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.
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, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Caselles, V., Kimmel, R., Sapiro, G.: Geodesic active contours. Int. J. Comput. Vis. 22(1), 61–79 (1997)
Chan, T., Vese, L.: Active contours without edges. IEEE TIP 10(2), 266–277 (2001)
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
Duarte, P., Torres, M.J.: Smoothness of boundaries of regular sets. J. Math. Imaging Vis. 48(1), 106–113 (2014)
Geman, S., Geman, D.: Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. TPAMI 6(6), 721–741 (1984)
Kass, M., Witkin, A., Terzopoulos, D.: Snakes: active contour models. IJCV 1(4), 321–331 (1988)
Latecki, L., Conrad, C., Gross, A.: Preserving topology by a digitization process. J. Math. Imaging Vis. 8, 131–159 (1998)
Litjens, G., et al.: A survey on deep learning in medical image analysis. MedIA 42, 60–88 (2017)
Mumford, D., Shah, J.: Optimal approximations by piecewise smooth functions and associated variational problems. Comm. Pure Appl. Math. 42, 577–684 (1989)
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
Ronse, C., Tajine, M.: Discretization in Hausdorff space. J. Math. Imaging Vis. 12(3), 219–242 (2000)
SDSS, S.D.S.S. https://www.sdss.org
Serra, J.: Image Analysis and Mathematical Morphology. Academic Press Inc., Orlando (1983)
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
Stelldinger, P., Köthe, U.: Towards a general sampling theory for shape preservation. Image Vision Comput. 23(2), 237–248 (2005)
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
V12.8.0, I.I.C.O.S. www.cplex.com
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)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
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)
