高程梯度算法与不确定性研究

发布时间：2018-01-20 23:30

本文关键词： 高程梯度高程梯度算法统计分布算法精度不确定性　出处：《西北大学》2017年硕士论文　论文类型：学位论文

【摘要】：高程梯度是坡度算法的基本计算项。在坡度算法θ=arctan(p2+q2)I/2中分别用p和q表示,因为高程梯度p和q算法的不同而衍生出多种坡度算法,因此对p和q算法的性质和精度的研究,是坡度算法精度评价的基础。p和q的算法的不同不但会影响坡度计算,而且P和q也是坡度分布理论模型研究的起点。本研究选取漫岗丘陵、黄土丘陵、秦岭、横断山四个不同地形类型样区,使用七种算法得到每个样区的高程梯度,对高程梯度性质、高程梯度的统计分布与结构特征、高程梯度算法的稳定性与精度进行了分析;并选取漫岗丘陵和黄土丘陵部分样区,分析高程梯度随不同分辨率的变化规律;从数学与物理学的角度对高程梯度的基本性质进行了初步分析。本文的主要研究结果如下:(1)高程梯度的统计学分布特征:p和q的均值十分接近零,p和q的标准差均近似相等,p和q均接近正态分布,p和q均相互独立。(2)结构特征:各种算法均能表现p和q局地结构和样区之间的差异,地形起伏越大,图像的纹理也越复杂。(3)高程梯度算法稳定性与精度:从算法的稳定性(直方图相似度指数、均方根误差)和精度(高程中误差、高程梯度联合方差误差、控制参数误差)来看,均表明改进的Evans-Young算法最好。(4)高程梯度p和q分布特征随分辨率变化的规律:统计分布特征方面,随着DEM分辨率的降低,p和q基本性质保持不变;结构特征方面,随着分辨率的降低,p和q图像的纹理与结构简化、图像表面逐渐变平滑。
[Abstract]:The elevation gradient is the basic calculation term of the gradient algorithm. In the slope algorithm 胃 arctanan p2 q2 / 2 I / 2, it is expressed by p and Q, respectively. Because of the difference of the elevation gradient P and Q algorithms, many gradient algorithms are derived, so the properties and accuracy of the p and Q algorithms are studied. It is the basis of accuracy evaluation of slope algorithm. P and Q will not only affect the calculation of slope, but also P and Q are the starting point of the theoretical model of slope distribution. Qinling, Hengduan Mountain four different topographic types of sample areas, using seven algorithms to obtain the height gradient of each sample area, the height gradient properties, the statistical distribution and structural characteristics of elevation gradient. The stability and accuracy of the elevation gradient algorithm are analyzed. The variation law of elevation gradient with different resolution is analyzed by selecting some sample areas of oversized hills and loess hills. The basic properties of elevation gradient are preliminarily analyzed from the point of view of mathematics and physics. The main results of this paper are as follows: 1) the statistical distribution characteristics of the elevation gradient: P and Q are very close to zero. The standard deviations of p and Q are approximately equal, p and Q are close to the normal distribution, p and Q are independent of each other. Each algorithm can show the difference between p and Q local structure and sample region. The larger the terrain fluctuation, the more complex the texture of the image.) the stability and accuracy of the elevation gradient algorithm: from the stability of the algorithm (histogram similarity index, root mean square error) and accuracy (elevation error). The joint variance error of elevation gradient, the error of control parameter). It is shown that the improved Evans-Young algorithm is the best. (4) the law of the variation of the P and Q distribution characteristics with the resolution: the statistical distribution feature, with the decrease of the DEM resolution. The basic properties of p and Q remain unchanged; In terms of structural features, the surface of the image becomes smoother as the resolution decreases and the texture and structure of the Q and Q images are simplified.
【学位授予单位】：西北大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：P931;P208

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