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 A 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.%现有的基于优化算法的三维物体重构方法只能将线画图重构为“粗糙”的三维物体,从而限制了这些方法的实际应用.为此提出一种基于优化算法的改进方法,该方法分2个阶段实现:第一阶段通过在目标函数中引入膨胀-规整平衡因子λ,利用λ的变化渐近优化得到线画图的初步重构结果；第二阶段重构使用不等式约束逐步逼近平行、垂直、共面的等式约束,利用非线性约束优化算法首先精确地重构出三维物体的主平面,然后得到其他非主平面顶点的精确三维坐标,完成整个线画图的精确重构.实验结果表明,文中方法有效和稳定,其重构结果的精度明显优于现有方法.
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