A Bibliography on Digital and Computational Convexity (1961-1988)
IEEE Transactions on Pattern Analysis and Machine Intelligence
Generating convex polyominoes at random
FPSAC '93 Proceedings of the 5th conference on Formal power series and algebraic combinatorics
A method for the enumeration of various classes of column-convex polygons
Discrete Mathematics
Reconstructing convex polyominoes from horizontal and vertical projections
Theoretical Computer Science
Computational geometry in C (2nd ed.)
Computational geometry in C (2nd ed.)
Simulation Modeling and Analysis
Simulation Modeling and Analysis
An algorithm reconstructing convex lattice sets
Theoretical Computer Science
Determination of Q-convex sets by X-rays
Theoretical Computer Science
A decomposition technique for reconstructing discrete sets from four projections
Image and Vision Computing
Theoretical Computer Science
Stability in Discrete Tomography: some positive results
Discrete Applied Mathematics - Special issue: Advances in discrete geometry and topology (DGCI 2003)
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
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The problem of randomly generating Q-convex sets is considered. We present two generators. The first one uses the Q-convex hull of a set of random points in order to generate a Q-convex set included in the square [0, n)2. This generator is very simple, but is not uniform and its performance is quadratic in n. The second one exploits a coding of the salient points, which generalizes the coding of a border of polyominoes. It is uniform, and is based on the method by rejection. Experimentally, this algorithm works in linear time in the length of the word coding the salient points. Besides, concerning the enumeration problem, we determine an asymptotic formula for the number of Q-convex sets according to the size of the word coding the salient points in a special case, and in general only an experimental estimation.