCV 61(2), 139–157 (2005)
Castillo, R., Castillo, E., Guerra, R., Johnson, V.E., McPhail, T., Garg, A.K., Guerrero, T.: A framework for evaluation of deformable image registration spatial accuracy using large landmark point sets. Physics in Medicine and Biology 54(7), 1849–1870 (2009)
Christensen, G., Rabbitt, R., Miller, M.: Deformable templates using large deformation kinematics. IEEE Transactions on Image Processing 5(10) (2002)
Cotter, C.J., Holm, D.D.: Singular solutions, momentum maps and computational anatomy. nlin/0605020 (May 2006)
Dupuis, P., Grenander, U., Miller, M.I.: Variational problems on flows of diffeomorphisms for image matching (1998)
Grenander, U.: General Pattern Theory: A Mathematical Study of Regular Structures. Oxford University Press, USA (1994)
Hernandez, M., Bossa, M., Olmos, S.: Registration of anatomical images using paths of diffeomorphisms parameterized with stationary vector field flows. International Journal of Computer Vision 85(3), 291–306 (2009)
Joshi, S., Davis, B., Jomier, B.M., Guido Gerig, B.: Unbiased diffeomorphic atlas construction for computational anatomy. NeuroImage 23, 151–160 (2004)
Micheli, M.: The differential geometry of landmark shape manifolds: metrics, geodesics, and curvature. Ph.D. thesis, Brown University, Providence, USA (2008)
Pennec, X., Stefanescu, R., Arsigny, V., Fillard, P., Ayache, N.: Riemannian elasticity: A statistical regularization framework for non-linear registration. In: Duncan, J.S., Gerig, G. (eds.) MICCAI 2005. LNCS, vol. 3750, pp. 943–950. Springer, Heidelberg (2005)
Risser, L., Vialard, F.-X., Wolz, R., Holm, D.D., Rueckert, D.: Simultaneous fine and coarse diffeomorphic registration: Application to atrophy measurement in alzheimer’s disease. In: Jiang, T., Navab, N., Pluim, J.P.W., Viergever, M.A. (eds.) MICCAI 2010. LNCS, vol. 6362, pp. 610–617. Springer, Heidelberg (2010), PMID: 20879366
Thirion, J.: Image matching as a diffusion process: an analogy with maxwell’s demons. Medical Image Analysis 2(3), 243–260 (1998)
Trouvé, A.: An infinite dimensional group approach for physics based models in patterns recognition (1995)
Vaillant, M., Miller, M., Younes, L., Trouvé, A.: Statistics on diffeomorphisms via tangent space representations. NeuroImage 23(suppl. 1), S161–S169 (2004)
Vercauteren, T., Pennec, X., Perchant, A., Ayache, N.: Diffeomorphic demons: efficient non-parametric image registration. NeuroImage 45(suppl. 1), 61–72 (2009)
Younes, L.: Shapes and Diffeomorphisms. Springer, Heidelberg (2010)
Younes, L., Arrate, F., Miller, M.I.: Evolutions equations in computational anatomy. NeuroImage 45(1, suppl. 1), S40–S50 (2009)
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
Sommer, S., Nielsen, M., Lauze, F., Pennec, X. (2011). A Multi-scale Kernel Bundle for LDDMM: Towards Sparse Deformation Description across Space and Scales. In: Székely, G., Hahn, H.K. (eds) Information Processing in Medical Imaging. IPMI 2011. Lecture Notes in Computer Science, vol 6801. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22092-0_51
Download citation
DOI: https://doi.org/10.1007/978-3-642-22092-0_51
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22091-3
Online ISBN: 978-3-642-22092-0
eBook Packages: Computer ScienceComputer Science (R0)