Interpretation of contradictory images by means of systems of linear inequalities

We consider the problem of interpretation of three-dimensional images from their flat projections up to the set of visible faces. For projections of convex polytopes, we present an interpretation algorithm based on maximum feasible subsystems of a certain infeasible system of linear inequalities modeling the visibility requirement for faces of the polytope. A number of model examples are given; in particular, the algorithm is applied for interpretation of the Necker cube.