On Some Geometric Aspects of the Class of hv-Convex Switching Components

Abstract

In the usual aim of discrete tomography, the reconstruction of an unknown discrete set is considered, by means of projection data collected along a set U of discrete directions. Possible ambiguous reconstructions can arise if and only if switching components occur, namely, if and only if non-empty images exist having null projections along all the directions in U. In order to lower the number of allowed reconstructions, one tries to incorporate possible extra geometric constraints in the tomographic problem, such as the request for connectedness, or some reconstruction satisfying special convexity constraints. In particular, the class \(\mathbb {P}\) of horizontally and vertically convex connected sets (briefly, hv-convex polyominoes) has been largely considered.