Abstract
Non-rigid registration of a pair of images depends on the generation of a dense deformation field across one of the images. Such deformation fields can be represented by the deformation of a set of knotpoints, interpolated to produce the continuous deformation field. This paper addresses the question of how best to choose the knotpoints of such a representation based on all of the available image information. These knotpoints are not landmarks, they can be positioned anywhere in the images, and do not necessarily correspond to any image feature. We use an iterative, data-driven algorithm for the selection of knotpoints, and a novel spline that interpolates smoothly between knotpoints. The algorithm produces a low-dimensional representation of the deformation field that can be successively refined in a multi-resolution manner. We demonstrate the properties of the algorithm on sets of 2D images and discuss the extension of the algorithm to 3D data.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Boggio, T.: Sulle funzioni di green d’ordine m. Rendiconti - Circolo Matematico di Palermo 20, 97–135 (1905)
Bookstein, F.L.: Morphometric tools for landmark data. CUP (1991)
Bro-Nielsen, M., Gramkow, C.: Fast fluid registration of medical images. In: Proceedings of Visualization in Biomedical Computing (VBC), pp. 267–276 (1996)
Chefd’Hotel, C., Hermosillo, G., Faugeras, O.: A variational approach to multimodal image matching. In: Proceedings of IEEE Workshop on Variational and Level Set Methods (VLSM 2001), pp. 21–28 (2001)
Forsey, D.R., Bartels, R.H.: Hierarchical B-spline refinement. ACM Transactions in Computer Graphics 22(4), 205–212 (1988)
Gee, J., Reivich, M., Bajcsy, R.: Elastically deforming 3D atlas to match anatomical brain images. Journal of Computer Assisted Tomography 17(2), 225–236 (1993)
Hartkens, T., Hill, D.L.G., Castellano-Smith, A.D., Hawkes, D.J., Maurer Jr., C.R., Martin, A.J., Hall, W.A., Liu, H., Truwit, C.L.: Using points and surfaces to improve voxel-based non-rigid registration. In: Dohi, T., Kikinis, R. (eds.) MICCAI 2002. LNCS, vol. 2489, pp. 565–572. Springer, Heidelberg (2002)
LeBriquer, L., Gee, J.: Design of a statistical model of brain shape. In: Duncan, J.S., Gindi, G. (eds.) IPMI 1997. LNCS, vol. 1230, pp. 477–482. Springer, Heidelberg (1997)
Maes, F., Collignon, A., Vandermeulen, D., Marchal, G., Suetens, P.: Multimodality image registration by maximization of mutual information. IEEE Transactions on Medical Imaging 16(2), 187–198 (1997)
Marsland, S., Twining, C.J.: Clamped-plate splines and the optimal flow of bounded diffeomorphisms. In: Statistics of Large Datasets, Proceedings of Leeds Annual Statistical Research Workshop, pp. 91–95 (2002)
Meyer, C.R., Boes, J.L., Kim, B., Bland, P.H., Zasadny, K.R., Kison, P.V., Koral, K., Frey, K.A., Wahl, R.L.: Demonstrations of accuracy and clinicial versatility of mutual information for automatic multimodality image fusion using affine and thin-plate spline warped geometric deformations. Medical Image Analysis 1(3), 195–206 (1997)
Roche, A., Malandain, G., Pennec, X., Ayache, N.: The correlation ratio as a new similarity measure for multimodal image registration. In: Wells, W.M., Colchester, A.C.F., Delp, S.L. (eds.) MICCAI 1998. LNCS, vol. 1496, pp. 1115–1124. Springer, Heidelberg (1998)
Rohlfing, T., Maurer Jr., C.R.: Intensity-based non-rigid registration using adaptive multilevel free-form deformation with an incompressibility constraint. In: Niessen, W.J., Viergever, M.A. (eds.) MICCAI 2001. LNCS, vol. 2208, pp. 111–119. Springer, Heidelberg (2001)
Rohr, K., Stiehl, H.S., Sprengel, R., Buzug, T.M., Weese, J., Kuhn, M.H.: Landmark-based elastic registration using approximating thin-plate splines. IEEE Transactions on medical imaging 20(6), 526–534 (2001)
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)
Schnabel, J.A., Rueckert, D., Quist, M., Blackall, J.M., Castellano-Smith, A.D., Hartkens, T., Penney, G.P., Hall, W.A., Liu, H., Truwit, C.L., Gerritsen, F.A., Hill, D.L.G., Hawkes, D.J.: A generic framework for non-rigid registration based on non-uniform multi-level free-form deformations. In: Niessen, W.J., Viergever, M.A. (eds.) MICCAI 2001. LNCS, vol. 2208, pp. 573–581. Springer, Heidelberg (2001)
Studholme, C., Hill, D., Hawkes, D.: Automated three-dimenensional registration of magnetic resonance and positron emission tomography by multiresolution optimisation of voxel similarity measures. Medical Physics 24(1), 25–35 (1997)
Twining, C.J., Marsland, S.: Constructing diffeomorphic representations of non-rigid registrations of medical images. In: Proceedings of IPMI (2003) (to appear)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Marsland, S., Twining, C.J. (2003). Constructing Data-Driven Optimal Representations for Iterative Pairwise Non-rigid Registration. In: Gee, J.C., Maintz, J.B.A., Vannier, M.W. (eds) Biomedical Image Registration. WBIR 2003. Lecture Notes in Computer Science, vol 2717. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39701-4_6
Download citation
DOI: https://doi.org/10.1007/978-3-540-39701-4_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20343-8
Online ISBN: 978-3-540-39701-4
eBook Packages: Springer Book Archive