| 基于小波分析的地貌多尺度表达与自动综合 |
| |
| 引用本文： | 吴凡,祝国瑞.基于小波分析的地貌多尺度表达与自动综合[J].武汉大学学报(信息科学版),2001,26(2):170-176. |
| |
| 作者姓名： | 吴凡 祝国瑞 |
| |
| 作者单位： | 武汉大学资源与环境科学学院, |
| |
| 基金项目： | 国家自然科学基金资助项目(69773048)；国家测绘科技发展基金资助项目(99013)；武汉测绘科技大学科技发展基金资助项目(9809)。 |
| |
| 摘 要： | 基于小波多分辨率分析原理，给出了一种尺度依赖的地表形态抽象与表达方法。基于该方法研究了多尺度的地貌自动综合，提出了利用小波系数的范数比作衡量相应尺度综合程度的数量化指标，并结合实例予以说明。
|
| 关 键 词： | 小波多分辨率分析 多尺度处理 DEM 自动综合 小波变换 空间数据库 GIS 遥感图像处理 |
| 文章编号： | 1000-050X(2001)02-0170-07 |
| 修稿时间： | 2000年10月29 |
Multi-scale Representation
and Automatic Generalization of Relief Based on Wavelet Analysis |
| |
| WU Fan,ZHU Guorui.Multi-scale Representation
and Automatic Generalization of Relief Based on Wavelet Analysis[J].Geomatics and Information Science of Wuhan University,2001,26(2):170-176. |
| |
| Authors: | WU Fan ZHU Guorui |
| |
| Institution: | WU Fan 1 ZHU Guorui 1 |
| |
| Abstract: | With the development of GIS application ceaselessly, a mass of multi-scale geospatial data need to be analyzed and represented because users require different detailed spatial data to dealwith different problems and output maps at different scales. It has become one of the key problemsto applied GIS. The logic relations have to be established between spatial data sets at differentscales so that one representation of spatial data can be transferred to another completely. The completeness refers that spatial precision and characteristics and a high information density that adaptsto relevant abstract detail must be preserved,and the consistency of spatial semantics and spatialrelations have to be maintained simultaneously.In addition, the deriving of new spatial data setsshould be bi-directional on some constraint in GIS, from fine-scale to broad-scale and vice versa.Automatic generalization of geographical information is the core content of multi-scale representation of spatial data, but the scale-dependent generalization methods are far from abundance becauseof its extreme complicacy.Most existing algorithms about automatic generalization do not relate toscale directly or accurately, not forecast and control the generalized effects, and cannot assess theholistic consistency of the generalized results. The rational and quantitative methods and criterionsof measuring the extent of generalization have not still been sought out. Wavelet analysis is a newbranch of mathematics burgeoning at the end of 1980s. It has double meanings simultaneously onprofundity of theory and extent of application. Because it has good local character at both time orspace and frequency field simultaneously, and sample interval of signal can be adjusted automatically with different frequency components, any details of function, such as a sign or image etc., canbe analyzed at any scales by using wavelet analysis. Therefore, wavelet analysis suggests a new solution to the problems mentioned above. The fundamental characteristics of multi-scale spatial datacan be detected and extracted,and represented by a set of wavelet coefficients, then handled andreconstructed, then the optimal representation of the spatial data sets can be got. This paper studies the multi-scale representation and automatic generalization of relief and the quantitative methodand criterion of investigating the extent of generalization based on the above idea. The paper formulates briefly the basic principle of multiresolution analysis (MRA) on wavelet transform atfirst, and describes a model for multi-scale handling of spatial data based on MRA of wavelet. Weknow that subspace at a higher resolution includes completely all information at a lower resolutionfrom the model, so multiple data sets such as Vi, V2,…, VJ may be derived from a basic set ofspatial data V0 at multiple scale by using MRA of wavelet, and the reverse procedure can be implemented completely by reconstructing. The decomposition and reconstruction are very stable.Accordingly, the model not only meets the need of automatic generalization but also is scale-dependent completely. Handling of automatic generalization is reverse based on the model.Two sections,approximation Ajf and detail Dejf, can be produced automatically by MRA of wavelet. The approximation describes the gentle and trend component of the characteristics of data, and the detaildescribes the fast and local one. They represent low and high frequency of data respectively. Whendata sets at scale j are derived from scale j + 1 , the loss of the approximation is Wj because Vj + 1 ＝ Vj Wj and Vj Vj+ 1, described by Deejf. Therefore,{Dej f} represents the detail generalized at stepped down scale. DEM is an abstract model about relief in GIS. The key problem of multi-scale representation of relief is how to derive the DEM at multiple scales. We propose a schemefor a multi-scale representation and generalization of scale-dependent relief based on the abovemodel,which can be represented by a four tuple:MultiGeomorph ＝ {φ(x ),ψ (x), (Vj)j∈z,( Wj )j∈z }. The tuple includes all information about relief representation at multiple scales. It is ananalysis system based on MRA of wavelet, and describes the mechanism about deriving multi-scaleDEM. Furthermore , it is a dynamic system studying the rule about state of data changing withscale. Therefore,We can get the multi-scale DEM from the MultiGeomorph, the size of the sequence DEMs derived is 2-ktimes of its original, and the relevant scale is stepped down a alf. Withthe scale decreased,the fine characteristics of relief are reduced and filtrated down step by step,but the main characteristics are represented. So the detail extent of relief represented changes withscale.The practical examples are demonstrated in Fig. 1. Model generalization is foundation forcartographical generalization based on DEM. As a result, it is more adapted to analysis and application of GIS,and avoids the harmonization between group contours, which is very difficult for themethods based on contour generalization. The precondition of generalization is derivative of multiscale DEM. The generalization can be considered as a procedure of information reducing on certanconditions. Using MRA of wavelet will erase the topographic points and details, which are minimum contribution for constructing topographical surface. For example, Figs. 2 and 3 demonstratethe original contour map and the generalized counterpart.Assuming { C-J } represents the coefficients of wavelet that include all information after MRA of wavelet, their energy is norm ‖ CJ ‖ .If { CP } represents the wavelet coefficients after generalized, norm ‖ CP ‖ is their energy. Accordingly, the percentage of ‖ CP ‖ to ‖ C-y ‖ can measure the detail extent between the original data sets and their counterparts derived. |
| |
| Keywords: | multi_resolution analysis of wavelet scale dependence multi_scale processing and representations DEM automatic generalization |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
|
