Three-Dimensional Statistical Data Security Problems
SIAM Journal on Computing
The number of convex polyominoes reconstructible from their orthogonal projections
Proceedings of the 6th conference on Formal power series and algebraic combinatorics
The discrete Radon transform and its approximate inversion via linear programming
Discrete Applied Mathematics
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]
On Stability, Error Correction, and Noise Compensation in Discrete Tomography
SIAM Journal on Discrete Mathematics
A reconstruction algorithm for L-convex polyominoes
Theoretical Computer Science - In honour of Professor Christian Choffrut on the occasion of his 60th birthday
Determination of Q-convex sets by X-rays
Theoretical Computer Science
Advances in Discrete Tomography and Its Applications (Applied and Numerical Harmonic Analysis)
Advances in Discrete Tomography and Its Applications (Applied and Numerical Harmonic Analysis)
Stability results for the reconstruction of binary pictures from two projections
Image and Vision Computing
Stability in Discrete Tomography: some positive results
Discrete Applied Mathematics - Special issue: Advances in discrete geometry and topology (DGCI 2003)
A tomographical characterization of l-convex polyominoes
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
| Hi-index | 0.04 |
In this paper we deal with uniqueness and reconstruction problems in Discrete Tomography. For a finite set D of directions in Z^2, we introduce the class of D-inscribable lattice sets, and give a detailed description of their geometric structure. This shows that such sets can be considered as the natural discrete counterpart of the same notion known in the continuous case, as well as a kind of generalization of the class of the so-called L-convex polyominoes (or moon polyominoes). In view of reconstruction from projections along the directions in D, two related questions of tomographic interest are investigated, namely uniqueness and additivity. We show that both properties are fulfilled by D-inscribable lattice sets. Moreover, concerning the case D={e"1,e"2}, we provide an explicit reconstruction algorithm from the knowledge of directed horizontal and vertical X-rays, jointly with a few preliminary results towards a possible sharp stability inequality.