Finding minimum-cost circulations by successive approximation
Mathematics of Operations Research
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Computational geometry in C
The discrete Radon transform and its approximate inversion via linear programming
Discrete Applied Mathematics
On the computational complexity of reconstructing lattice sets from their x-rays
Discrete Mathematics
The mathematics of computerized tomography
The mathematics of computerized tomography
Principles of computerized tomographic imaging
Principles of computerized tomographic imaging
Discrete tomography by convex-concave regularization and D.C. programming
Discrete Applied Mathematics - Special issue: IWCIA 2003 - Ninth international workshop on combinatorial image analysis
Advances in Discrete Tomography and Its Applications (Applied and Numerical Harmonic Analysis)
Advances in Discrete Tomography and Its Applications (Applied and Numerical Harmonic Analysis)
A Network Flow Algorithm for Reconstructing Binary Images from Discrete X-rays
Journal of Mathematical Imaging and Vision
Binary tomography by iterating linear programs from noisy projections
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
Adaptive thresholding of tomograms by projection distance minimization
Pattern Recognition
Grey level estimation for discrete tomography
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
A semi-automatic algorithm for grey level estimation in tomography
Pattern Recognition Letters
A method for feature detection in binary tomography
DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
Bounds on the quality of reconstructed images in binary tomography
Discrete Applied Mathematics
Approximate Discrete Reconstruction Algorithm
Fundamenta Informaticae - Strategies for Tomography
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Tomography is a powerful technique to obtain accurate images of the interior of an object in a nondestructive way. Conventional reconstruction algorithms, such as filtered backprojection, require many projections to obtain high quality reconstructions. If the object of interest is known in advance to consist of only a few different materials, corresponding to known image intensities, the use of this prior knowledge in the reconstruction procedure can dramatically reduce the number of required projections.In previous work we proposed a network flow algorithm for reconstructing a binary image defined on a lattice from its projections. In this paper we propose a new algorithm for the reconstruction of binary images that do not have an intrinsic lattice structure and are defined on a continuous domain, from a small number of their projections.Our algorithm relies on the fact that the problem of reconstructing an image from only two projections can be formulated as a network flow problem in a graph. We derive this formulation for parallel beam and fan beam tomography and show how it can be used to compute binary reconstructions from more than two projections.Our algorithm is capable of computing high quality reconstructions from very few projections. We evaluate its performance on both simulated and real experimental projection data and compare it to other reconstruction algorithms.