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International Conference on Scale Space and Variational Methods in Computer Vision

SSVM 2017: Scale Space and Variational Methods in Computer Vision pp 396–407Cite as

Local Mean Multiphase Segmentation with HMMF Models

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Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10302))

Abstract

This paper presents two similar multiphase segmentation methods for recovery of segments in complex weakly structured images, with local and global bias fields, because they can occur in some X-ray CT imaging modalities. Derived from the Mumford-Shah functional, the proposed methods assume a fixed number of classes. They use local image average as discriminative features. Region labels are modelled by Hidden Markov Measure Field Models. The resulting problems are solved by straightforward alternate minimisation methods, particularly simple in the case of quadratic regularisation of the labels. We demonstrate the proposed methods’ capabilities on synthetic data using classical segmentation criteria as well as criteria specific to geoscience. We also present a few examples using real data.

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References

  1. Bertsekas, D.: Incremental proximal methods for large scale convex optimization. Math. Program. Ser. B. 129, 163–195 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  2. Brox, T., Cremers, D.: On local regions models and a statistical interpretation of the piecewise smooth Mumford-Shah functional. Int. J. Comput. Vis. 84, 184–193 (2009)

    Article  Google Scholar 

  3. Buzug, T.N.: Computed Tomography from Photon Statistics to Modern Cone Beam CT. Springer, Berlin (2008)

    Google Scholar 

  4. Chambolle, A., Cremers, D., Pock, T.: A convex approach to minimal partitions. SIAM J. Imaging Sci. 5(4), 1113–1158 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  5. Chan, T.F., Vese, L.A.: Active contours without edges. Trans. Image Process. 10(2), 266–277 (2001)

    Article  MATH  Google Scholar 

  6. Hansen, P.C., O’Leary, D.P.: The use of the L-curve in the regularization of discrete ill-posed problems. SIAM J. Sci. Comput. 14(6), 1487–1503 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  7. Held, M., Crowder, P.W.W.: Validation of subgradient optimization. Math. Program. 6, 62–88 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  8. Huang, C., Zeng, L.: An active contour model for the segmentation of images with intensity inhomogeneities and bias field estimation. PloS One 10(4), e0120399 (2015)

    Article  Google Scholar 

  9. Lauze, F., Nielsen, M.: From inpainting to active contours. Int. J. Comput. Vis. 79(1), 31–43 (2008)

    Article  MATH  Google Scholar 

  10. Marroquin, J.L., Santana, E.A., Botello, S.: Hidden Markov measure field models for image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 25(11), 1380–1387 (2003)

    Article  Google Scholar 

  11. Mumford, D., Shah, J.: Optimal approximations by piecewise smooth functions and associated variational problems. Commun. Pure Appl. Math. 42(5), 577–685 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  12. Müter, D., Pedersen, S., Sørensen, H.O., Feidenhans’L, R., Stipp, S.L.S.: Improved segmentation of X-ray tomography data from porous rocks using a dual filtering approach. Comput. Geosci. 49, 131–139 (2012)

    Article  Google Scholar 

  13. Müter, D., Sørensen, H.O., Jha, D., Harti, R., Dalby, K.N., Suhonen, H., Feidenhans, R., Engstrøm, F., Stipp, S.L.S.: Resolution dependence of petrophysical parameters derived from X-ray tomography of chalk. Appl. Phys. Lett. 105, 4 (2014)

    Article  Google Scholar 

  14. Nielsen, M., Florack, L., Deriche, R.: Regularization, scale-space, and edge detection filters. J. Math. Imaging Vis. 7, 291–307 (1997)

    Article  MathSciNet  Google Scholar 

  15. Pham, D.L., Prince, J.L.: Adaptive fuzzy segmentation of magnetic resonance images. IEEE Trans. Med. Imaging 18(9), 737–752 (1999)

    Article  Google Scholar 

  16. Wang, X.-F., Huang, D.-S., Xu, H.: An efficient local chan-vese model for image segmentation. Pattern Recognit. 43(3), 603–618 (2010)

    Article  MATH  Google Scholar 

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Acknowledgements

J. Hansen and F. Lauze acknowledge funding from the Innovation Fund Denmark and Mærsk Oil and Gas A/S, for the P\(^3\) Project. We thank Henning Osholm Sørensen for giving us access to the experimental tomography data.

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Authors and Affiliations

  1. Department of Computer Science, University of Copenhagen, Copenhagen, Denmark

    Jacob Daniel Kirstejn Hansen & François Lauze

Authors
  1. Jacob Daniel Kirstejn Hansen
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  2. François Lauze
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Corresponding author

Correspondence to Jacob Daniel Kirstejn Hansen .

Editor information

Editors and Affiliations

  1. University of Copenhagen , Copenhagen, Denmark

    François Lauze

  2. Technical University of Denmark , Kongens Lyngby, Denmark

    Yiqiu Dong

  3. Technical University of Denmark , Kongens Lyngby, Denmark

    Anders Bjorholm Dahl

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Hansen, J.D.K., Lauze, F. (2017). Local Mean Multiphase Segmentation with HMMF Models. In: Lauze, F., Dong, Y., Dahl, A. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2017. Lecture Notes in Computer Science(), vol 10302. Springer, Cham. https://doi.org/10.1007/978-3-319-58771-4_32

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  • DOI: https://doi.org/10.1007/978-3-319-58771-4_32

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-58770-7

  • Online ISBN: 978-3-319-58771-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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