Tomographical aspects of 2-convex polyominoes

Following a well known hierarchy on hv-convex connected sets (say polyominoes), we say that a polyomino P is 2-convex if for every two cells belonging to P, there exists a monotone path included in P with at most two changes of direction. This study concerns the tomographical problem of the reconstruction of 2-convex polyominoes from their horizontal and vertical projections. We furnish the first known algorithm that fulfills this task in polynomial time. Such an approach can be generalized to each generic class of the hierarchy giving evidence, in the limit, to the known result of the polynomial reconstructability of the hv-convex polyominoes.