An algorithm for reconstructing convex bodies from their projections
Discrete & Computational Geometry
Reconstructing convex polyominoes from horizontal and vertical projections
Theoretical Computer Science
An algorithm reconstructing convex lattice sets
Theoretical Computer Science
Random generation of Q-convex sets
Theoretical Computer Science
A decomposition technique for reconstructing discrete sets from four projections
Image and Vision Computing
Reconstruction of convex lattice sets from tomographic projections in quartic time
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
Fast filling operations used in the reconstruction of convex lattice sets
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Discrete tomography for inscribable lattice sets
Discrete Applied Mathematics
Discrete tomography determination of bounded lattice sets from four X-rays
Discrete Applied Mathematics
| Hi-index | 5.23 |
In this paper, the problem of the determination of lattice sets from X-rays is studied. We define the class of Q-convex sets along a set D of directions which generalizes classical lattice convexity and we prove that for any D, the X-rays along D determine all the convex sets if and only if it determines all the Q-convex sets along D. As a consequence, any algorithm which reconstructs Q-convex sets from X-rays can be used to reconstruct convex lattice sets from X-rays along directions which provide uniqueness. This gives a constructive answer to the discrete version of Hammer's X-ray problem.