Skip to main content
SpringerLink
Log in
Book cover

International Conference on Scale Space and Variational Methods in Computer Vision

SSVM 2015: Scale Space and Variational Methods in Computer Vision pp 348–359Cite as

Nonlocal Joint Segmentation Registration Model

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 9087))

Abstract

In this paper, we address the issue of designing a theoretically well-motivated joint segmentation-registration method capable of handling large deformations. The shapes to be matched are implicitly modeled by level set functions and are evolved in order to minimize a functional containing both a nonlinear-elasticity-based regularizer and a criterion that forces the evolving shape to match intermediate topology-preserving segmentation results. Theoretical results encompassing existence of minimizers, \(\varGamma \)-convergence result and existence of a weak viscosity solution of the related evolution problem are provided.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aubert, G., Kornprobst, P.: Mathematical Problems in Image processing: Partial Differential Equations and the Calculus of Variations. Applied Mathematical Sciences., vol. 147. Springer, New York (2001)

    Google Scholar 

  2. Barles, G., Cardaliaguet, P., Ley, O., Monteillet, A.: Existence of weak solutions for general nonlocal and nonlinear second-order parabolic equations. Nonlinear Anal-Theor. 71(7–8), 2801–2810 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  3. Bourgoing, M.: Viscosity solutions of fully nonlinear second order parabolic equations with \(L^1\)-time dependence and Neumann boundary conditions. Discrete Contin. Dyn. S. 21(3), 763–800 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  4. Bousselsal, M.: Étude de Quelques Problèmes de Calcul des Variations Liés à la Mécanique. PhD Thesis, University of Metz, France (1993)

    Google Scholar 

  5. Brezis, H.: Analyse fonctionelle. Dunod, Théorie et Applications (2005)

    Google Scholar 

  6. Broit, C.: Registration of Deformed Images. PhD Thesis, University of Pennsylvania, USA (1981)

    Google Scholar 

  7. Burger, M., Modersitzki, J., Ruthotto, L.: A hyperelastic regularization energy for image registration. SIAM J. Sci. Comput. 35(1), B132–B148 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  8. Caselles, V., Kimmel, R., Sapiro, G.: Geodesic Active Contours. Int. J. Comput. Vis. 22(1), 61–87 (1993)

    Article  Google Scholar 

  9. Chan, T., Vese, L.: Active Contours Without Edges. IEEE T. Image Process. 10(2), 266–277 (2001)

    Article  MATH  Google Scholar 

  10. Ciarlet, P.G.: Elasticité Tridimensionnelle. Masson (1985)

    Google Scholar 

  11. Crandall, M.G., Ishii, H., Lions, P.-L.: User’s guide to viscosity solutions of second order partial differential equations. Bull. Amer. Math. Soc. 27, 1–67 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  12. Dacorogna, B.: Direct Methods in the Calculus of Variations. Applied Mathematical Sciences, vol. 78, 2nd edn. Springer, New York (2008)

    MATH  Google Scholar 

  13. Derfoul, R., Le Guyader, C.: A relaxed problem of registration based on the Saint Venant-Kirchhoff material stored energy for the mapping of mouse brain gene expression data to a neuroanatomical mouse atlas. SIAM J. Imaging Sci. 7(4), 2175–2195 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  14. Droske, M., Rumpf, M.: Multiscale joint segmentation and registration of image morphology. IEEE T. Pattern Anal. 29(12), 2181–2194 (2007)

    Article  Google Scholar 

  15. Forcadel, N., Le Guyader, C.: A short time existence/uniqueness result for a nonlocal topology-preserving segmentation model. J. Differ. Equations. 253(3), 977–995 (2012)

    Article  MATH  Google Scholar 

  16. Le Guyader, C., Vese, L.: Self-repelling snakes for topology-preserving segmentation models. IEEE T. Image Process. 17(5), 767–779 (2008)

    Article  Google Scholar 

  17. Le Guyader, C., Vese, L.: A combined segmentation and registration framework with a nonlinear elasticity smoother. Comput. Vis. Image Und. 115(12), 1689–1709 (2011)

    Article  Google Scholar 

  18. Lord, N.A., Ho, J., Vemuri, B.C., Eisenschenk, S.: Simultaneous Registration and Parcellation of Bilateral Hippocampal Surface Pairs for Local Asymmetry Quantification. IEEE Trans. Med. Imaging. 26(4), 471–478 (2007)

    Article  Google Scholar 

  19. Marrero-Negrón, P.V.: A numerical method for detecting singular minimizers of multidimensional problems in nonlinear elasticity. Numer. Math. 58, 135–144 (1990)

    Article  MathSciNet  Google Scholar 

  20. Ozeré, S., Gout, C., Le Guyader, C.: Joint segmentation/registration model by shape alignment via weighted total variation minimization and nonlinear elasticity. Under revision (2015)

    Google Scholar 

  21. Sotiras, A., Davatzikos, C., Paragios, N.: Deformable medical image registration: A survey. IEEE T. Med. Imaging. 32, 1153–1190 (2013)

    Article  Google Scholar 

  22. Vemuri, B., Ye, J., Chen, Y., Leonard, C.: Image Registration via level-set motion: Applications to atlas-based segmentation. Med. Image Anal. 7(1), 1–20 (2003)

    Article  Google Scholar 

  23. Weickert, J., Kühne, G.: Fast methods for implicit active contour models. In: Osher, S., Paragios, N. (eds.) Geometric Level Set Methods in Imaging, Vision, and Graphics, 43–57. Springer, New York (2003)

    Google Scholar 

  24. Yezzi, A., Zollei, L., Kapur, T.: A variational framework for joint segmentation and registration. In: IEEE Workshop on Mathematical Methods in Biomedical Image Analysis (MMBIA), pp. 44–51. IEEE (2001)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire de Mathématiques, Normandie Université, INSA de Rouen, 685 avenue de l’Université, 76801, Saint-Etienne-du-Rouvray Cedex, France

    Solène Ozeré & Carole Le Guyader

Authors
  1. Solène Ozeré
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Carole Le Guyader
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Carole Le Guyader .

Editor information

Editors and Affiliations

  1. University of Bordeaux, Talence, France

    Jean-François Aujol

  2. ENS Cachan, Cachan, France

    Mila Nikolova

  3. University of Bordeaux, Talence, France

    Nicolas Papadakis

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Ozeré, S., Le Guyader, C. (2015). Nonlocal Joint Segmentation Registration Model. In: Aujol, JF., Nikolova, M., Papadakis, N. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2015. Lecture Notes in Computer Science(), vol 9087. Springer, Cham. https://doi.org/10.1007/978-3-319-18461-6_28

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-18461-6_28

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-18460-9

  • Online ISBN: 978-3-319-18461-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation