Abstract
Enumeration and reconstruction of certain types of polyominoes, according to several parameters, are frequently studied problems in combinatorial image processing. Polyominoes with fixed projections play an important role in discrete tomography. In this paper, we provide a linear-time algorithm for reconstructing hv-convex polyominoes with minimal number of columns satisfying a given horizontal projection. The method can be easily modified to get solutions with any given number of columns. We also describe a direct formula for calculating the number of solutions with any number of columns, and a recursive formula for fixed number of columns.
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This work was supported by the OTKA PD100950 grant of the National Scientific Research Fund. The research was also supported by the European Union and the State of Hungary, co-financed by the European Social Fund in the framework of TÁMOP 4.2.4. A/2-11-1-2012-0001 ’National Excellence Program’, and under the grant agreement TÁMOP-4.2.2.A-11/1/KONV-2012-0073 ’Telemedicine-focused research activities on the field of Mathematics, Informatics and Medical sciences’.
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Hantos, N., Balázs, P. (2013). Reconstruction and Enumeration of hv-Convex Polyominoes with Given Horizontal Projection. In: Ruiz-Shulcloper, J., Sanniti di Baja, G. (eds) Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications. CIARP 2013. Lecture Notes in Computer Science, vol 8258. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41822-8_13
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DOI: https://doi.org/10.1007/978-3-642-41822-8_13
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