梯度约束SFS的月面地形重构

目的 解决月面着陆器在下降过程中可能得不到足够的匹配点进行着陆区地形恢复的问题。方法 基于特征边缘线梯度比例约束的明暗恢复形状（shape from shading）算法。首先以Lommel-Seeliger模型模拟月表反射情况，建立辐照度方程；然后以地形特征边缘提取结果为基础，经过最小二乘拟合与表面光滑模型约束后，演化得到剩余影像点的梯度比例因子，实现对辐照度方程的正则化约束。结果 经过测试得到模拟影像的平均相对恢复精度可以达到-0.199，真实影像月面可以达到0.051和0.022。结论 本文算法能够有效地进行3维地形恢复，且恢复精度优于经典SFS算法中对实际地形恢复效果最好的Tsai算法。

Lunar terrain reconstruction with SFS under gradient constraint

Objective Solving the problem of a lack of matching points to complete the terrain reconstruction for the landing area during the Lunar Lander landing process. Method An SFS(shape from shading) algorithm for 3D terrain recovery based on gradient constraints of the feature edges. The irradiance equation is established on the Lommel-Seeliger model to simulate the Lunar surface reflection. Based on the extract results of the terrain feature edge, gradient ratio of the rest part can be solved after least square fitting and surface smoothness constraint. The SFS problem becomes regularized after the quantitative constraints of irradiance equation. Result The average relative recovery accuracy can reach -0.199 for synthetic images, and also can reach 0.051 and 0.022 for real image after testing. Conclusion The proposed algorithm can work effectively for 3D terrain reconstruction, and the recovery accuracy is superior to the existing SFS algorithm.