Skip to main content
SpringerLink
Log in
Book cover

International Workshop on Graph-Based Representations in Pattern Recognition

GbRPR 2019: Graph-Based Representations in Pattern Recognition pp 204–214Cite as

Reconstructing Objects from Noisy Images at Low Resolution

  • 696 Accesses

Part of the Lecture Notes in Computer Science book series (LNIP,volume 11510)

Abstract

We study the problem of reconstructing small objects from their low-resolution images, by modelling them as r-regular objects. Previous work shows how the boundary constraints imposed by r-regularity allows bounds on estimation error for noise-free images. In order to utilize this for noisy images, this paper presents a graph-based framework for reconstructing noise-free images from noisy ones. We provide an optimal, but potentially computationally demanding algorithm, as well as a greedy heuristic for reconstructing noise-free images of r-regular objects from images with noise.

Keywords

  • Object reconstruction
  • r-regularity

This research was supported by Centre for Stochastic Geometry and Advanced Bioimaging, funded by a grant from the Villum Foundation. The authors thank François Lauze and Pawel Winter for valuable discussions.

This is a preview of subscription content, access via your 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 EPUB and 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

References

  1. Caselles, V., Kimmel, R., Sapiro, G.: Geodesic active contours. Int. J. Comput. Vis. 22(1), 61–79 (1997)

    CrossRef  Google Scholar 

  2. Chan, T., Vese, L.: Active contours without edges. IEEE TIP 10(2), 266–277 (2001)

    MATH  Google Scholar 

  3. Cootes, T.F., Taylor, C.J.: Active shape models - “smart snakes”. In: Hogg, D., Boyle, R. (eds.) BMVC92. Springer, London (1992). https://doi.org/10.1007/978-1-4471-3201-1_28

    CrossRef  Google Scholar 

  4. Duarte, P., Torres, M.J.: Smoothness of boundaries of regular sets. J. Math. Imaging Vis. 48(1), 106–113 (2014)

    CrossRef  MathSciNet  Google Scholar 

  5. Geman, S., Geman, D.: Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. TPAMI 6(6), 721–741 (1984)

    CrossRef  Google Scholar 

  6. Kass, M., Witkin, A., Terzopoulos, D.: Snakes: active contour models. IJCV 1(4), 321–331 (1988)

    CrossRef  Google Scholar 

  7. Latecki, L., Conrad, C., Gross, A.: Preserving topology by a digitization process. J. Math. Imaging Vis. 8, 131–159 (1998)

    CrossRef  MathSciNet  Google Scholar 

  8. Litjens, G., et al.: A survey on deep learning in medical image analysis. MedIA 42, 60–88 (2017)

    Google Scholar 

  9. Mumford, D., Shah, J.: Optimal approximations by piecewise smooth functions and associated variational problems. Comm. Pure Appl. Math. 42, 577–684 (1989)

    CrossRef  MathSciNet  Google Scholar 

  10. Pavlidis, T.: Algorithms for Graphics and Image Processing. Digital System Design Series. Springer, Heidelberg (1982). https://doi.org/10.1007/978-3-642-93208-3

    CrossRef  MATH  Google Scholar 

  11. Ronse, C., Tajine, M.: Discretization in Hausdorff space. J. Math. Imaging Vis. 12(3), 219–242 (2000)

    CrossRef  MathSciNet  Google Scholar 

  12. SDSS, S.D.S.S. https://www.sdss.org

  13. Serra, J.: Image Analysis and Mathematical Morphology. Academic Press Inc., Orlando (1983)

    Google Scholar 

  14. Stelldinger, P., Köthe, U.: Shape preservation during digitization: tight bounds based on the morphing distance. In: Michaelis, B., Krell, G. (eds.) DAGM 2003. LNCS, vol. 2781, pp. 108–115. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-540-45243-0_15

    CrossRef  Google Scholar 

  15. Stelldinger, P., Köthe, U.: Towards a general sampling theory for shape preservation. Image Vision Comput. 23(2), 237–248 (2005)

    CrossRef  Google Scholar 

  16. Svane, H., du Plessis, A.: Reconstruction of r-regular objects from trinary images, to be published in Ph.D thesis of H. Svane (2019). Until then available on Arxiv

    Google Scholar 

  17. V12.8.0, I.I.C.O.S. www.cplex.com

  18. Yezzi, A., Kichenassamy, S., Kumar, A., Olver, P., Tannenbaum, A.: A geometric snake model for segmentation of medical imagery. IEEE TMI 16(2), 199–209 (1997)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Aarhus University, Aarhus, Denmark

    Helene Svane

  2. Department of Computer Science (DIKU), University of Copenhagen, Copenhagen, Denmark

    Aasa Feragen

Authors
  1. Helene Svane
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Aasa Feragen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Helene Svane .

Editor information

Editors and Affiliations

  1. University of Tours, Tours, France

    Donatello Conte

  2. University of Tours, Tours, France

    Prof. Jean-Yves Ramel

  3. University of Salerno, Fisicano, Italy

    Pasquale Foggia

Rights and permissions

Reprints and Permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Svane, H., Feragen, A. (2019). Reconstructing Objects from Noisy Images at Low Resolution. In: Conte, D., Ramel, JY., Foggia, P. (eds) Graph-Based Representations in Pattern Recognition. GbRPR 2019. Lecture Notes in Computer Science(), vol 11510. Springer, Cham. https://doi.org/10.1007/978-3-030-20081-7_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-20081-7_20

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-20080-0

  • Online ISBN: 978-3-030-20081-7

  • eBook Packages: Computer ScienceComputer Science (R0)

search

Navigation