Fast filling operations used in the reconstruction of convex lattice sets

Authors:
Sara Brunetti;Alain Daurat;Attila Kuba
Affiliations:
Dipartimento di Scienze Matematiche e Informatiche, Università di Siena, Siena, Italy;LSIIT CNRS UMR 7005, Université Louis Pasteur (Strasbourg 1), Illkirch-Graffenstaden, France;Department of Image Processing and Computer Graphics, University of Szeged, Szeged, Hungary
Venue:
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Year:
2006

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Abstract

Filling operations are procedures which are used in Discrete Tomography for the reconstruction of lattice sets having some convexity constraints In [1], an algorithm which performs four of these filling operations has a time complexity of O(N2logN), where N is the size of projections, and leads to a reconstruction algorithm for convex polyominoes running in O(N6 logN)-time In this paper we first improve the implementation of these four filling operations to a time complexity of O(N2), and additionally we provide an implementation of a fifth filling operation (introduced in [2]) in O(N2logN) that permits to decrease the overall time-complexity of the reconstruction algorithm to O(N4logN) More generally, the reconstruction of Q-convex sets and convex lattice sets (intersection of a convex polygon with ℤ2) can be done in O(N4logN)-time.