Generating convex polyominoes at random
FPSAC '93 Proceedings of the 5th conference on Formal power series and algebraic combinatorics
Reconstructing convex polyominoes from horizontal and vertical projections
Theoretical Computer Science
Reconstructing hv-convex polyominoes from orthogonal projections
Information Processing Letters
The reconstruction of polyominoes from their orthogonal projections
Information Processing Letters
Reconstruction of hv-convex binary matrices from their absorbed projections
Discrete Applied Mathematics - The 2001 international workshop on combinatorial image analysis (IWCIA 2001)
Advances in Discrete Tomography and Its Applications (Applied and Numerical Harmonic Analysis)
Advances in Discrete Tomography and Its Applications (Applied and Numerical Harmonic Analysis)
A decomposition technique for reconstructing discrete sets from four projections
Image and Vision Computing
An evolutionary algorithm for discrete tomography
Discrete Applied Mathematics - Special issue: IWCIA 2003 - Ninth international workshop on combinatorial image analysis
Optimization and reconstruction of hv-convex (0,1)-matrices
Discrete Applied Mathematics - Special issue: IWCIA 2003 - Ninth international workshop on combinatorial image analysis
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One of the basic problems in discrete tomography is the reconstruction of discrete sets from few projections. Assuming that the set to be reconstructed fulfils some geometrical properties is a commonly used technique to reduce the number of possibly many different solutions of the same reconstruction problem. Since the reconstruction from two projections in the class of so-called hv-convex sets is NP-hard this class is suitable to test the efficiency of newly developed reconstruction algorithms. However, until now no method was known to generate sets of this class from uniform random distribution and thus only ad hoc comparison of several reconstruction techniques was possible. In this paper we first describe a method to generate some special hv-convex discrete sets from uniform random distribution. Moreover, we show that the developed generation technique can easily be adapted to other classes of discrete sets, even for the whole class of hv-convexes. Several statistics are also presented which are of great importance in the analysis of algorithms for reconstructing hv-convex sets.