Reconstructing hv-Convex Polyominoes from Orthogonal Projections

Tomography is the area of reconstructing objects from projections. In discrete tomography an object T we wish to reconstruct may be a set of cells of a multidimensional grid. We perform measurements of T , each one involving a projection that determines the number of cells in T on all lines parallel to the projection’s direction. Given a finite number of such measurements, we wish to reconstruct T or, if unique reconstruction is not possible, to compute any object consistent with these projections. Gardner et al. [7] proved that deciding if there is an object consistent with given measurements is NP-complete, even for three non-parallel projections in the 2D grid.