  Tomography is the area of reconstructing objects from projections. Here we
wish to reconstruct a set of cells in a two dimensional grid, given the number
of cells in every row and column. The set is required to be an hv-convex
polyomino, that is all its cells must be connected and the cells in every row
and column must be consecutive. A simple, polynomial algorithm for
reconstructing hv-convex polyominoes is provided, which is several orders of
magnitudes faster than the best previously known algorithm from Barcucci et al.
In addition, the problem of reconstructing a special class of centered
hv-convex polyominoes is addressed. (An object is centered if it contains a row
whose length equals the total width of the object). It is shown that in this
case the reconstruction problem can be solved in linear time.
