Advertisement

A Novel Similarity Measure for Image Sequences

  • Kai BrehmerEmail author
  • Benjamin Wacker
  • Jan Modersitzki
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10883)

Abstract

Quantification of image similarity is a common problem in image processing. For pairs of two images, a variety of options is available and well-understood. However, some applications such as dynamic imaging or serial sectioning involve the analysis of image sequences and thus require a simultaneous and unbiased comparison of many images.

This paper proposes a new similarity measure, that takes a global perspective and involves all images at the same time. The key idea is to look at Schatten-q-norms of a matrix assembled from normalized gradient fields of the image sequence. In particular, for \(q=0\), the measure is minimized if the gradient information from the image sequence has a low rank.

This global perspective of the novel \(\mathrm {S}q\mathrm {N}\)-measure does not only allow to register sequences from dynamic imaging, e.g. DCE-MRI, but is also a new opportunity to simultaneously register serial sections, e.g. in histology. In this way, an accumulation of small, local registration errors may be avoided.

First numerical experiments show very promising results for a DCE-MRI sequence of a human kidney as well as for a set of serial sections. The global structure of the data used for registration with \(\mathrm {S}q\mathrm {N}\) is preserved in all cases.

Notes

Acknowledgement

The authors acknowledge the financial support by the Federal Ministry of Education and Research of Germany in the framework of MED4D (project number 05M16FLA).

References

  1. 1.
    Fischer, B., Modersitzki, J.: Curvature based image registration. J. Math. Imaging Vis. 18(1), 81–85 (2003)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Candes, E.J., Wakin, M.B., Boyd, S.: Enhancing sparsity by reweighted \(l_{1}\) minimization. J. Fourier Anal. Appl. 14(5), 877–905 (2008)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Gaffling, S., Daum, V., Hornegger, J.: Landmark-constrained 3-D histological imaging: a morphology-preserving approach. In: VMV, pp. 309–316 (2011)Google Scholar
  4. 4.
    Golub, G.H., Van Loan, C.F.: Matrix Computations, vol. 3. JHU Press, Baltimore (2012)zbMATHGoogle Scholar
  5. 5.
    Guyader, J.M., et al.: Total correlation-based groupwise image registration for quantitative MRI. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Workshops, pp. 186–193 (2016)Google Scholar
  6. 6.
    Haber, E., Modersitzki, J.: Beyond Mutual Information: a simple and robust alternative. In: Meinzer, H.P., Handels, H., Horsch, A., Tolxdorff, T. (eds.) Bildverarbeitung für die Medizin 2005. Informatik aktuell, pp. 350–354. Springer, Heidelberg (2005).  https://doi.org/10.1007/3-540-26431-0_72CrossRefGoogle Scholar
  7. 7.
    Heck, C., Ruthotto, L., Modersitzki, J., Berkels, B.: Model-based parameterestimation in DCE-MRI without an Arterial input function. In: Deserno, T.M., Handels, H., Meinzer, H.-P., Tolxdorff, T. (eds.) Bildverarbeitung für die Medizin 2014. I, pp. 246–251. Springer, Heidelberg (2014).  https://doi.org/10.1007/978-3-642-54111-7_47CrossRefGoogle Scholar
  8. 8.
    Heck, C., Benning, M., Modersitzki, J.: Joint registration and parameter estimation of T1 relaxation times using variable flip angles. In: Handels, H., Deserno, T.M., Meinzer, H.-P., Tolxdorff, T. (eds.) Bildverarbeitung für die Medizin 2015. I, pp. 215–220. Springer, Heidelberg (2015).  https://doi.org/10.1007/978-3-662-46224-9_38CrossRefGoogle Scholar
  9. 9.
    Hodneland, E., et al.: Segmentation-driven image registration-application to 4D DCE-MRI recordings of the moving kidneys. IEEE Trans. Image Process. 23(5), 2392–2404 (2014)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Huizinga, W., et al.: PCA-based groupwise image registration for quantitative MRI. Med. Image Anal. 29, 65–78 (2016)CrossRefGoogle Scholar
  11. 11.
    Lotz, J., Berger, J., Müller, B., Breuhahn, K., et al.: Zooming in: high resolution 3D reconstruction of differently stained histological whole slide images, medical imaging 2014: digital pathology 9041: 904104. International Society for Optics and Photonics (2014)Google Scholar
  12. 12.
    Modersitzki, J.: Numerical Methods for Image Registration. Oxford University Press, Oxford (2004)zbMATHGoogle Scholar
  13. 13.
    Modersitzki, J.: FAIR: flexible algorithms for image registration. Society for Industrial and Applied Mathematics (2009)Google Scholar
  14. 14.
    Möllenhoff, T., Strekalovskiy, E., Moeller, M., Cremers, D.: Low rank priors for color image regularization. In: Tai, X.-C., Bae, E., Chan, T.F., Lysaker, M. (eds.) EMMCVPR 2015. LNCS, vol. 8932, pp. 126–140. Springer, Cham (2015).  https://doi.org/10.1007/978-3-319-14612-6_10CrossRefGoogle Scholar
  15. 15.
    Nocedal, J., Wright, S.J.: Numerical Optimization, 2nd edn. Springer, New York (2006).  https://doi.org/10.1007/978-0-387-40065-5CrossRefzbMATHGoogle Scholar
  16. 16.
    Polfliet, M., et al.: Laplacian Eigenmaps for multimodal groupwise image registration. Medical Imaging 2017: Image Processing 10133: 101331N, International Society for Optics and Photonics (2017)Google Scholar
  17. 17.
    Sotiras, A., Davatzikos, C., Paragios, N.: Deformable medical image registration: a survey. IEEE Trans. Med. Imaging 32(7), 1153–1190 (2013)CrossRefGoogle Scholar
  18. 18.
    Sourbron, S.P., Buckley, D.L.: Classic models for dynamic contrast-enhanced MRI. NMR Biomed. 26(8), 1004–1027 (2013)CrossRefGoogle Scholar
  19. 19.
    Schmitt, O.: Die multimodale Architektonik des menschlichen Gehirns, Habilitation, Institute of Anatomy, Medical University of Lübeck (2001)Google Scholar
  20. 20.
    Streicher, J., Weninger, W.J., Müller, G.B.: External marker-based automatic congruencing: a new method of 3D reconstruction from serial sections. Anat. Rec. 248(4), 583–602 (1997)CrossRefGoogle Scholar
  21. 21.
    Tao, Q., et al.: Robust motion correction for myocardial T1 and extracellular volume mapping by principle component analysis-based groupwise image registration. J. Magn. Reson. Imaging 47(5), 1397–1405 (2017). Wiley Online LibraryCrossRefGoogle Scholar
  22. 22.
    Viola, P., Wells III, W.M.: Alignment by maximization of mutual information. Int. J. Comput. Vis. 24(2), 137–154 (1997)CrossRefGoogle Scholar
  23. 23.
    Wang, C.-W., Gosno, E.B., Li, Y.-S.: Fully automatic and robust 3D registration of serial-section microscopic images. Sci. Rep. 5, 15051 (2015). Nature Publishing GroupCrossRefGoogle Scholar
  24. 24.
    Watrous, J.: Theory of Quantum Information, 2.3 Norms of operators, Lecture Notes, University of Waterloo (2011)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Kai Brehmer
    • 1
    Email author
  • Benjamin Wacker
    • 1
  • Jan Modersitzki
    • 1
    • 2
  1. 1.Institute of Mathematics and Image ComputingUniversity of LübeckLübeckGermany
  2. 2.Fraunhofer MEVISLübeckGermany

Personalised recommendations