Recovering the shape of polyhedra using line-drawing analysis and complex reflectance models

Following Sugihara, we represent the geometric constraints imposed by the line-drawing of a polyhedron as a set of linear equalities and inequalities. Unlike him, we explicitly take into account the uncertainty in vertex position. This allows us to circumvent the superstrictness of the constraints without deleting any of them. For a given error bound, deciding whether a line-drawing is the correct projection of a polyhedron is reduced to linear programming, and 3D shape recovery is reduced to optimization under linear constraints. Our method can be used for recovering the shape of polyhedral objects whose reflectance can be modelled accurately. We have implemented if for the Lambertian model and the Lambertian model with interreflections. We present results obtained using real images