Abstract
For non-rigid registration, the objects in medical images are usually treated as a single deformable body with homogeneous stiffness distribution. However, this assumption is invalid for certain parts of the human body, where bony structures move rigidly, while the others may deform. In this paper, we introduce a novel registration technique that models local rigidity of pre-identified rigid structures as well as global non-rigidity in the transformation field using triangular B-splines. In contrast to the conventional registration method based on tensor-product B-splines, our approach recovers local rigid transformation with fewer degrees of freedom (DOFs), and accurately simulates sharp features (C 0 continuity) along the interface between deformable regions and rigid structures, because of the unique advantages offered by triangular B-splines, such as flexible triangular domain, local control and space-varying smoothness modeling. The accurate matching of the source image with the target one is accomplished through the use of a variational framework, in which a composite energy, measuring the image dissimilarity and enforcing local rigidity and global smoothness, is minimized subject to pre-defined point-based constraints. The algorithm is tested on both synthetic and real 2D images for its applicability. The experimental results show that, by accurately modeling sharp features using triangular B-splines, the deformable regions in the vicinity of rigid structures are less constrained by the global smoothness regularization and therefore contribute extra flexibility to the optimization process. Consequently, the registration quality is improved considerably.
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.
References
Brown, L.G.: A survey of image registration techniques. ACM Comput. Surv. 24, 325–376 (1992)
Maintz, J., Viergever, M.: A survey of medical image registration. Medical Image Analysis 2, 1–36 (1998)
Zitová, B., Flusser, J.: Image registration methods: a survey. Image Vision Comput 21, 977–1000 (2003)
Peters, T., Davey, B., Munger, P., Comeau, R., Evans, A., Olivier, A.: Three-dimensional multimodal image-guidance for neurosurgery. IEEE Transactions on medical imaging 15, 121–128 (1996)
Potamianos, P., Davies, B., Hibberd, R.D.: Intraoperative registration for percutaneous surgery. In: First International Symposium on Medical Robotics and Computer Asisted Surgery, vol. 1, pp. 98–105 (1995)
Cachier, P., Mangin, J.F., Pennec, X., Rivière, D., Papadopoulos-Orfanos, D., Régis, J., Ayache, N.: Multisubject non-rigid registration of brain mri using intensity and geometric features. In: Niessen, W.J., Viergever, M.A. (eds.) MICCAI 2001. LNCS, vol. 2208, pp. 734–742. Springer, Heidelberg (2001)
Rueckert, D., Sonoda, L., Hayes, C., Hill, D.L., Leach, M.O., Hawkes, D.J.: Non-rigid registration using free-form deformations: Application to breast mr images. IEEE Trans. Med. Imaging 18, 712–721 (1999)
Edwards, P.J., Hill, D.L.G., Little, J.A., Sahni, V.A.: Medical image registration incorporating deformations. In: BMVC, pp. 691–699 (1995)
Little, J.A., Hill, D.L.G., Hawkes, D.J.: Deformations incorporating rigid structures. Computer Vision And Image Understanding 66, 223–232 (1997)
Rohr, K., Fornefett, M., Stiehl, H.S.: Spline-based elastic image registration: Integration of landmark errors and orientation attributes. Computer Vision And Image Understanding 90, 153–168 (2003)
Duay, V., D’Haese, P.F., Li, R., Dawant, B.M.: Non-rigid registration algorithm with spatially varying stiffness properties. In: ISBI, pp. 408–411 (2004)
Tanner, C., Schnabel, J.A., Chung, D., Clarkson, M.J., Rueckert, D., Hill, D.L.G., Hawkes, D.J.: Volume and shape preservation of enhancing lesions when applying non-rigid registration to a time series of contrast enhancing MR breast images. In: Delp, S.L., DiGoia, A.M., Jaramaz, B. (eds.) MICCAI 2000. LNCS, vol. 1935, pp. 327–337. Springer, Heidelberg (2000)
Loeckx, D., Maes, F., Vandermeulen, D., Suetens, P.: Nonrigid image registration using free-form deformations with a local rigidity constraint. In: Barillot, C., Haynor, D.R., Hellier, P. (eds.) MICCAI 2004. LNCS, vol. 3216, pp. 639–646. Springer, Heidelberg (2004)
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.: Demonstration of accuracy and clinical versatility of mutual information for automatic multimodality image fusion using affine and thin-plate spline warped geometric deformations. Med. Image Anal. 1, 195–206 (1996, 1997)
Rohlfing, T., Jr., C.R.M, Bluemke, D.A., Jacobs, M.A.: An alternating-constraints algorithm for volume-preserving non-rigid registration of contrast-enhanced mr breast images. In: WBIR (2003)
Vemuri, B.C., Huang, S., Sahni, S., Leonard, C.M., Mohr, C., Gilmore, R., Fitzsimmons, J.: An efficient motion estimator with application to medical image registration. Medical Image Analysis 2, 79–98 (1998)
Dahmen, W., Micchelli, C.A., Seidel, H.P.: Blossoming begets b-spline built better by b-patches. Mathematics of Computation 59, 97–115 (1992)
Fong, P., Seidel, H.P.: An implementation of triangular b-spline surfaces over arbitrary triangulations. Computer Aided Geometric Design 10, 267–275 (1993)
Pfeifle, R., Seidel, H.P.: Faster evaluation of qudartic bivariate dms spline surfaces. In: Proceedings of Graphics Interface 1994, pp. 182–189 (1994)
Franssen, M., Veltkamp, R.C., Wesselink, W.: Efficient evaluation of triangular b-spline surfaces. Computer Aided Geometric Design 17, 863–877 (2000)
Micchelli, C.A.: On a numerically efficient method for computing multivariate b-splines. Multivariate approximation theory 51, 211–248
Shewchuk, J.R.: Automated three-dimensional registration of magnetic resonance and positron emission tomography brain images by multiresolution optimization of voxel similarity measures. Med. Phys. 24, 25–35 (1997)
Collignon, A.: Multi-modality medical image registration by maximization of mutual information. PhD thesis, Catholic University of Leuven, Leuven, Belgium (1998)
Viola, P.A.: Alignment by maximization of mutual information. PhD thesis, Massachusetts Institute of Technology, Boston, MA, USA (1995)
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)
Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes in C: The Art of Scientific Computing. Cambridge University Press, Cambridge (1992)
Gill, P., Murray, W., Wright, M.: Practical Optimization. Academic Press, London (1981)
He, Y., Qin, H.: Surface reconstruction with triangular b-splines. In: GMP, pp. 279–290 (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wang, K., He, Y., Qin, H. (2005). Incorporating Rigid Structures in Non-rigid Registration Using Triangular B-Splines. In: Paragios, N., Faugeras, O., Chan, T., Schnörr, C. (eds) Variational, Geometric, and Level Set Methods in Computer Vision. VLSM 2005. Lecture Notes in Computer Science, vol 3752. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11567646_20
Download citation
DOI: https://doi.org/10.1007/11567646_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29348-4
Online ISBN: 978-3-540-32109-5
eBook Packages: Computer ScienceComputer Science (R0)