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Abstract: A riverbed topographic survey is one of the most important tasks for river model experiments. To improve measurement efficiency and solve the riverbed interference problem in traditional methods, this study discussed two measurement methods that use digital image-processing technology to obtain topographic information. A new and improved approach for calibrating camera radial distortion, which comes from originally distorted images captured by our camera, was proposed to enhance the accuracy of image measurement. Based on perspective projection transformation, we described a 3D reconstruction method based upon multiple images, which is characterized by using an approximated maximum likelihood estimation method (AMLE) considering the first-order error propagation of the residual error to compute transformation parameters. Moreover, a theoretical derivation of 3D topography according to grey information from a single image was carried out. With the diffuse illumination model, assuming that the ideal grey value and topographic elevation value are positively correlated, we derived a novel closed formula to explain the relationship of 3D topographic elevation, grey value, grey gradient, and the solar direction vector. Experimental results showed that our two methods both have some positive advantages even if they are not perfect.

一种基于二维图像信息的三维地形测量

研究目的：利用数字图像测量技术对河流模型实验中的河床地形测量研究。
创新方法：以高质量的图像径向畸变校正为基础，依据多幅图像间映射换算以及单幅图像灰度信息变换两方面的研究，来提取三维地形信息。
研究手段：使用考虑残差的一阶误差传播的最大似然估计方法求解图像与地形坐标的映射变换参数；借助漫反射光照模型，通过适当假设，推导出地形高程与图像灰度、灰度梯度及太阳方向的关系式。
重要结论：1.以Devernay基于直线的图像畸变校正方法为基础，通过使用更高精度的Canny边缘检测算子提取图像边缘，黄金分割法和二次插值法相结合的最优化方法求取畸变系数等，可以得到较好的校正效果，求算的畸变系数精度更高，求算过程更快；2.利用图像与地面间的透视投影关系方法求解地形高程坐标，均匀并尽可能多地将控制点布置在控制区域内，使计算值更接近实测值，并满足河流演变实验的精度要求；3.通过推导关系式，理论上可以根据图像灰度、灰度梯度、太阳方向向量算得地形高程。

关键词：河床地形测量；数字图像测量技术；径向畸变矫正；投影变换；灰度信息变换

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