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Reconstruction of lattice sets from their horizontal, vertical and diagonal $$X$$-rays. (English) Zbl 1001.68177
Summary: We study the problem of reconstructing a lattice set from its X-rays in a finite number of prescribed directions. The problem is NP-complete when the number of prescribed directions is greater than two. We provide a polynomial-time algorithm for reconstructing an interesting subclass of lattice sets (having some connectivity properties) from its X-rays in directions $$(1,0)$$, $$(0,1)$$ and $$(1, 1)$$. This algorithm can be easily extended to contexts having more than three X-rays.

##### MSC:
 68U10 Computing methodologies for image processing 05B50 Polyominoes
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