General Entropy Model of Line Segments Uncerta,nty in GIS

Spatial data uncertainty can directly affect the quality of digital products and GIS-based decision making. On the basis of the characteristics of randomicity of positional data and fuzziness of attribute data, taking entropy as a measure, the stochastic entropy model of positional data uncertainty and fuzzy entropy model of attribute data uncertainty are proposed. As both randomicity and fuzziness usually simultaneously exist in linear segments, their omnibus effects are also investigated and quantified. A novel uncertainty measure, general entropy, is presented. The general entropy can be used as a uniform measure to quantify the total uncertainty caused by stochastic uncertainty and fuzzy uncertainty in GIS.     

General entropy model of line segments uncertainty in GIS

Spatial data uncertainty can directly affect the quality of digital products and GIS-based decision making. On the basis of the characteristics of randomicity of positional data and fuzziness of attribute data, taking entropy as a measure, the stochastic entropy model of positional data uncertainty and fuzzy entropy model of attribute data uncertainty are proposed. As both randomicity and fuzziness usually simultaneously exist in linear segments, their omnibus effects are also investigated and quantified. A novel uncertainty measure, general entropy, is presented. The general entropy can be used as a uniform measure to quantify the total uncertainty caused by stochastic uncertainty and fuzzy uncertainty in GIS.     

GIS中空间数据不确定性的混合熵模型研究

基于信息理论和模糊集合理论，针对GIS中部分空间数据既具有随机性又具有模糊性的特点，建立了空间数据不确定性的混合熵模型。以GIS中线元不确定性为例，讨论了线元不确定性的统计熵、模糊熵和混合熵估计方法，并针对特例给出了线元不确定性的熵带分布。     

熵理论在确定点位不确定性指标上的应用

分析了传统点位不确定性指标的局限性，基于信息论中的联合熵和最大熵定理导出了n维随机点熵不确定指标以及落入其内概率的统一公式；提出了以熵误差椭圆与熵误差椭球作为2维、3维GIS中点元的位置不确定性度量指标。提出的熵指标具有唯一确定、不受置信水平选取的主观性影响等特点，适合于度量未知分布的点位不确定性。     

GIS中线元的误差熵带研究

基于现有的线元位置不确定性模型大多与置信水平的选取有关,而置信水平的选取带有一定程度的主观性,因而不能惟一确定,引入信息熵理论,提出了线元的误差熵带模型,并将它与“E－带”进行了比较,计算了落入其内的概率。该模型根据联合熵惟一确定,与置信水平的选取无关。     

GIS中三维空间直线的误差熵模型

从信息熵的角度提出了三维空间直线的误差熵模型，该模型由以垂直直线的平面误差熵为半径的圆柱体和两端点的误差球组成，是一种完全确定的度量空间线元不确定性的模型。理论分析与实验表明，本文所提出的模型具有较好的效果。     

基于模糊综合评判的选址空间决策支持系统

传统的选址空间决策支持系统的数学模型难以全面考虑复杂、抽象的选址影响因素,难以把一些模糊的约束条件纳入数学模型,因而模型存在一定缺陷。利用模糊综合评判进行选址空间决策支持系统的研究,可以充分利用GIS的空间和非空间信息,且考虑的因素更为全面,极大地避免了人为因素的影响,是对选址决策支持系统数学模型的改进。     

Entropy error model of planar geometry features in GIS

Positional error of line segments is usually described by using “g-band”, however, its band width is in relation to the confidence level choice. In fact, given different confidence levels, a series of concentric bands can be obtained. To overcome the effect of confidence level on the error indicator, by introducing the union entropy theory, we propose an entropy error ellipse index of point, then extend it to line segment and polygon, and establish an entropy error band of line segment and an entropy error donut of polygon. The research shows that the entropy error index can be determined uniquely and is not influenced by confidence level, and that they are suitable for positional uncertainty of planar geometry features.     

GIS图上地理区域空间不确定性的分析

区域是GIS空间分析的基本单元。它是环境科学、土壤科学等领域中广泛存在的一类地理实体。这类实体抽象概括为GIS中空间目标时不可避免地带有模糊性。利用模糊集这个强有力的数学工具，首先基于场模型提出了表达GIS中模糊区域目标的方法，分析了其空间不确定性。继而，建立了模糊区域的形态描述模式，即模糊区域边界、内部和外部，并指出了Cohn给出的定义中的不足。在此基础上，对Egenhofer提出的九元组进行了扩展，构建了适合于描述确定和模糊区域目标间拓扑空间关系的模型。     

空间数据处理模型误差和不确定性分析

在GIS应用中,涉及到大量的模型应用,这些模型包括了利用GIS进行空间信息处理的大部分阶段中所用到的模型。模型处理以及分析结果往往是进行下一步应用的基础,因此模型处理结果的误差和不确定性制约了实际的GIS应用。影响空间数据处理模型的误差和不确定性的因素主要包括:定位和特征信息,制图,空间分析,空间数据库以及空间数据处理模型等所具有的误差和不确定性。主要分析了空间数据处理模型误差和不确定性的表达、来源以及分析方法。     

空间数据处理模型误差和不确定性分析

在GIS应用中,涉及到大量的模型应用,这些模型包括了利用GIS进行空间信息处理的大部分阶段中所用到的模型.模型处理以及分析结果往往是进行下一步应用的基础,因此模型处理结果的误差和不确定性制约了实际的GIS应用.影响空间数据处理模型的误差和不确定性的因素主要包括:定位和特征信息,制图,空间分析,空间数据库以及空间数据处理模型等所具有的误差和不确定性.主要分析了空间数据处理模型误差和不确定性的表达、来源以及分析方法.     

Entropy error model of planar geometry features in GIS

Positional error of line segments is usually described byusing “g-band”,however,its band width is in relation to the confidence level choice.In fact,given different confidence levels,a series of concentric bands can be obtained.To overcome the effect of confidence level on the error indicator,by introducing the union entropy theory,we propose an entropy error ellipse index of point,then extend it to line segment and polygon.and establish an entropy error band of line segment and an entropy error do-nut of polygon.The research shows that the entropy error index can be determined uniquely and is not influenced by confidence level,and that they are suitable for positional uncertainty of planar geometry features.     

Exploring uncertainty in remotely sensed data with parallel coordinate plots

The existence of uncertainty in classified remotely sensed data necessitates the application of enhanced techniques for identifying and visualizing the various degrees of uncertainty. This paper, therefore, applies the multidimensional graphical data analysis technique of parallel coordinate plots (PCP) to visualize the uncertainty in Landsat Thematic Mapper (TM) data classified by the Maximum Likelihood Classifier (MLC) and Fuzzy C-Means (FCM). The Landsat TM data are from the Yellow River Delta, Shandong Province, China. Image classification with MLC and FCM provides the probability vector and fuzzy membership vector of each pixel. Based on these vectors, the Shannon's entropy (S.E.) of each pixel is calculated. PCPs are then produced for each classification output. The PCP axes denote the posterior probability vector and fuzzy membership vector and two additional axes represent S.E. and the associated degree of uncertainty. The PCPs highlight the distribution of probability values of different land cover types for each pixel, and also reflect the status of pixels with different degrees of uncertainty. Brushing functionality is then added to PCP visualization in order to highlight selected pixels of interest. This not only reduces the visualization uncertainty, but also provides invaluable information on the positional and spectral characteristics of targeted pixels.     

八方向模糊不均匀划分及参考点位误差所致不确定性分析

方向概念的模糊性和空间数据固有的不确定性导致了方向关系的复杂性,在空间关系描述和推理研究中需要考虑空间数据的不确定性和方向概念的模糊性。在四方向模型中各方向片是等角划分;在八方向模型中4个主要方向片各占60°,4个次要方向片各占30°。利用区间二型模糊集理论建立了顾及参考点点位误差的八方向模糊不均匀划分模型,基于区间二型模糊集讨论了方向主隶属度成员函数和隶属度的不确定性。对比分析了八方向模糊不均匀划分模型与锥形模型的区别,讨论了具有点位误差的参考点与线和多边形的方向关系计算过程,通过两个实例分析了该模型的特点和点与多边形方向关系的确定方法。     

利用误差熵评价光斑中点云不确定性

三维激光扫描点位精度受光斑影响较大,激光点在光斑中呈现了不确定性,该不确定性的准确描述关系到激光点位精度的评价。将误差熵模型引入到点位不确定性的评价中,利用激光点位在光斑中不确定性的概率密度函数,推导了激光点位信息熵,并依据误差熵与信息熵的关系得到了激光点位的误差熵。通过分析误差熵与光斑面积的关系,得到点云光斑平均误差熵,实现了将平均误差熵引入到点云不确定性的评价中。通过设置不同扫描间隔得到的点云数据,分析了平均熵模型进行基于光斑影响下的点云精度评价的可行性,最终实现了对光斑中点云不确定性的准确评价。     

矢量GIS中属性数据的不确定性分析

本文从属性区域分类不确定性、边界定位误差和区域内部定量属性数据的抽样误差出发,综合进行属性数据不确定性的度量和传播分析。针对由边界定位误差引起的属性分类不确定性,在顾及区域面积与边界线数等因素下,提出了一种定量度量指标。对于属性区域内部的定量属性抽样值,则建立了抽样值的相关函数表达式。针对ＧＩＳ中常见的两大类操作,即逻辑操作和算术操作,分别根据模糊集合论和概率统计理论建立了相应的属性不确定性传播模     

空间数据不确定性研究现状分析

归纳总结了位置不确定性、属性不确定性、时域不确定性、逻辑不一致性等方面的研究现状，重点归纳了位置不确定研究成果；最后指出了GIS不确定性研究存在的问题，并对GIS数据质量控制研究重点进行了分析。     

分层递阶近似空间下的GIS属性数据不确定性描述

GIS属性数据作为GIS实体的属性,具有模糊性、不确定性。由GIS实体对象和对象的属性组成的二元关系满足近似空间的特性。本研究从GIS信息系统的对象、属性出发,利用格概念,认为GIS属性数据集合可以构成偏序关系,并且(P(A),)构成一个完备的偏序格。如果从属性链的角度分析,GIS实体集在的细分划分空间关系下,可以构成分层递阶近似空间,并且随着属性个数的增加,知识颗粒将逐渐"细化"。     

A Framework for Modeling Uncertainty in Spatial Databases

Geographic Information Systems and spatial databases are inherently suited for fuzziness, because of the uncertainty inherent in the assimilation, storage, and representation of spatial data. These objects may also have naturally occurring imprecise boundaries. It is difficult to store and represent these objects while continuing to demonstrate the uncertainty inherent in the objects. This paper describes a fuzzy object–oriented framework to model spatial objects with either precise or uncertain boundaries that will also provide for fuzzy querying of these objects. A prototype system, FOOSBALL, which implements this framework is also discussed.     

关于“新的点位误差度量”的讨论

多维点位误差度量应该反映点的位置的不确定度,它可以是方差或方差的某种函数.实践中,有多种点位误差的表示形式,不同的表示形式有不同的几何意义或概率意义.文献[1]提出采用坐标分量方差的均值作为点位误差的度量.为了将其与现有点位误差度量进行比较,本文列出4种点住误差度量表达式,并讨论了它们的几何意义.强调指出,点位误差度量的具体数值应大于等于最大可能的误差,以保证用户使用数据的安全性.