X-rays characterizing some classes of discrete sets

DOI10.1016/S0024-3795(01)00431-1zbMath0994.65142OpenAlexW2163145185MaRDI QIDQ5955122

Elena Barcucci, Renzo Pinzani, Alberto del Lungo, Maurice Nivat

Publication date: 29 September 2002

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0024-3795(01)00431-1

zbMATH Keywords

Radon transformreconstructioncomputational geometrydiscrete tomographyconvex polyominoesthree-dimensional structureX-rays

Mathematics Subject Classification ID

Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Radon transform (44A12) Numerical methods for integral transforms (65R10)

Related Items

On the geometric structure of lattice \(U\)-polygons ⋮ Discrete tomography determination of bounded lattice sets from four X-rays ⋮ Ghosts in discrete tomography ⋮ Characterization of hv-convex sequences ⋮ How many points can be reconstructed from k projections? ⋮ Approximating Bicolored Images from Discrete Projections ⋮ Convex decomposition of \(U\)-polygons ⋮ Determination of Q-convex sets by X-rays ⋮ Stability in discrete tomography: some positive results ⋮ On some geometric aspects of the class of \(hv\)-convex switching components ⋮ On the existence of \(U\)-polygons of class \(c\geq 4\) in planar point sets ⋮ Further steps on the reconstruction of convex polyominoes from orthogonal projections ⋮ Ambiguous reconstructions of hv-convex polyominoes ⋮ On the computational complexity of reconstructing lattice sets from their \(X\)-rays ⋮ An experimental study of the stability problem in discrete tomography ⋮ Unique reconstruction of bounded sets in discrete tomography

Uses Software

• POLYLAB

Cites Work

• Unnamed Item
• Reconstructing convex polyominoes from horizontal and vertical projections
• Reconstructing plane sets from projections
• Invariant sets of arcs in network flow problems
• Sets uniquely determined by projections on axes. II: Discrete case
• Switching components and the ambiguity problem in the reconstruction of pictures from their projections
• On the computational complexity of reconstructing lattice sets from their \(X\)-rays
• Polyominoes defined by two vectors
• The discrete Radon transform and its approximate inversion via linear programming
• Generating convex polyominoes at random
• The number of convex polyominoes reconstructible from their orthogonal projections
• Three-dimensional Statistical Data Security Problems
• Discrete tomography: Determination of finite sets by X-rays
• The reconstruction of binary patterns from their projections
• A Problem of Plane Measure

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