Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-22T15:10:23.509Z Has data issue: false hasContentIssue false
  • English
  • Français

Two and Three Dimensional Image Registration Based on B-Spline Composition and Level Sets

Part of: Physiological, cellular and medical topics Applications

Published online by Cambridge University Press:  07 February 2017

Chiu Ling Chan ,
Cosmin Anitescu ,
Yongjie Zhang  and
Timon Rabczuk
Chiu Ling Chan*
Affiliation:
Institute of Structural Mechanics, Bauhaus Universität Weimar, Germany
Cosmin Anitescu*
Affiliation:
Institute of Structural Mechanics, Bauhaus Universität Weimar, Germany
Yongjie Zhang*
Affiliation:
Department of Mechanical Engineering, Carnegie Mellon University, USA
Timon Rabczuk*
Affiliation:
Division of Computational Mechanics, Ton Duc Thang University, Ho Chi Minh City, Vietnam Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam Institute of Structural Mechanics, Bauhaus Universität Weimar, Germany
*
*Corresponding author.Email addresses:[email protected] (C. L. Chan), [email protected] (C. Anitescu), [email protected] (Y. Zhang), [email protected] (T. Rabczuk)
*Corresponding author.Email addresses:[email protected] (C. L. Chan), [email protected] (C. Anitescu), [email protected] (Y. Zhang), [email protected] (T. Rabczuk)
*Corresponding author.Email addresses:[email protected] (C. L. Chan), [email protected] (C. Anitescu), [email protected] (Y. Zhang), [email protected] (T. Rabczuk)
*Corresponding author.Email addresses:[email protected] (C. L. Chan), [email protected] (C. Anitescu), [email protected] (Y. Zhang), [email protected] (T. Rabczuk)
Get access

Abstract

Amethod for non-rigid image registration that is suitable for large deformations is presented. Conventional registration methods embed the image in a B-spline object, and the image is evolved by deforming the B-spline object. In this work, we represent the image using B-spline and deform the image using a composition approach. We also derive a computationally efficient algorithm for calculating the B-spline coefficients and gradients of the image by adopting ideas from signal processing using image filters. We demonstrate the application of our method on several different types of 2D and 3D images and compare it with existing methods.

Keywords

Image registrationB-splinelevel setfree-form deformation

MSC classification

Secondary: 68U10: Image processing 92C55: Biomedical imaging and signal processing 62P10: Applications to biology and medical sciences
Type
Computational Software
Information
Communications in Computational Physics , Volume 21 , Issue 2 , February 2017 , pp. 600 - 622
Copyright
Copyright © Global-Science Press 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Brainweb: Simulated brain database. Available at http://brainweb.bic.mni.mcgill.ca/brainweb/.Google Scholar
[2] Diffeomorphic log demons image registration. Available at http://www.mathworks.com/matlabcentral/fileexchange/39194-diffeomorphic-log-demons-image-registration.Google Scholar
[3] Ashburner, J.. A fast diffeomorphic image registration algorithm. NeuroImage, 38(1):95–113, 2007.CrossRefGoogle ScholarPubMed
[4] Beg, M. F., Miller, M. I., Trouv, A., and Younes, L.. Computing large deformation metric mappings via geodesic flows of diffeomorphisms. International Journal of Computer Vision, 61(2):139–157, 2005.Google Scholar
[5] Bro-Nielsen, M. and Gramkow, C.. Fast fluid registration of medical images. In Hhne, KarlHeinz and Kikinis, Ron, editors, Visualization in Biomedical Computing, volume 1131 of Lecture Notes in Computer Science, pages 265–276. Springer Berlin Heidelberg, 1996.Google Scholar
[6] Cachier, P., Bardinet, E., Dormont, D., Pennec, X., and Ayache, N.. Iconic feature based nonrigid registration: the PASHA algorithm. Computer Vision and Image Understanding, 89(2-3):272–298, 2003. Nonrigid Image Registration.CrossRefGoogle Scholar
[7] Choi, Y. and Lee, S.. Injectivity conditions of 2D and 3D uniform cubic B-spline functions. Graphical Models, 62(6):411–427, 2000.CrossRefGoogle Scholar
[8] Christensen, G. E., Rabbitt, R. D., and Miller, M. I.. Deformable templates using large deformation kinematics. IEEE Transactions on Image Processing, 5(10):1435–1447, Oct 1996.CrossRefGoogle ScholarPubMed
[9] Davatzikos, C.. Spatial transformation and registration of brain images using elastically deformable models. Computer Vision and Image Understanding, 66(2):207–222, 1997.Google Scholar
[10] Gee, J.C.. On matching brain volumes. Pattern Recognition, 32(1):99–111, 1999.Google Scholar
[11] Jia, Y., Zhang, Y., and Rabczuk, T.. A novel dynamic multilevel technique for image registration. Computers and Mathematics with Applications, 69(9):909–925, May 2015.Google Scholar
[12] Leng, J., Xu, G., and Zhang, Y.. Medical image interpolation based on multi-resolution registration. Computers & Mathematics with Applications, 66(1):1–18, 2013.Google Scholar
[13] Pawar, A., Zhang, Y., Jia, Y., Wei, X., Rabczuk, T., Chan, C. L., and Anitescu, C.. Adaptive FEM-based nonrigid image registration using truncated hierarchical b-splines. A Special Issue of FEF 2015 in Computers and Mathematics with Applications, 2016.Google Scholar
[14] Pennec, X., Cachier, P., and Ayache, N.. Understanding the demons algorithm: 3D non-rigid registration by gradient descent. In Taylor, Chris and Colchester, Alain, editors, Medical Image Computing and Computer-Assisted Intervention MICCAI99, volume 1679 of Lecture Notes in Computer Science, pages 597–605. Springer Berlin Heidelberg, 1999.Google Scholar
[15] Rueckert, D., Aljabar, P., Heckemann, R. A., Hajnal, J. V., and Hammers, A.. Diffeomorphic registration using B-splines. In Larsen, Rasmus, Nielsen, Mads, and Sporring, Jon, editors, Medical Image Computing and Computer-Assisted Intervention MICCAI 2006, volume 4191 of Lecture Notes in Computer Science, pages 702–709. Springer Berlin Heidelberg, 2006.Google Scholar
[16] Rueckert, D., Sonoda, L.I., Hayes, C., Hill, D.L.G., Leach, M.O., and Hawkes, D.J.. Nonrigid registration using free-form deformations: application to breast MR images. Medical Imaging, IEEE Transactions on, 18(8):712–721, Aug 1999.Google Scholar
[17] Szeliski, R. and Coughlan, J.. Spline-based image registration. International Journal of Computer Vision, 22(3):199–218, 1997.CrossRefGoogle Scholar
[18] Thirion, J.-P.. Image matching as a diffusion process: an analogy with Maxwell's demons. Medical Image Analysis, 2(3):243–260, 1998.Google Scholar
[19] Tustison, N.J., Avants, B.B., and Gee, J.C.. Directly manipulated free-form deformation image registration. Image Processing, IEEE Transactions on, 18(3):624–635, March 2009.Google Scholar
[20] Unser, M.. Splines: a perfect fit for signal and image processing. Signal Processing Magazine, IEEE, 16(6):22–38, Nov 1999.Google Scholar
[21] Vemuri, B. C., Ye, J., Chen, Y., and Leonard, C. M.. Image registration via level-set motion: applications to atlas-based segmentation. Medical Image Analysis, 7(1):1–20, 2003.Google Scholar
[22] Vercauteren, T., Pennec, X., Perchant, A., and Ayache, N.. Non-parametric diffeomorphic image registration with the demons algorithm. In Ayache, N., Ourselin, S., and Maeder, A., editors, Medical Image Computing and Computer-Assisted Intervention MICCAI 2007, volume 4792 of Lecture Notes in Computer Science, pages 319–326. Springer Berlin Heidelberg, 2007.Google Scholar
[23] Vercauteren, T., Pennec, X., Perchant, A., and Ayache, N.. Diffeomorphic demons: efficient non-parametric image registration. NeuroImage, 45(1, Supplement 1):S61–S72, 2009. Mathematics in Brain Imaging.Google Scholar
[24] Verhoosel, C. V., van Zwieten, G. J., van Rietbergen, B., and de Borst, R.. Image-based goal-oriented adaptive isogeometric analysis with application to the micro-mechanical modeling of trabecular bone. Computer Methods in Applied Mechanics and Engineering, 284:138–164, February 2015.Google Scholar