基于傅里叶变换的谷间距特征信息提取及其影响因素研究

谷间距(Valley Spacing)是描述相邻沟谷距离的特征参数,它能较好地反映沟谷的次序等级和空间分布特征。本研究以黑河正义峡和兰州大岭岘2个样区为例,利用ArcGIS软件,将无人机测绘获取的0.12 m分辨率地表高程数据通过重采样生成不同分辨率的数字地表模型。通过MATLAB软件,将不同分辨率、不同空间域的数字地表模型作为二维空间域信号进行傅里叶变换。通过傅里叶变换及频谱分析研究地形的频谱特征与地表谷间距之间的转换关系。分析结果显示:①当区域内只有一级沟谷时,频谱中谷间距特征信号的有效提取要求地形分辨率至少优于1/5谷间距,分辨率的粗略化则直接影响着地形频谱中谷间距特征信号的识别,但是分析空间域对频谱谷间距特征信号的捕获影响较小;②当区域内有多级沟谷时,分辨率优于1/3谷间距时即可有效提取到该级沟谷的谷间距特征信号,分辨率的粗略化和空间域的增大都会使得频谱中较低序次等级沟谷的谷间距特征信号减弱,而较高序次等级沟谷的谷间距特征信号增强。

Valley Spacing Character Information and Its Influencing Factors based on the Fourier Transform

Valley spacing is an important characteristic to describe the distance between adjacent valleys. It can reflect the structural feature and spatial distribution of valleys. In this study, we took the Heihe Zhengyixia region and Lanzhou Dalingxian region as examples. We used the ArcGIS to resample the digital surface models (DSM) at 0.12 m resolution which were obtained by unmanned aerial vehicle to different resolution DSM. The different resolution DSM data were further processed by Fourier transform in MATLAB software. We compared different spectrums to build the relationship between land surface spectral feature and valley spacing. Analytical results show that: (1) for the first-order valley region, the effective identification of valley spacing feature signal in the spectrum required a terrain resolution higher than 1/5 of valley spacing. The terrain resolution could directly affect the identification accuracy of valley spacing signal. While the space domain had less influence on the valley spacing signal identification. (2) for the multi-order valley region, the effective identification of valley spacing feature signal in the spectrum required a terrain resolution higher than 1/3 of valley spacing. Either the decrease in terrain resolution or the increase in the spatial domain could decrease the spacing signal of lower-order valleys and increase the spacing signal of higher-order valleys in the spectrum.