Rank Constrained Diffeomorphic Density Motion Estimation for Respiratory Correlated Computed Tomography

  • Markus FooteEmail author
  • Pouya Sabouri
  • Amit Sawant
  • Sarang Joshi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10551)


Motion estimation of organs in a sequence of images is important in numerous medical imaging applications. The focus of this paper is the analysis of 4D Respiratory Correlated Computed Tomography (RCCT) Imaging. It is hypothesized that the quasi-periodic breathing induced motion of organs in the thorax can be represented by deformations spanning a very low dimension subspace of the full infinite dimensional space of diffeomorphic transformations. This paper presents a novel motion estimation algorithm that includes the constraint for low-rank motion between the different phases of the RCCT images. Low-rank deformation solutions are necessary for the efficient statistical analysis and improved treatment planning and delivery. Although the application focus of this paper is RCCT the algorithm is quite general and applicable to various motion estimation problems in medical imaging.


Diffeomorphisms Image registration 


  1. 1.
    Bauer, M., Joshi, S., Modin, K.: Diffeomorphic density matching by optimal information transport. SIAM J. Imaging Sci. 8(3), 1718–1751 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm. Soc. Ind. Appl. Math. J. Imaging Sci. 2(1), 183–202 (2009)zbMATHGoogle Scholar
  3. 3.
    Beg, M.F., Miller, M.I., Trouvé, A., Younes, L.: Computing large deformation metric mappings via geodesic flows of diffeomorphisms. Int. J. Comput. Vis. 61(2), 139–157 (2005)CrossRefGoogle Scholar
  4. 4.
    Cai, J.F., Candès, E.J., Shen, Z.: A singular value thresholding algorithm for matrix completion. SIAM J. Optim. 20(4), 1956–1982 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Khesin, B., Lenells, J., Misiołek, G., Preston, S.C.: Geometry of diffeomorphism groups, complete integrability and geometric statistics. Geom. Funct. Anal. 23(1), 334–366 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Li, R., Lewis, J.H., Jia, X., Zhao, T., Liu, W., Wuenschel, S., Lamb, J., Yang, D., Low, D.A., Jiang, S.B.: On a PCA-based lung motion model. Phys. Med. Biol. 56(18), 6009–6030 (2011)CrossRefGoogle Scholar
  7. 7.
    Modin, K.: Generalized hunter-saxton equations, optimal information transport, and factorization of diffeomorphisms. J. Geom. Anal. 25(2), 1306–1334 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Preston, J., Hinkle, J., Singh, N., Rottman, C., Joshi, S.: PyCA: Python for Computational Anatomy.
  9. 9.
    Recht, B., Fazel, M., Parrilo, P.A.: Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization. SIAM Rev. 52(3), 471–501 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Rottman, C., Bauer, M., Modin, K., Joshi, S.C.: Weighted diffeomorphic density matching with applications to thoracic image registration. In: 5th MICCAI Workshop on Mathematical Foundations of Computational Anatomy (MFCA 2015), pp. 1–12 (2015)Google Scholar
  11. 11.
    Rottman, C., Larson, B., Sabouri, P., Sawant, A., Joshi, S.: Diffeomorphic density registration in thoracic computed tomography. In: Ourselin, S., Joskowicz, L., Sabuncu, M.R., Unal, G., Wells, W. (eds.) MICCAI 2016. LNCS, vol. 9902, pp. 46–53. Springer, Cham (2016). doi: 10.1007/978-3-319-46726-9_6 CrossRefGoogle Scholar
  12. 12.
    Sabouri, P., Foote, M., Ranjbar, M., Tajdini, M., Mossahebi, S., Joshi, S., Sawant, A.: A novel method using surface monitoring to capture breathing-induced cycle-to-cycle variations with 4DCT. In: 59th Annual Meeting of The American Association of Physicists in Medicine. Denver, CO (2017)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Markus Foote
    • 1
    Email author
  • Pouya Sabouri
    • 2
  • Amit Sawant
    • 2
  • Sarang Joshi
    • 1
  1. 1.Department of Bioengineering, Scientific Computing and Imaging InstituteUniversity of UtahSalt Lake CityUSA
  2. 2.University of Maryland School of MedicineBaltimoreUSA

Personalised recommendations