An algorithm for reconstructing convex bodies from their projections
Discrete & Computational Geometry
Sets uniquely determined by projections on Axes I. continuous case
SIAM Journal on Applied Mathematics
American Mathematical Monthly
Generating convex polyominoes at random
FPSAC '93 Proceedings of the 5th conference on Formal power series and algebraic combinatorics
Approximating Binary Images from Discrete X-Rays
SIAM Journal on Optimization
Stability and Instability in Discrete Tomography
Digital and Image Geometry, Advanced Lectures [based on a winter school held at Dagstuhl Castle, Germany in December 2000]
Theoretical Computer Science
An algorithm reconstructing convex lattice sets
Theoretical Computer Science
Random generation of Q-convex sets
Theoretical Computer Science
Discrete Q-convex sets reconstruction from discrete point X-rays
IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
On the stability of reconstructing lattice sets from x-rays along two directions
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
Uniqueness in Discrete Tomography: Three Remarks and a Corollary
SIAM Journal on Discrete Mathematics
Discrete tomography for inscribable lattice sets
Discrete Applied Mathematics
Bounds on the quality of reconstructed images in binary tomography
Discrete Applied Mathematics
Hi-index | 0.00 |
The problem of reconstructing finite subsets of the integer lattice from X-rays has been studied in discrete mathematics and applied in several fields like data security, electron microscopy, and medical imaging. In this paper, we focus on the stability of the reconstruction problem for some special lattice sets. First we prove that if the sets are additive, then a stability result holds for very small errors. Then, we study the stability of reconstructing convex sets from both an experimental and a theoretical point of view. Numerical experiments are conducted by using linear programming and they support the conjecture that convex sets are additive with respect to a set of suitable directions. Consequently, the reconstruction problem is stable. The theoretical investigation provides a stability result for convex lattice sets. This result permits to address the problem proposed by Hammer (in: Convexity, vol. VII, Proceedings of the Symposia in Pure Mathematics, American Mathematical Society, Providence, RI, 1963, pp. 498-499).