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Journal of Mathematical Imaging and Vision

, Volume 49, Issue 2, pp 335–351 | Cite as

Efficient Binary Tomographic Reconstruction

  • Stéphane RouxEmail author
  • Hugo Leclerc
  • François Hild
Article

Abstract

Tomographic reconstruction of a binary image from few projections is considered. A novel heuristic algorithm is proposed, the central element of which is a nonlinear transformation ψ(p)=log(p/(1−p)) of the probability p that a pixel of the sought image be 1-valued. It consists of backprojections based on ψ(p) and iterative corrections. Application of this algorithm to a series of artificial test cases leads to exact binary reconstructions, (i.e., recovery of the binary image for each single pixel) from the knowledge of projection data over a few directions. Images up to 106 pixels are reconstructed in a few seconds. A series of test cases is performed for comparison with previous methods, showing a better efficiency and reduced computation times.

Keywords

Tomographic reconstruction Discrete reconstruction Binary reconstruction Binary image 

Notes

Acknowledgements

Communication of the raw tomographic data shown in Fig. 4 by E. Gouillart (CNRS/Saint-Gobain, Aubervilliers, France) and C. Zang (RWTH, Aachen, Germany) is gratefully acknowledged. We are also indebted to E. Gouillart for the suggestion that boundary sites may be an appropriate measure of complexity as proposed in Ref. [24]. We also thank an anonymous reviewer for interesting and constructive remarks. This work is supported by the French Agence Nationale de la Recherche through “RUPXCUBE” (ANR-09-BLAN-0009-01) and “EDDAM” (ANR-11-BS09-027) projects.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.LMT-Cachan (ENS de Cachan/CNRS/UPMC/PRES UniverSud Paris)CachanFrance

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