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Image Reconstruction by Multilabel Propagation

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Scale Space and Variational Methods in Computer Vision (SSVM 2017)

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

Abstract

This work presents a non-convex variational approach to joint image reconstruction and labeling. Our regularization strategy, based on the KL-divergence, takes into account the smooth geometry on the space of discrete probability distributions. The proposed objective function is efficiently minimized via DC programming which amounts to solving a sequence of convex programs, with guaranteed convergence to a critical point. Each convex program is solved by a generalized primal dual algorithm. This entails the evaluation of a proximal mapping, evaluated efficiently by a fixed point iteration. We illustrate our approach on few key scenarios in discrete tomography and image deblurring.

Acknowledgments: We gratefully acknowledge support by the German Science Foundation, grant GRK 1653.

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References

  1. Hanke, R., Fuchs, T., Uhlmann, N.: X-ray based methods for non-destructive testing and material characterization. Nucl. Instrum. Methods Phys. Res. Sect. A: Accel. Spectrom. Detect. Assoc. Equip. 591(1), 14–18 (2008)

    Article  Google Scholar 

  2. Zach, C., Gallup, D., Frahm, J., Niethammer, M.: Fast global labeling for real-time stereo using multiple plane sweeps. In: VMV, pp. 243–252 (2008)

    Google Scholar 

  3. 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 

  4. Lellmann, J., Kappes, J., Yuan, J., Becker, F., Schnörr, C.: Convex multi-class image labeling by simplex-constrained total variation. In: Tai, X.-C., Mørken, K., Lysaker, M., Lie, K.-A. (eds.) SSVM 2009. LNCS, vol. 5567, pp. 150–162. Springer, Heidelberg (2009). doi:10.1007/978-3-642-02256-2_13

    Chapter  Google Scholar 

  5. Lellmann, J., Schnörr, C.: Continuous multiclass labeling approaches and algorithms. SIAM J. Imaging Sci. 4(4), 1049–1096 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  6. Åström, F., Petra, S., Schmitzer, B., Schnörr, C.: Image labeling by assignment. J. Math. Imaging Vis. 58, 1–28 (2017)

    Article  MathSciNet  Google Scholar 

  7. Bergmann, R., Fitschen, J.H., Persch, J., Steidl, G.: Iterative multiplicative filters for data labeling. Int. J. Comput. Vis., 1–19 (2017)

    Google Scholar 

  8. Martin, D., Fowlkes, C., Tal, D., Malik, J.: A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics. In: Proceedings of the ICCV, pp. 416–423 (2001)

    Google Scholar 

  9. Zisler, M., Kappes, J.H., Schnörr, C., Petra, S., Schnörr, C.: Non-binary discrete tomography by continuous non-convex optimization. IEEE Trans. Comput. Imaging 2(3), 335–347 (2016)

    Article  MathSciNet  Google Scholar 

  10. Zisler, M., Petra, S., Schnörr, C., Schnörr, C.: Discrete tomography by continuous multilabeling subject to projection constraints. In: Rosenhahn, B., Andres, B. (eds.) GCPR 2016. LNCS, vol. 9796, pp. 261–272. Springer, Cham (2016). doi:10.1007/978-3-319-45886-1_21

    Chapter  Google Scholar 

  11. Kass, R.E.: The geometry of asymptotic inference. Stat. Sci. 4(3), 188–234 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  12. Amari, S.I., Cichocki, A.: Information geometry of divergence functions. Bull. Pol. Acad. Sci.: Tech. Sci. 58(1), 183–195 (2010)

    Google Scholar 

  13. Potts, R.B.: Some generalized order-disorder transformations. Math. Proc. Camb. Philos. Soc. 48, 106–109 (1952)

    Article  MathSciNet  MATH  Google Scholar 

  14. Weinmann, A., Demaret, L., Storath, M.: Total variation regularization for manifold-valued data. SIAM J. Imaging Sci. 7(4), 2226–2257 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  15. Cover, T., Thomas, J.: Elements of Information Theory, 2nd edn. Wiley, Hoboken (2006)

    MATH  Google Scholar 

  16. Pham Dinh, T., El Bernoussi, S.: Algorithms for solving a class of nonconvex optimization problems. Methods of subgradients. In: Hiriart-Urruty, J.B. (ed.) Fermat Days 85: Mathematics for Optimization. North-Holland Mathematics Studies, vol. 129, pp. 249–271. North-Holland, Amsterdam (1986)

    Chapter  Google Scholar 

  17. Pham-Dinh, T., Hoai An, L.: Convex analysis approach to D.C. programming: theory, algorithms and applications. Acta Math. Vietnam. 22(1), 289–355 (1997)

    MathSciNet  MATH  Google Scholar 

  18. Rockafellar, R.T., Wets, R.J.B.: Variational Analysis. Springer, Heidelberg (2009)

    MATH  Google Scholar 

  19. Chambolle, A., Pock, T.: On the ergodic convergence rates of a first-order primal-dual algorithm. Math. Program. 159(1), 253–287 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  20. Batenburg, K., Sijbers, J.: DART: a practical reconstruction algorithm for discrete tomography. IEEE Trans. Image Process. 20(9), 2542–2553 (2011)

    Article  MathSciNet  Google Scholar 

  21. Varga, L., Balázs, P., Nagy, A.: An energy minimization reconstruction algorithm for multivalued discrete tomography. In: 3rd International Symposium on Computational Modeling of Objects Represented in Images, Italy, pp. 179–185 (2012)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Image and Pattern Analysis Group, Heidelberg University, Heidelberg, Germany

    Matthias Zisler, Freddie Åström & Christoph Schnörr

  2. Mathematical Imaging Group, Heidelberg University, Heidelberg, Germany

    Stefania Petra

Authors
  1. Matthias Zisler
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  2. Freddie Åström
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  3. Stefania Petra
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  4. Christoph Schnörr
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Corresponding author

Correspondence to Matthias Zisler .

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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Zisler, M., Åström, F., Petra, S., Schnörr, C. (2017). Image Reconstruction by Multilabel Propagation. 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_20

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  • DOI: https://doi.org/10.1007/978-3-319-58771-4_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-58770-7

  • Online ISBN: 978-3-319-58771-4

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