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Image Registration Using Hierarchical B-Splines
January-February 2004 (vol. 10 no. 1)
pp. 85-94

Abstract—Hierarchical B-splines have been widely used for shape modeling since their discovery by Forsey and Bartels. In this paper, we present an application of this concept, in the form of free-form deformation, to image registration by matching two images at increasing levels of detail. Results using MRI brain data are presented that demonstrate high degrees of matching while unnecessary distortions are avoided. We compare our results with the nonlinear ICP (Iterative Closest Point) algorithm (used for landmark-based registration) and optical flow (used for intensity-based registration).

[1] L. Arata, A. Dhawan, J. Broderick, M. Gaskil-Shipley, N. Volkow, and A. Levy, Three-Dimensional Anatomical Model-Based Segmentation of MR Brain Images through Principal Axes Registration IEEE Trans. Biomedical Eng., vol. 42, no. 11, pp. 1069-1078, 1995.
[2] J. Ashburner and K. Friston, Nonlinear Spatial Normalization Using Basis Functions Human Brain Mapping, vol. 7, no. 4, pp. 254-266, 1999. .
[3] P.J. Besl and N.D. McKay, "A Method for Registration of 3D Shapes," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 14, no. 2, pp. 239-256, Feb. 1992.
[4] P. Bezier, General Distortion of an Ensemble of Biparametric Patches Computer Aided Design, vol. 10, no. 2, pp. 116-120, 1978.
[5] L. Bookstein, "Principal Warps: Thin-Plate Splines and the Decomposition of Deformations," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, no. 6, pp. 567-585, June 1989.
[6] G. Borgefors, Distance Transformation in Digital Images Computer Vision, Graphics, and Image Processing, vol. 34, pp. 344-371, 1986.
[7] G. Borgefors, "Hierarchical Chamfer Matching: A Parametric Edge Matching Algorithm," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 10, pp. 849-865, 1988.
[8] L. Brown, A Survey of Image Registration Techniques ACM Computing Surveys, vol. 24, no. 4, pp. 325-376, 1992.
[9] S. Conte, C. De Boor, Elementary Numerical Analysis, third ed. McGraw-Hill, 1980.
[10] S. Coquillart, Extended Free-Form Deformation: A Sculpturing Tool for 3D Geometric Modeling Computer Graphics (SIGGRAPH '90), vol. 24, no. 4, pp. 187-196, 1990.
[11] M. Crombie, Coordination of Stereo Image Registration and Pixel Classification Photogrammetric Eng. and Remote Sensing, vol. 49, no. 4, pp. 529-532, 1983.
[12] E. Davies, Machine Vision: Theory, Algorithms and Practicalities. Wesley Publishing, 1990.
[13] P. Dierckx, Curve and Surface Fitting with Splines. Oxford: Clarendon Press, 1993.
[14] J. Duncan and N. Ayache, Medical Image Analysis: Progress over Two Decades and the Challenges Ahead IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 22, no. 1, pp. 85-106, Jan. 2000.
[15] G. Farin, Curves and Surfaces for CAGD, fifth ed. Morgan-Kaufmann, 2001.
[16] J. Feldmar and N. Ayache, Rigid, Affine and Locally Affine Registration of Free-Form Surfaces Technical Report 2220, Institut National de Recherche en Informatique et en Automatique, 1994.
[17] D. Forsey and R. Bartels, Hierarchical B-Spline Refinement Computer Graphics (Proc. SIGGRAPH '88), vol. 22, no. 4, pp. 205-212, 1988.
[18] U. Grenander and M. Miller, Computational Anatomy: An Emerging Discipline Quarterly Applied Math., pp. 617-694, 1998.
[19] A. Guimond, A. Roche, N. Ayache, and J. Meunier, Multimodal Brain Warping Using the Demons Algorithm and Adaptive Intensity Corrections Technical Report 3796, Institut National de Recherche en Informatique et en Automatique, 1999.
[20] S. Kovacic and R. Bajcsy, Multiscale/Multiresolution Representations Brain Warping W. Toga, ed., pp. 45-65, Academic Press, 1998.
[21] S. Lavellee, E. Bittar, and R. Szeliski, Elastic Registration and Inference Using Oct-Tree Splines Brain Warping, W. Toga, ed., pp. 283-296, Academic Press, 1998.
[22] S. Lee, G. Wolberg, and S.Y. Shin, Scattered Data Interpolation with Multilevel B-Splines Visualization&Computer Graphics, vol. 3, no. 3, pp. 228-244, 1997.
[23] R.A. MacCracken and K.I. Joy, Free-Form Deformations with Lattices of Arbitrary Topology Proc. SIGGRAPH '96, Ann. Conf. Series, pp. 181-188, 1996.
[24] J. Maintz and M. Viergever, A Survey of Medical Image Registration Medical Image Analysis, vol. 2, no. 1, pp. 1-16, 1998.
[25] S. Mallat, "Wavelets for a Vision," Proc. IEEE, vol. 84, no. 4, pp. 604-614, 1996.
[26] T. McInerney and D. Terzopoulos, Deformable Models in Medical Images Analysis: A Survey Medical Image Analysis, vol. 1, no. 2, pp. 91-108, 1996.
[27] H. Muller and D. Ruprecht, Spatial Interpolants for Warping Brain Warping, W. Toga, ed., pp. 199-220, Academic Press, 1998.
[28] T. Satio and J. Toriwaki, New Algorithms for Euclidean Distance Transformation of an n-Dimension Digitized Picture with Applications Pattern Recognition, vol. 27, no. 11, pp. 1551-1565, 1994.
[29] T. Sederberg and S. Parry, Free Form Deformation of Solid Geometric Models Computer Graphics, vol. 20, no. 4, pp. 151-159, 1986.
[30] A. Signh, Optic Flow Computation. IEEE CS Press, 1991.
[31] E. Stollnitz, T. DeRose, and D. Salesin, Wavelets for Computer Graphics: Theory and Applications. Morgan-Kaufmann, 1996.
[32] J. Thirion, Fast Non-Rigid Matching of 3D Medical Images Proc. Medical Robotics and Computer Aided Surgery (MRCAS '95), pp. 47-54, 1995.
[33] W. Toga and P. Thompson, An Introduction to Brain Warping Brain Warping, W. Toga, ed., pp. 1-26, Academic Press, 1998.
[34] P. Viola, Alignment by Maximization of Mutual Information PhD thesis, Massachusetts Inst. of Tech nology, 1995.
[35] R. Woods, Automated Global Polynomial Warping Brain Warping, W. Toga, ed., pp. 365-376, Academic Press, 1998.

Index Terms:
Index Terms - Image registration, free form deformation, hierarchical B-splines, scattered data approximation, iterative closest point, optical flow.
Zhiyong Xie, Gerald E. Farin, "Image Registration Using Hierarchical B-Splines," IEEE Transactions on Visualization and Computer Graphics, vol. 10, no. 1, pp. 85-94, Jan.-Feb. 2004, doi:10.1109/TVCG.2004.1260760
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