基于EMD的线状要素自动综合研究
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摘要
随着地理信息系统(GIS)在现代社会中的地位日益提高,人们对地理信息的需求不断扩大,需求层次不断提高,越来越多地需要在不同分辨率、不同空间尺度上对地理现象进行观察、理解和描述,对变比例尺的空间数据进行分析、处理和表达。随着网络与移动服务的普及,这也促进变比例尺特征GIS的出现和发展,使得制图学领域中最古老、最经典的领域——制图综合又焕发新的活力、面临新的挑战,成为GIS研究领域内的热点和前沿问题。
如何基于计算机利用地图数据库快速地进行地图在多个尺度下的表达,对地图在新的数字环境下进行承载和传输信息将是非常有意义的,也是传统制图综合在制图领域顺应时代发展的新要求。GIS中的图形数据信息主要通过线状图形要素来表达,开展线状要素的自动综合是进行地理信息多尺度表达的重要方面。滤波方法逐渐成为空间信息综合的新方法,其中经验模式分解(EMD)方法具有数据自适应的特点,在信号处理等领域取得了成功的应用。目前,采用空间几何约束进行线状要素综合的理论和方法已经得到了广泛的应用,而滤波方法中经验模式分解方法应用到地理信息综合却较少受到关注。经验模式分解方法的基于数据的自适应特性,能够很好地对线状要素综合进行简化和压缩。而基于曲率等空间几何方法在线状要素综合过程中能够很好地保持曲线的形状特征。因此,本文采用滤波与空间几何约束相结合的方法,用于线状要素的自动综合研究,主要研究内容包括以下几个部分：
1)分析了数字环境下地图制图特点以及线状要素综合中存在问题,探讨了引入频率域过滤方法在线状要素简化中的必要性。通过分析总结曲线化简方法中存在的主要问题,本文提出了采用二维空间中曲线经验模式分解用于曲线综合的技术路线,用于线状要素的压缩和化简。
2)研究了滤波理论用于空间信息综合的多种方法,在总结分析小波理论、傅里叶变换和经验模式分解理论的基础上,提出了曲线的经验模式分解方法。通过曲线在二维空间的经验模式分解和重构,采用贝塞尔和BSpline曲线拟合方法,建立了基于二维经验模式分解的线要素多尺度表达方法。
3)引入了可视化曲率的概念,探讨了曲率方法在曲线特征点提取中的优缺点,在分析总结以往曲率计算方法的基础上,提出了基于高度角计算的可视化曲率方法。通过开展可视化曲率在多边形形状提取上的示范,建立基于可视化曲率的线要素简化方法。
4)综合经验模式分解与可视化曲率方法,设计了二维空间经验模式分解算法和特征约束的曲线重构算法,采用空间语义关系等约束,提出了线状要素化简后的形状特征保持方法,实现了滤波和空间几何相结合的线状要素多尺度表达技术。
5)开展了线状要素综合结果的分析和评价,提出一种经过改进的Hausdorff曲线相似度评价方法,检验曲线综合后形状特征的保持；并提出采用几何特征评估和位置精度评估方法对线状要素综合结果进行了分析、评价,指出基于EMD线要素简化方法的特点,指出了曲线二维经验模式分解在线要素综合中的适用性。
As the status of geographic information system (GIS) continuously improves in modern society, the needs of geographical information are increasingly expanded and demand levels become higher and higher. Furthermore, more and more geographic phenomena are observed, understood and descripted in different resolution, different spatial scales according to a variety of requirements. Also, the variable-scale spatial data are analyzed, processed and expressed. The Internet and the popularity of mobile services have promoted the emergence and development of variable scale characteristic GIS. Therefore, the oldest and classical cartography field——the cartographic generalization is energetic again as well as faces new challenges, making cartographic generalization a hot area of research and cutting-edge issues in GIS area.
The research on how to use computer-based map database so as to express map quickly and in multiple-scale is not only very significant and meaningful to maps for their information carriage and transmission in the new digital environment, but also makes the traditional cartographic generalization conform to the new requirements in the field of mapping. The data and information in GIS is expressed mainly through linear graphic elements, thus automatically linear features generalization is an important aspect of multi-scale expression of the geographic information. At present, the theory and methods that use spatial geometric constraints to linear features generalization have been widely used. However, not much attention has been paid to the geographic information generalization by filtering method, especially through empirical mode decomposition, which is an adaptive and natural approach for signal analysis. Empirical Mode Decomposition Method can well simplify and compress the linear elements. In addition, spatial geometric methods based on curvature have strong ability to maintain the shape of the characteristics curve in linear features generalization process. Therefore, the combination of spatial geometric constraints and filtering method is used for the automatic linear features generalization, and the main contents of this research include the following aspects:
1) The existing problems of cartographic characteristics as well as the linear features generalization in digital environment has been analyzed, and the necessity of using frequency domain filtering method in linear features generalization is discussed. By analyzing and summarizing the main problems in line generalization methods, the technical route, which uses curve empirical mode decomposition in two-dimensional space, is proposed to compress and simplify the linear elements.
2) A variety of spatial information generalization methods using filtering theory are studied. The empirical mode decomposition method is put forward based on summarizing and analyzing the theory of wavelet, Fourier transform and empirical mode decomposition theory. Through the empirical mode decomposition of lines in the two-dimensional space, multi-scale representation of linear features method is brought forward by using Bessel and BSpline curve approximation method.
3) The concept of visual curvature has been introduced, what is more, the advantages and disadvantages of curvature method in curve feature point detection are probed. Secondly, by summarizing the previous methods of curvature calculation, visual curvature computation based on elevating angular height calculation is proposed. Through experiments of polygon shape extraction based on visual curvature, curvature-based visualization method for curve simplifying is adopted.
4) The empirical mode decomposition algorithm for two-dimensional space and the curve reconstruction algorithm based on constraint features have been designed by combining empirical mode decomposition and curvature visualization method. By adopting the constraints such as spatial semantic relationship, the method for preserving the shape characteristics of linear features after generalization is establised.
5) The analysis and evaluation on results of linear features generalization is carried out, and an improved Hausdorff similarity curve evaluation method is proposed to examine the shape of curve characteristics after generalization. At the same time, both geometric characteristics assessment method and location accuracy evaluation method are used to analyze, evaluate the linear features generalization outcome. At last, the characteristics of simplifying linear features based on EMD have been pointed out. Also, the applicability of two-dimensional curves empirical mode decomposition in linear features generalization is indicated.
如何基于计算机利用地图数据库快速地进行地图在多个尺度下的表达,对地图在新的数字环境下进行承载和传输信息将是非常有意义的,也是传统制图综合在制图领域顺应时代发展的新要求。GIS中的图形数据信息主要通过线状图形要素来表达,开展线状要素的自动综合是进行地理信息多尺度表达的重要方面。滤波方法逐渐成为空间信息综合的新方法,其中经验模式分解(EMD)方法具有数据自适应的特点,在信号处理等领域取得了成功的应用。目前,采用空间几何约束进行线状要素综合的理论和方法已经得到了广泛的应用,而滤波方法中经验模式分解方法应用到地理信息综合却较少受到关注。经验模式分解方法的基于数据的自适应特性,能够很好地对线状要素综合进行简化和压缩。而基于曲率等空间几何方法在线状要素综合过程中能够很好地保持曲线的形状特征。因此,本文采用滤波与空间几何约束相结合的方法,用于线状要素的自动综合研究,主要研究内容包括以下几个部分：
1)分析了数字环境下地图制图特点以及线状要素综合中存在问题,探讨了引入频率域过滤方法在线状要素简化中的必要性。通过分析总结曲线化简方法中存在的主要问题,本文提出了采用二维空间中曲线经验模式分解用于曲线综合的技术路线,用于线状要素的压缩和化简。
2)研究了滤波理论用于空间信息综合的多种方法,在总结分析小波理论、傅里叶变换和经验模式分解理论的基础上,提出了曲线的经验模式分解方法。通过曲线在二维空间的经验模式分解和重构,采用贝塞尔和BSpline曲线拟合方法,建立了基于二维经验模式分解的线要素多尺度表达方法。
3)引入了可视化曲率的概念,探讨了曲率方法在曲线特征点提取中的优缺点,在分析总结以往曲率计算方法的基础上,提出了基于高度角计算的可视化曲率方法。通过开展可视化曲率在多边形形状提取上的示范,建立基于可视化曲率的线要素简化方法。
4)综合经验模式分解与可视化曲率方法,设计了二维空间经验模式分解算法和特征约束的曲线重构算法,采用空间语义关系等约束,提出了线状要素化简后的形状特征保持方法,实现了滤波和空间几何相结合的线状要素多尺度表达技术。
5)开展了线状要素综合结果的分析和评价,提出一种经过改进的Hausdorff曲线相似度评价方法,检验曲线综合后形状特征的保持；并提出采用几何特征评估和位置精度评估方法对线状要素综合结果进行了分析、评价,指出基于EMD线要素简化方法的特点,指出了曲线二维经验模式分解在线要素综合中的适用性。
As the status of geographic information system (GIS) continuously improves in modern society, the needs of geographical information are increasingly expanded and demand levels become higher and higher. Furthermore, more and more geographic phenomena are observed, understood and descripted in different resolution, different spatial scales according to a variety of requirements. Also, the variable-scale spatial data are analyzed, processed and expressed. The Internet and the popularity of mobile services have promoted the emergence and development of variable scale characteristic GIS. Therefore, the oldest and classical cartography field——the cartographic generalization is energetic again as well as faces new challenges, making cartographic generalization a hot area of research and cutting-edge issues in GIS area.
The research on how to use computer-based map database so as to express map quickly and in multiple-scale is not only very significant and meaningful to maps for their information carriage and transmission in the new digital environment, but also makes the traditional cartographic generalization conform to the new requirements in the field of mapping. The data and information in GIS is expressed mainly through linear graphic elements, thus automatically linear features generalization is an important aspect of multi-scale expression of the geographic information. At present, the theory and methods that use spatial geometric constraints to linear features generalization have been widely used. However, not much attention has been paid to the geographic information generalization by filtering method, especially through empirical mode decomposition, which is an adaptive and natural approach for signal analysis. Empirical Mode Decomposition Method can well simplify and compress the linear elements. In addition, spatial geometric methods based on curvature have strong ability to maintain the shape of the characteristics curve in linear features generalization process. Therefore, the combination of spatial geometric constraints and filtering method is used for the automatic linear features generalization, and the main contents of this research include the following aspects:
1) The existing problems of cartographic characteristics as well as the linear features generalization in digital environment has been analyzed, and the necessity of using frequency domain filtering method in linear features generalization is discussed. By analyzing and summarizing the main problems in line generalization methods, the technical route, which uses curve empirical mode decomposition in two-dimensional space, is proposed to compress and simplify the linear elements.
2) A variety of spatial information generalization methods using filtering theory are studied. The empirical mode decomposition method is put forward based on summarizing and analyzing the theory of wavelet, Fourier transform and empirical mode decomposition theory. Through the empirical mode decomposition of lines in the two-dimensional space, multi-scale representation of linear features method is brought forward by using Bessel and BSpline curve approximation method.
3) The concept of visual curvature has been introduced, what is more, the advantages and disadvantages of curvature method in curve feature point detection are probed. Secondly, by summarizing the previous methods of curvature calculation, visual curvature computation based on elevating angular height calculation is proposed. Through experiments of polygon shape extraction based on visual curvature, curvature-based visualization method for curve simplifying is adopted.
4) The empirical mode decomposition algorithm for two-dimensional space and the curve reconstruction algorithm based on constraint features have been designed by combining empirical mode decomposition and curvature visualization method. By adopting the constraints such as spatial semantic relationship, the method for preserving the shape characteristics of linear features after generalization is establised.
5) The analysis and evaluation on results of linear features generalization is carried out, and an improved Hausdorff similarity curve evaluation method is proposed to examine the shape of curve characteristics after generalization. At the same time, both geometric characteristics assessment method and location accuracy evaluation method are used to analyze, evaluate the linear features generalization outcome. At last, the characteristics of simplifying linear features based on EMD have been pointed out. Also, the applicability of two-dimensional curves empirical mode decomposition in linear features generalization is indicated.
引文
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