Optimization-Based Precise Reconstruction of 3D Objects from Line Drawings

Existing optimization-based methods can only roughly reconstruct a 3D object from its line drawing,and thus are limited in practical applications.We propose an optimization-based method to tackle this problem in two steps.First,a factor λ which balances the inflation and other regularities is involved in the objective function to reconstruct a rough 3D object progressively.Second,geometric properties,such as line parallelism,face planarity,and line orthogonality,are identified from the reconstruction result of the first stage.Then the equality constraints which precisely present line parallelism,face planarity,and line orthogonality are approximated with inequality constraints.The whole line drawing is reconstructed after the 3D coordinates of the vertices in the primary face are obtained with a nonlinear constraint optimization algorithm.Our experiments show that the proposed method is robust and efficient,and its results are more precise than those obtained by other existing methods.