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Cardiac Motion Estimation Using Covariant Derivatives and Helmholtz Decomposition

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Statistical Atlases and Computational Models of the Heart. Imaging and Modelling Challenges (STACOM 2011)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 7085))

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Abstract

Quantification of cardiac function is important for the assessment of abnormalities and response to therapy. We present a method to reconstruct dense cardiac motion from sparse features in tagging MRI, decomposed into solenoidal and irrotational parts using multi-scale Helmholtz decomposition. Reconstruction is based on energy minimization using covariant derivatives exploiting prior knowledge about the motion field. The method is tested on cardiac motion images. Experiments on phantom data show that both covariant derivatives and multi-scale Helmholtz decomposition improve motion field reconstruction.

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References

  1. Horn, B.K.P., Shunck, B.G.: Determining optical flow. AI 17, 185–203 (1981)

    Google Scholar 

  2. Lucas, B., Kanade, T.: An iterative image registration technique with application to stereo vision. In: DARPA, Image Process, vol. 21, pp. 85–117 (1981)

    Google Scholar 

  3. Florack, L., van Assen, H.: Dense multiscale motion extraction from cardiac cine MR tagging using HARP technology. In: ICCV Workshop on MMBIA (2007)

    Google Scholar 

  4. Thirion, J.: Image matching as a diffusion process: an analogy with Maxwell’s demons. Med. Imag. Anal. 2(3), 243–260 (1998)

    Article  Google Scholar 

  5. Janssen, B., Florack, L., Duits, R., ter Haar Romeny, B.: Optic Flow from Multi-scale Dynamic Anchor Point Attributes. In: Campilho, A., Kamel, M.S. (eds.) ICIAR 2006. LNCS, vol. 4141, pp. 767–779. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  6. Kohlberger, T., Mémin, E., Schnörr, C.: Variational Dense Motion Estimation Using the Helmholtz Decomposition. In: Griffin, L.D., Lillholm, M. (eds.) Scale-Space 2003. LNCS, vol. 2695, pp. 432–448. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  7. Corpetti, T., Mémin, E., Pérez, P.: Dense estimation of fluid flows. IEEE Trans. Pattern Anal. Mach. Intell. 24(3), 365–380 (2002)

    Article  MATH  Google Scholar 

  8. Cuzol, A., Hellier, P., Mémin, E.: A low dimensional fluid motion estimator. IJCV 75, 329–349 (2007), doi:10.1007/s11263-007-0037-0

    Article  Google Scholar 

  9. Mansi, T., Pennec, X., Sermesant, M., Delingette, H., Ayache, N.: iLogDemons: A demons-based registration algorithm for tracking incompressible elastic biological tissues. IJCV 92(1), 92–111 (2011)

    Article  Google Scholar 

  10. von Helmholtz, H.: Üeber integrale der hydrodynamischen Gleichungen, welche den Wirbelbewegungen entsprechen. Crelles J. 55(25) (1858)

    Google Scholar 

  11. Axel, L., Dougherty, L.: MR imaging of motion with spatial modulation of magnetization. Radiology 171(3), 841–845 (1989)

    Article  Google Scholar 

  12. Prince, J.L., McVeigh, E.R.: Motion estimation from tagged MR image sequences. IEEE Trans. Med. Imaging 11(2), 238–249 (1992)

    Article  Google Scholar 

  13. Gupta, S.N., Prince, J.L.: On Variable Brightness Optical Flow for Tagged MRI. In: Proc. of 14th Int. Conf., IPMI 1995. Kluwer, Dordrecht (1995)

    Google Scholar 

  14. Young, A.A.: Model tags: direct three–dimensional tracking of heart wall motion from tagged magnetic resonance images. Med. Image Anal. 3(4), 361–372 (1999)

    Article  Google Scholar 

  15. Chandrashekara, R., Mohiaddin, R., Rueckert, D.: Analysis of myocardial motion in tagged mr images using nonrigid image registration. In: Proc. of SPIE, vol. 4684, pp. 1168–1179 (2002)

    Google Scholar 

  16. Amini, A., Chen, Y., Elayyadi, M., Radeva, P.: Tag surface reconstruction and tracking of myocardial beads from spamm-mri with parametric b-spline surfaces. IEEE Trans. Med. Imaging 20(2), 94–103 (2001)

    Article  Google Scholar 

  17. Axel, L., Chen, T., Manglik, T.: Dense Myocardium Deformation Estimation for 2D Tagged MRI. In: Frangi, A.F., Radeva, P., Santos, A., Hernandez, M. (eds.) FIMH 2005. LNCS, vol. 3504, pp. 446–456. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  18. Osman, N.F., Kerwin, W.S., McVeigh, E.R., Prince, J.L.: Cardiac motion tracking using CINE harmonic phase (HARP). Magnetic Resonance Imaging, MRM 42(6), 1048–1060 (1999)

    Article  Google Scholar 

  19. Pan, L., Prince, J.L., Lima, J.A.C., Osman, N.F.: Fast tracking of cardiac motion using 3D–HARP. IEEE Trans. Biomed. Eng. 52(8), 1425–1435 (2005)

    Article  Google Scholar 

  20. Arts, T., Prinzen, F.W., Delhaas, T., Milles, J.R., Rossi, A.C., Clarysse, P.: Mapping displacement and deformation of the heart with local sine-wave modeling. IEEE Trans. Med. Imaging 29(5), 1114–1123 (2010)

    Article  Google Scholar 

  21. Chen, T., Wang, X., Chung, S., Metaxas, D., Axel, L.: Automated 3d motion tracking using gabor filter bank, robust point matching, and deformable models. IEEE Trans. Med. Imaging 29(1), 1–11 (2010)

    Article  Google Scholar 

  22. Ozturk, C., Derbyshire, J.A., McVeigh, E.R.: Estimating motion from MRI data. Proc. of the IEEE 91(10), 1627–1648 (2003)

    Article  Google Scholar 

  23. Gabor, D.: Theory of communication. J. IEE 93(26), 429–457 (1946)

    Google Scholar 

  24. Florack, L., Kuijper, A.: The topological structure of scale-space images. JMIV 12(1), 65–79 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  25. Dassios, G., Lindell, I.: Uniqueness and reconstruction for the anisotropic Helmholtz decomposition. J. Phys. Math. Gen. 35, 5139–5146 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  26. Duits, R., Janssen, B.J., Becciu, A., van Assen, H.C.: A variational approach to cardiac motion estimation based on covariant derivatives and multi-scale helmholtz decomposition. Quarterly of Applied Mathematics (accepted)

    Google Scholar 

  27. Barron, J., Fleet, D., Beauchemin, S.: Performance of optical flow techniques. IJCV 12(1), 43–77 (1994)

    Article  Google Scholar 

  28. Young, A.A., Axel, L., Dougherty, L., Bogen, D.K., Parenteau, C.S.: Validation of tagging with mr imaging to estimate material deformation. Radiology 188(1), 101–108 (1993)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Dept. of Biomedical Engineering, Eindhoven University of Technology, Netherlands

    Alessandro Becciu, Remco Duits, Luc M. J. Florack & Hans C. van Assen

  2. Dept. of Mathematics, Eindhoven University of Technology, Netherlands

    Remco Duits, Bart J. Janssen & Luc M. J. Florack

Authors
  1. Alessandro Becciu
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  2. Remco Duits
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  3. Bart J. Janssen
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  4. Luc M. J. Florack
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  5. Hans C. van Assen
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Editor information

Editors and Affiliations

  1. Department of Information and Communication Technologies, University of Pompeu Fabra, Center for ComputationalImaging and Simulation Technologies in Biomedicine (CISTIB), Plaça de la Mercè 10-12, 08002, Barcelona, Spain

    Oscar Camara

  2. Machine Learning and Perception, Microsoft Research, 7 J J Thomson Avenue, CB3 0FB, Cambridge, UK

    Ender Konukoglu

  3. Department of Medical Biophysics, Ontario Cancer Institute, princess Margaret Hospital, University of Toronto, Faculty of Medicien, 610 University Avenue, M5G 2M9, Toronto, ON, Canada

    Mihaela Pop

  4. Division of Imaging Sciences, King’s College London, St. Thomas Hospital, Lambeth Wing, SE1 7EH, London, UK

    Kawal Rhode

  5. Research Centre, Ascöepios Team, Inria Sophia Antipolis- Méditerranée, 2004 Route des Lucioles, BP 93, 06902, Sophia Antipolis Cedex, France

    Maxime Sermesant

  6. Auckland Bioengineering Institute, Medical and Health Sciences, University of Auckland, Grafton Campus, Building 502, Auckland, New Zealand

    Alistair Young

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Becciu, A., Duits, R., Janssen, B.J., Florack, L.M.J., van Assen, H.C. (2012). Cardiac Motion Estimation Using Covariant Derivatives and Helmholtz Decomposition. In: Camara, O., Konukoglu, E., Pop, M., Rhode, K., Sermesant, M., Young, A. (eds) Statistical Atlases and Computational Models of the Heart. Imaging and Modelling Challenges. STACOM 2011. Lecture Notes in Computer Science, vol 7085. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28326-0_27

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  • DOI: https://doi.org/10.1007/978-3-642-28326-0_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28325-3

  • Online ISBN: 978-3-642-28326-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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