基于Shape-from-Shading的月球表面三维形状恢复算法研究

Research on 3-D Reconstruction Algorithm of the Moon Surface Based on Shape-from-shading Method

提出了一种基于Shape-from-Shading的月球表面三维形状恢复算法。首先分析了在太阳光照射下月球表面成像模型,建立了使用Lommel-Seeliger反射模型描述的反射图方程。然后用有限差分近似微分运算,将反射图方程所示的一阶变系数线性偏微分方程进行离散化处理,得到关于表面高度函数的代数方程。进而采用超松弛迭代法进行求解,获得月球表面三维高度函数值。最后使用合成图像和实际月球图像进行三维形状恢复仿真实验。实验结果表明提出的算法可以有效地恢复月球表面三维形状。

An algorithm of 3-D shape reconstruction of the Moon surface based on shape-from-shading method was proposed. Imaging model of the Moon surface under the illumination of the sun was discussed firstly. And Lommel-Seeliger reflectance model was used to establish reflectance map equation. When the finite difference approximated differential operator, the reflectance map equation described by the first order yawing-coefficient linear partial differential equation turned into a group of algebraic equations about the unknown surface height functions. Then SOR iterative method was used to solve the equations and heights of 3-D surface were achiered. At last, 3-D shape reconstruction experiments on synthetic image and real image of the Moon were performed to il- luminate the efficiency of the proposed method.