Polyominoes defined by two vectors
Theoretical Computer Science
Generating convex polyominoes at random
FPSAC '93 Proceedings of the 5th conference on Formal power series and algebraic combinatorics
The number of convex polyominoes reconstructible from their orthogonal projections
Proceedings of the 6th conference on Formal power series and algebraic combinatorics
The reconstruction of polyominoes from their orthogonal projections
Information Processing Letters
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]
Reconstruction of 8-connected but not 4-connected hv-convex discrete sets
Discrete Applied Mathematics - Special issue: Advances in discrete geometry and topology (DGCI 2003)
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
The number of line-convex directed polyominoes having the same orthogonal projections
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
A benchmark set for the reconstruction of hv-convex discrete sets
Discrete Applied Mathematics
Generation and empirical investigation of hv-convex discrete sets
SCIA'07 Proceedings of the 15th Scandinavian conference on Image analysis
On the number of hv-convex discrete sets
IWCIA'08 Proceedings of the 12th international conference on Combinatorial image analysis
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Reconstructing binary matrices from their row, column, diagonal, and antidiagonal sums (also called projections) plays a central role in discrete tomography. One of the main difficulties in this task is that in certain cases the projections do not uniquely determine the binary matrix. This can yield an extremely large number of (sometimes very different) solutions. This ambiguity can be reduced by having some prior knowledge about the matrix to be reconstructed. The main challenge here is to find classes of binary matrices where ambiguity is drastically reduced or even completely eliminated. The goal of this paper is to study the class of hv-convex matrices which have decomposable configurations from the viewpoint of ambiguity. First, we give a negative result in the case of three projections. Then, we present a heuristic for the reconstruction using four projections and analyze its performance in quality and running time.