由离散点和特征线构建DEM的优化控制方法

摘要

A new interpolation method for Digital Elevation Model(DEM) generation called Laplace-based Optimal Control(OC) is proposed, by minimizing the square of finite difference of Laplace equations, subject to bound constraints and equality constraints from scattered points, inequality constraints from stream lines. Thus a standard OC problem is formed, by solving this problem, a reasonable DEM can be generated. In the final DEM, terrain information from scattered points and terrain feature lines are incorporated. By adjusting the parameter values (e.g the lower and upper bound constraints) of OC, different DEM can be generated. One real case study is given, and results from OC is compared with that from Constraint Triangulated Irregular Network(CTIN). CTIN result is not desirable. OC method is preferable in DEM construction from scattered points and stream lines, for its result is smooth and of more fidelity to original data source.%基于拉普拉斯方程和优化控制(OC)理论,提出一种构建地形的OC方法.以极小化拉普拉斯方程左端项平方和为目标函数、采样离散点作为等式约束条件、河流线作为不等式约束条件、格网点附近的离散点集的高程范围为上下界约束条件,形成一个标准的OC问题,求解该问题即可获得融合原始数据中隐含信息的数字高程模型(DEM).通过调节OC的参数值,可以获得不同的DEM.实际案例表明,OC方法既能保证地形曲面的整体光滑性,又能保证DEM结果对于原始数据的忠实性,其模拟结果优于约束不规则三角网方法.