An algebraic approach to line-drawing analysis in the presence of uncertainty

Following the work of K. Sugihara (1984), the authors represent the geometric constraints imposed by the line-drawing of a polyhedron as a set of linear equalities and inequalities. They, however, explicitly take into account the uncertainty in the vertex position. This allows the circumvention of the superstrictness of the constraints without deleting any constraints. For a given error bound, the condition whether a line-drawing is the correct projection of a polyhedron is reduced to linear programing, and the 3D shape recovery is reduced to optimization under linear constraints. The approach has been implemented, and examples are presented