DEM坡向提取的向量场模板匹配方法

A Vector Field Template Matching Method of DEM Slope Extraction

利用几何代数的多维统一性与运动表达的简明性特征,设计了用几何代数向量场拟合进行地表坡向表达和提取的新算法。基于高斯合成曲面模型模拟的多尺度格网DEM数据,对坡向计算的正确性、抗噪性及空间整体性进行验证和统计分析,显示几何代数向量场拟合方法能正确提取地表坡向,且较之三阶反距离平方权算法具有更强的抗噪性;选取5类典型的不同地貌类型数据进行最优窗口和坡向提取试验,黄土丘陵,梁、峁、塬和风沙地貌的最优窗口大小分别为13、11、11、11、17,所提取的坡向可以较好地反映不同地貌类型的结构特征。

Based on the multidimension-unified and simple expression of movement characteristics of geometric algebra, a new algorithm for expressing and extracting slope of surface multi-dimensional vector fields with the geometric algebra-based vector field matching method was proposed. The correctness, noise immunity and statistical spatial integrity of the slope extraction of our method was tested with multi-scale simulated grid DEMs generated with Gaussian composite surface. The results suggested the geometric algebra-based vector field matching method could correctly extract the slope of the surface, and the algorithm had stronger noise immunity than three-order inverse distance square weight algorithm. The optimized window size finding and slope extraction experiments were constructed with five different real world data reflecting different terrain morphology. The optimized window sizes for loess hills, loess ridge, loess knolls, loess plateau, and toese sand geomorphology are 13, 11, 11, 11, 17 respectively. The extracted slop conld well reflect the structure characteristics of different geomorphology of different terrains.