Diffusion-based cartogram on spheres

A planar cartogram is a two-dimensional map, on which the area of each closed region is in direct proportion to a chosen extensive property. To date, various algorithms have been proposed to construct planar cartograms. This work extends the two-dimensional, diffusion-based, topologically invariant cartogram algorithm proposed by Gastner and Newman onto spheres. Unlike its planar counterpart, the spherical formulation does not require boundary conditions and is invariant to the rotation of input data on the sphere. An implementation of this spherical cartogram transformation is designed to generate readable topology-preserving cartograms on spheres. Lastly, the method is illustrated with applications to global data such as worldwide human population, gross domestic product (purchasing power parity), carbon dioxide emissions and regional data such as the Electoral College of the United States presidential election of 2016.     

面向双/多变量的连续面域拓扑图可视化方法

面域拓扑图是一种利用区域面积大小定量表达区域属性信息的可视化方法。由于其区域面积本身已经表示某一变量,因此这更有利于双/多变量的制图表达。针对目前基于面域拓扑图的双/多变量表达方法中存在的难以表达相邻区域之间基本状况和不利于不同地理现象的空间分布规律及差异表达的问题,本文提出一种面向双/多变量的连续面域拓扑图可视化方法。首先通过格网密度补偿和积分步长逐步试探的方法对基于扩散模型的连续面域拓扑图生成算法进行部分优化,完成基本变量的表达,然后分别通过空间内插和符号扩展完成第2和第3变量在连续面域拓扑图中的表达。最后以慕尼黑市人口密度和银行/ATM分布(双变量)数据以及奥格斯堡市人口密度数据、幼儿园分布以及规模数据(多变量)为试验数据进行可视化,并通过实证分析验证了该方法的有效性和优越性。     

Manual construction of continuous cartograms through mesh transformation

A computer-assisted framework is proposed to support the manual construction of cartograms. The framework employs a joint triangulation, similar to that used in rubber-sheeting, to define a piecewise affine transformation between map space and cartogram space. This guarantees preservation of all topological relations within and among transformed datasets with insertion of a finite number of points. To support intuitive user control of cartogram appearance, methods are developed to translate generically defined user adjustments of the cartogram into mesh vertex positions on either the source map mesh or cartogram mesh. The framework is implemented in a working prototype application and used to create sample cartograms of the USA and China. Results are compared with cartograms produced using diffusion and carto3f algorithms in terms of accuracy, aesthetic appearance, and approximate construction time. Qualitative aspects of the manual construction process are also discussed.     

Communication Aspects of Value-by-Area Cartograms

The value-by-area cartogram is a form of mapping often used for its visual impact. The average reaction to cartogram area is potentially error free in that the components of a typical value-by-area cartogram are areal shapes. When not in map form, map readers generally respond to these areas in a linear fashion. Results of a testing program to measure this ability suggest that the accuracy of the average response depends upon whether shapes are amorphous or square and whether the anchor stimulus is relatively large or small. The accuracy of responses to the cartogram compare favorably with responses to a five-class Flannery circle map. Map reader attitudes point out that these cartograms are thought to be confusing and difficult to read. At the same time they appear interesting, generalized, innovative, unusual, and having—as opposed to lacking—style. Communication depends on how well the cartographer has maintained the overall shape quality of the original geographical units and the provision of an adequate stimulus anchor, a geographical-base inset map, and labeling on the statistical units.     

Effectiveness of Cartogram for the Representation of Spatial Data

Abstract

<title/>

Cartogram is a technique for visualisation of the geographical distribution of spatial data. It has two main types, i.e. distance cartogram and area cartogram. Area cartogram is a transformed map in which areas are resized in proportion to an attribute value. A number of techniques have been developed for the generation of area cartograms. Some researchers consider cartogram as a very effective technique for visualisation of spatial data, while others doubt about the effectiveness because of the possible distortion in shape and/or disconnectivity in topology. This study aims to evaluate the effectiveness of area cartogram for visualizing spatial data. In this study, two comparative experiments have been conducted. One is the comparison between thematic maps and cartograms, and the other is the comparison among different types of area cartogram. Two sets of data with different characteristics are used, i.e. 2005 China population data and 1996 US election data. Results show that cartogram is more effective in the representation of the 1996 US election data which provides a qualitative result (i.e. in binary form or nominal data), but thematic map is far more effective in the representation of 2005 China population data which provides a quantitative result (in classes or ordinal data). It is also found that among different types of area cartogram, pseudo-cartogram is the most preferred technique and Dorling cartogram is the least preferred one.     

一种尺度效应指数修正的格网数据示意地图制图算法

示意地图是统计数据可视化的一种新方法,但已有的面域示意地图制图算法不适用于局部数据差别大的应用。针对此问题,结合多尺度格网统计数据的尺度效应,修正了diffusionbasedmethod算法,并将该算法应用于北京市100m格网人口统计数据上,证明了算法的有效性。该算法可应用于格网统计数据示意地图制图。     

Value-by-alpha maps: An alternative technique to the cartogram

The cartogram, or value-by-area map, is a popular technique for cartographically representing social data. Such maps visually equalize a basemap prior to mapping a social variable by adjusting the size of each enumeration unit by a second, related variable. However, to scale the basemap units according to an equalizing variable, cartograms must distort the shape and/or topology of the original geography. Such compromises reduce the effectiveness of the visualization for elemental and general map-reading tasks. Here we describe a new kind of representation, termed a value-by-alpha map, which visually equalizes the basemap by adjusting the alpha channel, rather than the size, of each enumeration unit. Although not without its own limitations, the value-by-alpha map is able to circumvent the compromise inherent to the cartogram form, perfectly equalizing the basemap while preserving both shape and topology.     

Cartograms for Use in Forecasting Weather-Driven Natural Hazards

This paper evaluates the potential of using cartograms for visualizing and interpreting forecasts of weather-driven natural hazards in the context of global weather forecasting and early warning systems. The use of cartograms is intended to supplement traditional cartographic representations of the hazards in order to highlight the severity of an upcoming event. Cartogrammetric transformations are applied to forecasts of floods, heatwaves, windstorms and snowstorms taken from the European Centre for Medium-range Weather Forecasts (ECMWF) forecast archive. Key cartogram design principles in standard weather forecast visualization are tested. Optimal cartogram transformation is found to be dependent on geographical features (such as coastlines) and forecast features (such as snowstorm intensity). For highly spatially autocorrelated weather variables used in analysing several upcoming natural hazards such as 2m temperature anomaly, the visualization of the distortion provides a promising addition to standard forecast visualizations for highlighting upcoming weather-driven natural hazards.     

Value-by-alpha Maps: An Alternative Technique to the Cartogram

Abstract

<title/>

The cartogram, or value-by-area map, is a popular technique for cartographically representing social data. Such maps visually equalize a basemap before mapping a social variable by adjusting the size of each enumeration unit by a second, related variable. However, to scale the basemap units according to an equalizing variable, cartograms must distort the shape and/or topology of the original geography. Such compromises reduce the effectiveness of the visualisation for elemental and general map-reading tasks. Here we describe a new kind of representation, termed a value-by-alpha map, which visually equalizes the basemap by adjusting the alpha channel, rather than the size, of each enumeration unit. Although not without its own limitations, the value-by-alpha map is able to circumvent the compromise inherent to the cartogram form, perfectly equalizing the basemap while preserving both shape and topology.     

正交距离圆曲线拟合方法

在分析圆曲线拟合准则基础上,提出采用正交最小二乘法拟合圆曲线。该方法以圆曲线正交距离残差平方和极小为准则。基于间接平差原理详细推导了相关模型和算法,并以实际算例说明了该方法的效果。     

包含圆形的单幅图像距离量测

提出了两种基于圆形的单幅图像平面几何量测方法。第一种算法首先计算出与待测对象平行的直径,然后获得圆形所在平面上任意两点之间的距离。受待测线段位置、方向等影响,量测结果的精度各向差异大。第二种算法首先求取圆形的外接正方形,将问题转化为包含正方形的平面距离量测。模拟图像与真实图像的测试结果表明,第二种算法的量测精度更具有稳定性。     

一种顾及制图区域要素密度均衡的地图变换算法

制图区域要素密度分布不均衡会增加地图表达难度,常规地图表达方式无法解决视觉不平衡的问题。在Gastner-Newman地图变形算法的基础上,提出了一种顾及制图区域要素密度平衡和公众地图认知一致性的地图变换算法。首先,设计多种变形单元尺度以及配置制图要素密度权重组合;然后,代入线性扩散方程,构建变形格网并映射各离散控制点;最后,生成多种变形地图结果。开展了地图认知实验,获得56份问卷结果,针对中国广西南宁市青秀区行政区划图的形态控制,应控制S_周长 > 0.975、S_{周长面积比} > 0.961、S_形状比 > 0.966,能兼顾地图形变以及公众认知的一致性。为解决地图要素密度不均衡的问题提供了新的思路,变形后的地图达到视觉平衡,同时,通过调整形变权重参数实现了公众地图认知的一致性。     

基于等距圆的极球面投影距离量测方法

研究了极球面投影海图上准确便捷地量测距离的方法。推导了极球面投影下大圆航线和等角航线的方程,形状分析表明极区宜采用大圆航线量测距离;根据极球面投影下直线的几何意义推导了其距离计算公式,距离差值分析表明可用直线代替大圆航线准确量测距离;根据极球面投影上小圆线投影为圆的性质,提出了一种基于等距圆的准确便捷的距离量测方法,以满足极球面投影海图的极区导航应用需要。     

DSSRM级联分割的SAR图像变化检测

SRM(Statistical Region Merging)分割算法具有快速、稳定和抗噪强的优点,基于此,本文提出一种基于DSSRM(Dynamic Sorting Statistical Region Merging)级联分割的SAR图像变化检测方法。首先,针对SRM算法基于单特征静态排序导致的过分割问题,提出一种动态排序模式的DSSRM算法以减少差异图像分割错误,该算法建立基于合并区域的多特征马氏距离排序准则,在每次合并之后更新区域邻接矩阵并重新排序;然后,基于互信息最小化准则构造多通道差异数据集以提高算法对区域合并的约束能力;最后,提出一种级联分割变化检测框架,第1级利用SRM算法将差异图像映射到超像素空间,第2级采用DSSRM算法对超像素进行动态合并获得收敛的分割结果,第3级采用简化SRM方法进行三次合并获得最终的变化检测图。实验结果表明,该方法可以获得比SRM方法和目前流行方法更好的检测性能。     

矩形Cartogram自动构建方法探究

矩形Cartogram作为一种同时表达拓扑及数据属性的面域Cartogram,因其表达内容简单、直观的特点,具有较大的潜力。矩形Cartogram尝试用简单的矩形表示复杂地理所具有的拓扑及数据属性,这两个属性在其自动构建过程中往往是矛盾的,因此产生了很多截然不同的构造方法。对其自动构建方法进行研究,有助于地理信息与统计数据融合方法的探索。本文首先简要介绍了矩形Cartogram的研究背景、研究现状及其意义;归纳了矩形Cartogram的特点与评价标准,进而分析了两类构造矩形Cartogram的典型算法,总结了自动构建算法难点;最后探讨了现有矩形Cartogram研究存在的问题,并对其发展方向进行了展望。     

线/面Voronoi图的分解合并生成算法

Voronoi图生成算法受到计算效率或生长源类型的限制,难以支撑线/面生长源Voronoi图的构建。本文提出一种生成线/面生长源Voronoi图的分解合并算法,其主要过程是将线/面生长源离散为特征点表达,通过特征点交叉建立最近特征点对,并以最近特征点对Voronoi子区域的交来部分地代替线/面生长源的等距离边界,算法以前后迭代离散计算的Voronoi子区域面积差分作为条件,可有选择地将部分生长源置入迭代过程,使线/面生长源Voronoi子区域逐步调整并达到精度要求。     

空间关系中两相邻实体间最近距离算法研究

空间距离关系是最基本、最重要的一类空间关系。通过先考虑二维空间中两任意实体之间不同的相对位置关系,再利用构建Delaunay三角网寻找两者的邻近区域,从而计算出两者之间的最近距离。本文还提出了基于约束圆寻找并计算任意两个实体多边形之间的最近距离方法,并给出了约束圆的特征。这种方法适用于不用区分实体多边形的形状与位置的各种情况。     

脉冲耦合神经网络支持下的网络Voronoi图构建

针对网络Voronoi图中点与点之间通过实际路径距离而非传统欧式距离相连,在实际应用中较平面Voronoi图更加合理,该文提出了一种基于改进脉冲耦合神经网络的网络Voronoi图构建算法。借助模型的自动波发放及并行处理特性,较好地实现了基于路网的网络空间剖分,顾及了道路网及其点群自身属性对其服务范围的影响。实验表明,该算法实现了点群网络Voronoi图的构建,最短路径思想的引入使得构建的网络Voronoi图符合Voronoi图基本特征,可以用来表示点群的服务范围,不仅如此,算法的并行特性保证了算法的高效率。     

基于时空影响因子的未来社区生活圈公共服务设施优化配置北大核心CSCD

公共服务设施作为社区生活圈的核心内容,直接决定了社区生活圈的生活品质。对社区公共服务设施建设情况进行量化评价,并对设施建设的未来规划提供科学决策支持逐渐成为规划者和决策者的一大难题。本文通过ArcGIS工具对POI数据进行处理、统计和可视化,在总结他人社区生活圈量化评价方法的基础上,结合温州本地特色,搭建了一套社区生活圈公共服务设施评价模型。利用该模型可对各类社区进行综合评分和分级,并根据模型评分结果挖掘公共服务设施未来优化方向。此外,还实现了社区生活圈评分的动态计算与展示,为社区服务设施建设选址、路网建设与公共服务设施建设优先级评定等提供决策支持。既可帮助规划者和决策者快速建立对整个区域生活圈建设现状的量化认知,又可助力公共服务设施的优化配置,为社区生活圈公共服务品质评价与提升探寻全新的思路与方法。