Reconstructing convex polyominoes from horizontal and vertical projections
Theoretical Computer Science
On the computational complexity of reconstructing lattice sets from their x-rays
Discrete Mathematics
On Stability, Error Correction, and Noise Compensation in Discrete Tomography
SIAM Journal on Discrete Mathematics
Advances in Discrete Tomography and Its Applications (Applied and Numerical Harmonic Analysis)
Advances in Discrete Tomography and Its Applications (Applied and Numerical Harmonic Analysis)
On the index of Siegel grids and its application to the tomography of quasicrystals
European Journal of Combinatorics
A method for feature detection in binary tomography
DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
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Discrete tomography is concerned with the reconstruction of images that are defined on a discrete set of lattice points from their projections in several directions. The range of values that can be assigned to each lattice point is typically a small discrete set. In this paper we present a framework for studying these problems from an algebraic perspective, based on ring theory and commutative algebra. A principal advantage of this abstract setting is that a vast body of existing theory becomes accessible for solving discrete tomography problems. We provide proofs of several new results on the structure of dependencies between projections, including a discrete analogon of the well-known Helgason-Ludwig consistency conditions from continuous tomography.