基于DEM的地形尺度相似性度量方法研究
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摘要
分析尺度因其与DEM数据分析、解释与应用等内容相关联而在数字地形分析的尺度体系中具有重要地位。如何采用多尺度分析方法刻画地形具有自相似、多层次、多尺度等基本特征,并对其进行量化与分析一直是地学研究的重点与难点。由于受到数据和方法的限制,现有的地形尺度特征研究方法还不能有效地刻画地形的相似性特征。本论文从频率域的视角出发,以陕西省1：50,000比例尺DEM为基本数据源,借鉴计算机视觉、景观生态学、图像处理等相关理论与方法,提出了基于傅立叶频谱分析、连续小波变换(Continuous Wavelet Transformation,CWT)的地形尺度相似性度量方法,分析了陕西省地形尺度相似性的空间分布规律,验证了论文的计算结果。论文的主要研究内容和成果如下：
(1)基于傅立叶频谱的地形尺度相似性研究
-维地形剖面线直观地刻画了地形的起伏特征,论文基于地形剖面数据,采用傅立叶频谱法,分析了陕西省的地形尺度相似性特征。结果表明：地形剖面的傅立叶功率谱与频率存在双对数线性相关关系,地形尺度相似性程度在陕北黄土高原区域较高,在宝鸡-汉中安康一带、秦岭一带次之,而在陕北黄土风沙区、关中盆地较低,该趋势与地表的形态特征具有较高的一致性。
(2)基于连续小波的地形尺度相似性研究
连续小波变换能够以尺度连续的方式刻画地形相似性特征。论文针对地形的空间各向异性,设计了面向一维小波分析的剖面线处理方法,构建了基于连续小波的地形尺度相似性度量模型,对比分析了不同小波基函数对于地形尺度相似性度量的影响。实验结果显示,二维连续小波在地形尺度相似性度量方面明显优于一维连续小波；依据分析结果,二维连续母小波可以分为两类,第一类为mexican2d, esmex2d, wheel2d, dergauss2d, gaussz2d, dog2d, sdog2d, sqdog2d, endstop2,第二类为,es2cauchy2d, endstop1,第一类二维母小波对地形尺度相似性度量能力优于第二类；二维连续小波变换模局部极值点不仅能够刻画地形尺度相似性,而且能反映局部地形变化的空间尺度。
(3)陕西省地形尺度相似性空间分异研究
在对比分析基于傅立叶频谱分析、连续小波分析结果数据的基础上,研究了地形尺度相似性在整个陕西省的空间分布规律,研究结果显示：陕西省地形尺度相似性呈现有序的空间分异特征,基于傅立叶频谱分析和连续小波分析方法得到的陕西省地形尺度相似性具有较高的一致性,均表现为在北部丘陵沟壑区和陕西省东南部的低山区较高,汉中盆地、安康一带次之,在北部的风沙过渡区、关中盆地一带较低,这种特征与地表形态的空间分异具有较高的相关性。傅立叶频谱分析在度量地形平坦区域、陕北的黄土高原区域的尺度相似性较好,而二维连续小波在度量地表破碎的黄土丘陵区具有优势。
基于频率域的地形特征分析方法,从一个新的视角揭示了地形的自相似、多尺度特征,得到的地形尺度相似性度量值具有良好的空间连续性,有助于进一步深入认识地表形态的本质特征；其结果可为地表形态的量化提供参考,为地貌类型的划分提供依据。本文所构建的面向地形尺度相似性的频率域分析方法进一步丰富和完善了数字地形分析的方法体系。
Analysis scale is one of the five foundmental scale issues in DEM data analysis, data interpretation and application. The methods for characterizing and analyzing such basic characteristics like self-similarity, hierarchy and multi-scale properties possed by the landform morphology become difficult and important issues. The now existing researches of multi-scale terrain analysis are either limited by the data sources or by the methods used for landform morphology analysis, thus these researches can not fulfil requirements of characterizing landform morphology scale similarity. In the thesis, a series of DEMs in the whole Shannxi province are selected as the source data. The DEMs cover the whole Shannxi province with671DEMs of25m-resolution. These DEMs guarantee the complexity, diversity, integrity and availability of the landform data. A series of Fourier frequency domain based methods are employed to analyze the terrain data sets. The methods include fouries spectrum analysis, continuous wavelet analysis and spatial point pattern analysis. These methods are investigated to analyze the similarity characteristics and their spatial distributions of the loess landforms, the spatial point patterns and their spatial distribution in the whole area over different scales. The paper adopts the similarity to landform classification and the accuracy evaluation.
The main contents and achievements of the thesis are as follows:
(1) Research on landform scale similarity by Fourier spectrum analysis
Profiles are the most intuitive reflection of fluctuations of terrain features and landform morphology. The thesis proposes a method based on Fourier spectrum analysis and its second order statistics the profiles for landform scale similarity characterizing. Experiments in the whole area of Shannxi province show that:there is obvious linear relationship between the Fourier power spectrum and the frequencies of the landform profile. The linear relationship reflects the landform scale similarity. Experiments show that landform scale similarity is high in the northern area of loess plateau, Baoji and Hanzhong Basin belts and the Qin mountain zones of Shannxi province; while the landform scale similarity is low in the inbetweens areas of loess and sandy landforms in the northern area of Shannxi province, Guanzhong Basin and the Hanzhong Basin. This spatial distribution of landform scale similarity has high coincidence with the landform complexity.
(2) Research on landform scale similarity by continuous wavelet analysis
The wavelet transform modules maxima reflect landform scale similarity. Firstly, this thesis designs a workflow for one dimensional profile data acquisizition and preprocessing. Then the thesis proposes a new model which could be used to characterizing landform scale similarity by construction and analysis of the wavelet transformation scale representation—scale space. Finall comparisons among different mother wavelets in landform scale similarity characterizing are investigated. The experiments in the Shannxi province show that there exists high correspondence by different wavelets in different test areas. The experiments show that the landform scale similarity characterized by two dimensional profiles Fourier spectrum analysis is more obvious the the one dimensionl cases. The mother wavelets used for landform scale similarity characterizing could be departed into two kinds. The first kind wavelets include mexican2d, esmex2d, wheel2d, dergauss2d, gaussz2d, dog2d, sdog2d, sqdog2d and endstop2; while the other kind of mother wavelets includes es2cauchy2d and endstopl. The first kind performs bettern than the second ones. The two dimensional wavelet transform modoule maxima not only characterize landform scale similarity, but their spatial scale as well.
(3) Research on spatial distribution regularity of landform scale similarity in Shannxi province
By comparing the results obtained by the methods in the thesis, namely fourier,2D continuous wavelet transform (CWT), the thesis investigates the spatial distributions regularity of landform scale similarity in the whole Shannxi province. The experiments show that there are orderly spatial variations of landform scale similarity. There is high coincidence between results achieved by Fourier spectrum analysis and continuous wavelet transformation analysis. They all trend higher in the gully and hilly area in the northern loess plateau, low and hilly area in southeastern part of Shannxi province. While the landform scale similarity trends low in areas like Hanzhong&Ankang Basin, Guanzhong Basin and inbetween areas of sandy and loess areas. These characteristics reflect their terrain relief. Experiments show that Fourier and wavelet based methods perform better than the traditional statistical methods, the Fourier based method performs bettern than the wavelet based method in the plain area while the wavelet based method behaves better in the loess hilly area.
The frequency domain based multi-scale analysis method reflects similarity, multi-scale characteristics of landform morphology in a new scope. There is high continuity in landform scale similarity quantitation and it benefits cognition of landform origins. The spatial distribution of landform scale similarity would offer helpful reference for landform classification and geographical comprehensive zoning. The frequency domain based landform scale analysis method would enrich and improve the methodology of digital terrain analysis.
(1)基于傅立叶频谱的地形尺度相似性研究
-维地形剖面线直观地刻画了地形的起伏特征,论文基于地形剖面数据,采用傅立叶频谱法,分析了陕西省的地形尺度相似性特征。结果表明：地形剖面的傅立叶功率谱与频率存在双对数线性相关关系,地形尺度相似性程度在陕北黄土高原区域较高,在宝鸡-汉中安康一带、秦岭一带次之,而在陕北黄土风沙区、关中盆地较低,该趋势与地表的形态特征具有较高的一致性。
(2)基于连续小波的地形尺度相似性研究
连续小波变换能够以尺度连续的方式刻画地形相似性特征。论文针对地形的空间各向异性,设计了面向一维小波分析的剖面线处理方法,构建了基于连续小波的地形尺度相似性度量模型,对比分析了不同小波基函数对于地形尺度相似性度量的影响。实验结果显示,二维连续小波在地形尺度相似性度量方面明显优于一维连续小波；依据分析结果,二维连续母小波可以分为两类,第一类为mexican2d, esmex2d, wheel2d, dergauss2d, gaussz2d, dog2d, sdog2d, sqdog2d, endstop2,第二类为,es2cauchy2d, endstop1,第一类二维母小波对地形尺度相似性度量能力优于第二类；二维连续小波变换模局部极值点不仅能够刻画地形尺度相似性,而且能反映局部地形变化的空间尺度。
(3)陕西省地形尺度相似性空间分异研究
在对比分析基于傅立叶频谱分析、连续小波分析结果数据的基础上,研究了地形尺度相似性在整个陕西省的空间分布规律,研究结果显示：陕西省地形尺度相似性呈现有序的空间分异特征,基于傅立叶频谱分析和连续小波分析方法得到的陕西省地形尺度相似性具有较高的一致性,均表现为在北部丘陵沟壑区和陕西省东南部的低山区较高,汉中盆地、安康一带次之,在北部的风沙过渡区、关中盆地一带较低,这种特征与地表形态的空间分异具有较高的相关性。傅立叶频谱分析在度量地形平坦区域、陕北的黄土高原区域的尺度相似性较好,而二维连续小波在度量地表破碎的黄土丘陵区具有优势。
基于频率域的地形特征分析方法,从一个新的视角揭示了地形的自相似、多尺度特征,得到的地形尺度相似性度量值具有良好的空间连续性,有助于进一步深入认识地表形态的本质特征；其结果可为地表形态的量化提供参考,为地貌类型的划分提供依据。本文所构建的面向地形尺度相似性的频率域分析方法进一步丰富和完善了数字地形分析的方法体系。
Analysis scale is one of the five foundmental scale issues in DEM data analysis, data interpretation and application. The methods for characterizing and analyzing such basic characteristics like self-similarity, hierarchy and multi-scale properties possed by the landform morphology become difficult and important issues. The now existing researches of multi-scale terrain analysis are either limited by the data sources or by the methods used for landform morphology analysis, thus these researches can not fulfil requirements of characterizing landform morphology scale similarity. In the thesis, a series of DEMs in the whole Shannxi province are selected as the source data. The DEMs cover the whole Shannxi province with671DEMs of25m-resolution. These DEMs guarantee the complexity, diversity, integrity and availability of the landform data. A series of Fourier frequency domain based methods are employed to analyze the terrain data sets. The methods include fouries spectrum analysis, continuous wavelet analysis and spatial point pattern analysis. These methods are investigated to analyze the similarity characteristics and their spatial distributions of the loess landforms, the spatial point patterns and their spatial distribution in the whole area over different scales. The paper adopts the similarity to landform classification and the accuracy evaluation.
The main contents and achievements of the thesis are as follows:
(1) Research on landform scale similarity by Fourier spectrum analysis
Profiles are the most intuitive reflection of fluctuations of terrain features and landform morphology. The thesis proposes a method based on Fourier spectrum analysis and its second order statistics the profiles for landform scale similarity characterizing. Experiments in the whole area of Shannxi province show that:there is obvious linear relationship between the Fourier power spectrum and the frequencies of the landform profile. The linear relationship reflects the landform scale similarity. Experiments show that landform scale similarity is high in the northern area of loess plateau, Baoji and Hanzhong Basin belts and the Qin mountain zones of Shannxi province; while the landform scale similarity is low in the inbetweens areas of loess and sandy landforms in the northern area of Shannxi province, Guanzhong Basin and the Hanzhong Basin. This spatial distribution of landform scale similarity has high coincidence with the landform complexity.
(2) Research on landform scale similarity by continuous wavelet analysis
The wavelet transform modules maxima reflect landform scale similarity. Firstly, this thesis designs a workflow for one dimensional profile data acquisizition and preprocessing. Then the thesis proposes a new model which could be used to characterizing landform scale similarity by construction and analysis of the wavelet transformation scale representation—scale space. Finall comparisons among different mother wavelets in landform scale similarity characterizing are investigated. The experiments in the Shannxi province show that there exists high correspondence by different wavelets in different test areas. The experiments show that the landform scale similarity characterized by two dimensional profiles Fourier spectrum analysis is more obvious the the one dimensionl cases. The mother wavelets used for landform scale similarity characterizing could be departed into two kinds. The first kind wavelets include mexican2d, esmex2d, wheel2d, dergauss2d, gaussz2d, dog2d, sdog2d, sqdog2d and endstop2; while the other kind of mother wavelets includes es2cauchy2d and endstopl. The first kind performs bettern than the second ones. The two dimensional wavelet transform modoule maxima not only characterize landform scale similarity, but their spatial scale as well.
(3) Research on spatial distribution regularity of landform scale similarity in Shannxi province
By comparing the results obtained by the methods in the thesis, namely fourier,2D continuous wavelet transform (CWT), the thesis investigates the spatial distributions regularity of landform scale similarity in the whole Shannxi province. The experiments show that there are orderly spatial variations of landform scale similarity. There is high coincidence between results achieved by Fourier spectrum analysis and continuous wavelet transformation analysis. They all trend higher in the gully and hilly area in the northern loess plateau, low and hilly area in southeastern part of Shannxi province. While the landform scale similarity trends low in areas like Hanzhong&Ankang Basin, Guanzhong Basin and inbetween areas of sandy and loess areas. These characteristics reflect their terrain relief. Experiments show that Fourier and wavelet based methods perform better than the traditional statistical methods, the Fourier based method performs bettern than the wavelet based method in the plain area while the wavelet based method behaves better in the loess hilly area.
The frequency domain based multi-scale analysis method reflects similarity, multi-scale characteristics of landform morphology in a new scope. There is high continuity in landform scale similarity quantitation and it benefits cognition of landform origins. The spatial distribution of landform scale similarity would offer helpful reference for landform classification and geographical comprehensive zoning. The frequency domain based landform scale analysis method would enrich and improve the methodology of digital terrain analysis.
引文
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