3D Surface Models by Geometric Constraints Propagation

This paper proposes a technique for estimating piece-wise planar models of objects from their images and geometric constraints. First, assuming a bounded noise in the localization of 2D points, the position of the 3D point is estimated as a polyhedron containing all the possible solutions of the triangulation. Then, given the topological structure of the 3D points cloud, geometric relationships among facets, such as coplanarity, parallelism, orthogonality, and angle equality, are automatically detected. A subset of them that is sufficient to stabilize the 3D model estimation is selected with a flow-network based algorithm. Finally a feasible instance of the 3D model, i.e. one that satisfies the selected geometric relationships and whose 3D points lie within the associated polyhedral bounds, is computed by solving a Constraint Satisfaction Problem