Abstract
Since the 1970’s B-splines have evolved to become the de facto standard for use in curve and surface representation. This resulted in a relatively recent proliferation of nonrigid image registration techniques based on B-splines. These techniques fall under the general Free-Form Deformation (FFD) approach in which the object to be registered is embedded within a B-spline object. The deformation of the B-spline object represents the transformation space of the registered object. In this paper, we describe the implementation of our finite element methodological (FEM) approach using B-splines. This registration framework subsumes essential components of currently popular FFD image registration algorithms, while providing a more principled and generalized control mechanism for nonrigid deformation. Our implementation constitutes an extension of the existing FEM library of the Insight Toolkit (ITK). We discuss the theoretical implications and provide experimental results of our proposed methodology.
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References
de Boor, C.: B-spline basics. In: Fundamental Developments of Computer-Aided Geometric Modeling, pp. 27–49. American Press (1993)
Crum, W.R., Hartkens, T., Hill, D.L.G.: Non-rigid image registration: theory and practice. The British Journal of Radiology 77, 140–153 (2004)
Ibanez, L., Ng, L., Gee, J.C., Aylward, S.: Registration patterns: The generic framework for image registration of the Insight Toolkit. In: IEEE International Symposium on Biomedical Imaging, pp. 345–348 (2002)
Brown, L.G.: A survey of image registration techniques. ACM Computing Surveys 24, 325–376 (1992)
Gee, J.C., Bajcsy, R.K.: Elastic Matching: Continuum Mechanical and Probabilistic Analysis. In: Toga, A.W. (ed.) Brain Warping, pp. 183–198. Academic Press, London (1999)
Szeliski, R., Coughlan, J.: Spline-based image registration. International Journal of Computer Vision 22, 199–218 (1997)
Thevénaz, P., Ruttimann, U.E., Unser, M.: A pyramid approach to subpixel registration based on intensity. IEEE Transactions on Image Processing 7, 27–41 (1998)
Sorzano, C.O.S., Thevénaz, P., Unser, M.: Elastic registration of biological images using vector-spline regularization. IEEE Transactions on Biomedical Engineering 52, 652–663 (2005)
Rueckert, D., Sonoda, L.I., Hayes, C., Hill, D.L.G., Leach, M.O., Hawkes, D.J.: Nonrigid registration using free-form deformations: Application to breast MR images. IEEE Transactions on Medical Imaging 18, 712–721 (1999)
Mattes, D., Haynor, D.R., Vesselle, H., Lewellen, T.K., Eubank, W.: PET-CT image registration in the chest using free-form deformations. IEEE Transactions on Medical Imaging 22, 120–128 (2003)
Rohlfing, T., Maurer Jr., C.R., Bluemke, D.A., Jacobs, M.A.: Volume-preserving nonrigid registration of mr breast images using free-form deformation with an incompressibility constraint. IEEE Transactions on Medical Imaging 22, 730–741 (2003)
Bajcsy, R., Broit, C.: Matching of deformed images. In: International Conference on Pattern Recognition (1982)
Zienkiewicz, O.C., Taylor, R.L.: The Finite Element Method, 5th edn. The Basis, vol. 1. Butterworth Heinemann (2000)
Sabin, M.A.: Spline Finite Elements. PhD thesis, Leeds University (1997)
Lee, S., Wolberg, G., Shin, S.Y.: Scattered data interpolation with multilevel b-splines. IEEE Transactions on Visualization and Computer Graphics 3, 228–244 (1997)
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Tustison, N.J., Avants, B.B., Sundaram, T.A., Duda, J.T., Gee, J.C. (2006). A Generalization of Free-Form Deformation Image Registration Within the ITK Finite Element Framework. In: Pluim, J.P.W., Likar, B., Gerritsen, F.A. (eds) Biomedical Image Registration. WBIR 2006. Lecture Notes in Computer Science, vol 4057. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11784012_29
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DOI: https://doi.org/10.1007/11784012_29
Publisher Name: Springer, Berlin, Heidelberg
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