THE NOMENCLATURE OF MAP PROJECTIONS

Abstract

Map Projections.—A matter that should have been mentioned in the original article under this title (E.S.R., vii, 51, 190) is the definition of a map projection. In the list of carefully worded “Definitions of Terms used in Surveying and Mapping” prepared by the American Society of Photogrammetry (Photogrammetrie Engineering, vol. 8,1942, pp. 247–283), a map projection is defined as “a systematic drawing of lines on a plane surface to represent the parallels of latitude and the meridians of longitude of the earth or a section of the earth”, and most other published works in which a definition appears employ a somewhat similar wording. This, however, is an unnecessary limitation of the term. Many projections are (and all projections can be) plotted from rectangular grid co-ordinates, and meridians and parallels need not be drawn at all; but a map is still on a projection even when a graticule is not shown. Objection could be raised also to the limitation to “plane surface”, since we may speak of the projection of the spheroid upon a sphere, or of the sphere upon a hemisphere. Hence, it is suggested that “any systematic method of representing the whole or a part of the curved surface of the Earth upon another (usually plane) surface” is an adequate definition of a map projection.     

Ellipsoidal terrain correction based on multi-cylindrical equal-area map projection of the reference ellipsoid

An operational algorithm for computation of terrain correction (or local gravity field modeling) based on application of closed-form solution of the Newton integral in terms of Cartesian coordinates in multi-cylindrical equal-area map projection of the reference ellipsoid is presented. Multi-cylindrical equal-area map projection of the reference ellipsoid has been derived and is described in detail for the first time. Ellipsoidal mass elements with various sizes on the surface of the reference ellipsoid are selected and the gravitational potential and vector of gravitational intensity (i.e. gravitational acceleration) of the mass elements are computed via numerical solution of the Newton integral in terms of geodetic coordinates {,,h}. Four base- edge points of the ellipsoidal mass elements are transformed into a multi-cylindrical equal-area map projection surface to build Cartesian mass elements by associating the height of the corresponding ellipsoidal mass elements to the transformed area elements. Using the closed-form solution of the Newton integral in terms of Cartesian coordinates, the gravitational potential and vector of gravitational intensity of the transformed Cartesian mass elements are computed and compared with those of the numerical solution of the Newton integral for the ellipsoidal mass elements in terms of geodetic coordinates. Numerical tests indicate that the difference between the two computations, i.e. numerical solution of the Newton integral for ellipsoidal mass elements in terms of geodetic coordinates and closed-form solution of the Newton integral in terms of Cartesian coordinates, in a multi-cylindrical equal-area map projection, is less than 1.6×10^–8 m²/s² for a mass element with a cross section area of 10×10 m and a height of 10,000 m. For a mass element with a cross section area of 1×1 km and a height of 10,000 m the difference is less than 1.5×10^–4m²/s². Since 1.5× 10^–4 m²/s² is equivalent to 1.5×10^–5m in the vertical direction, it can be concluded that a method for terrain correction (or local gravity field modeling) based on closed-form solution of the Newton integral in terms of Cartesian coordinates of a multi-cylindrical equal-area map projection of the reference ellipsoid has been developed which has the accuracy of terrain correction (or local gravity field modeling) based on the Newton integral in terms of ellipsoidal coordinates.Acknowledgments. This research has been financially supported by the University of Tehran based on grant number 621/4/859. This support is gratefully acknowledged. The authors are also grateful for the comments and corrections made to the initial version of the paper by Dr. S. Petrovic from GFZ Potsdam and the other two anonymous reviewers. Their comments helped to improve the structure of the paper significantly.     

Channels of synthesis forty years on: integrated analysis of spatial economic systems

Isards vision of integrated modeling that was laid out in the 1960s book Methods of Regional Science provided a road map for the development of more sophisticated analysis of spatial economic systems. Some forty years later, we look back at this vision and trace developments in a sample of three areas – demographic-econometric integrated modeling, spatial interaction modeling, and environmental-economic modeling. Attention will be focused on methodological advances and their motivation by new developments in theory as well as innovations in the applications of these models to address new policy challenges. Underlying the discussion will be an evaluation of the way in which spatial issues have been addressed, ranging from concerns with regionalization to issues of spillovers and spatial correlation.     

地图制图软件中境界跳绘技术研究

境界跳绘处理是地图制图中比较特殊的一个制图步骤。本文在分析境界线属性的基础上,提出了将跳绘境界线分为跳绘符号段和跳绘间隔段两部分,通过计算各个跳绘符号段中点来确定跳绘符号段坐标串的方法。在计算符号段中点时,首先分别计算境界线的明显拐弯点和距离两端半个符号段长度的点作为跳绘符号段中点,将这些中点进行一定的合并与删除后,再计算两两中点间可能存在的其余符号段中点。实验证明该方法可行有效。     

经验爬虫应用于网络地图服务获取

网络地图服务已经渗透到国民经济的方方面面,如何从海量的地图服务中获取需要的数据成为当下研究的热点问题。本文针对目前Web地图服务数据在使用爬虫技术获取中,存在效率和准确性低的问题,提出在经典网络爬虫基础上,增加"经验树"环节,实现了"经验爬虫"。将改进后的"经验爬虫"与其他3种经典爬虫爬取的结果对比分析,"经验爬虫"爬取的效率和准确性是其他3种经典爬虫均值的2倍以上。     

Problems of mapping a nature reserve: Aberlady Bay LNR and SSSI

Abstract

A new five-colour map of Aberlady Bay Local Nature Reserve and Site of Special Scientific Interest at 1:7,500 scale is published as a loose insert with the June 1993 issue of The Cartographic Journal. This accompanying paper describes the problems of producing the map at minimal cost, considers some of the cartographic issues particular to the site, and provides specification details of the compilation.

Such individual map sheets, which are used for environmental planning, research and teaching, have in the past been produced mainly by universities with the support of conservancy and countryside agencies. Future production costs at universities will inevitably rise although some economies may be possible by the use of digital database methods of cartography.     

关于地理信息系统未来发展的思考

在Geographic Information System(GIS)近60年的发展演进中,理论和技术都取得了长足的进步;应用领域扩大到社会的方方面面,社会影响力越来越大;体系结构、开发模式和服务模式等都发生了深刻的变化。为了推动GISystem进一步向前发展,在综述GIS中之“S”的三种含义即System（系统）、Science（科学）和Service（服务）以及GIS近60年来取得的丰硕成果的基础上,重点就以下三个问题进行了讨论：（1）如何认识地理信息系统（GISystem）。首先解析地理信息系统的三个关键词（系统、信息、地理信息）,据此论述了地理信息系统的内涵,分析了地理信息系统同地图、计算机地图制图、地图数据库的关系,认为地理信息系统源于又超越了地图、计算机地图制图和地图数据库,并认为地理信息系统具有装备的特性。（2）地理信息系统是怎样发展演进的。重点分析了由“地理信息系统”到“地理信息服务”的发展演进的社会需求背景、技术背景、学科背景,从应用领域、数据资源和功能的扩展及体系结构、开发模式和服务模式等方面,分析了地理信息系统发展演进的主要表现。（3）地理信息系统的未来发展将走向...     

A Study of the Local Geometric Accuracy of Count de Ferraris's Carte de cabinet (1770s) Using Differential Distortion Analysis

The eighteenth century Carte de cabinet of count de Ferraris is the first large-scale (1:11?520) topographic map of the entire Belgian territory, making it a valuable source of historical information. In the past, a number of studies have tried to assess the geometric accuracy of this map, but they all suffer from restricted technical capabilities for computing and visualizing the distortions, and most of them only focus on a limited number of the 275 map sheets. This paper therefore seeks to provide the first systematic and in-depth investigation of the map’s local geometric accuracy. Recently, two Belgian government agencies georeferenced the Flemish and Walloon part of the Carte de cabinet with a high level of detail, using some 30,000 ground control points to link the old map to the modern topographic map of Belgium. These data sets represent a new and unprecedented potential source of accuracy information. However, the high number of control points and our desire to compute distortions in an exact, local, quantitative and continuous way meant prominent techniques for studying the geometric accuracy of old maps, such as displacement vectors, distortion grids, triangular nets and the popular MapAnalyst software, were unsuited for this task. To meet all our requirements a new technique called Differential Distortion Analysis, which is influenced by the treatment of distortions in map projection theory, was used instead. Its advantages, structure and application to the Carte de cabinet are discussed in detail. The new technique allows calculating and displaying the map’s local angular and surface distortions with a very high spatial resolution. Consequently, it was possible to identify trends in the obtained levels of accuracy and to relate these to historical facts about the Carte de cabinet’s production process. This has resulted in important new insights into the map’s geometric accuracy.     

Design, analysis, and inference for studies comparing thematic accuracy of classified remotely sensed data: a special case of map comparison

Assessing thematic map accuracy is a special type of map comparison that is frequently applied to remote sensing classification problems. For map comparisons in the accuracy assessment setting, one map represents the classified output and the other map represents the true or “reference” condition. Several articles in this special issue describe state-of-the-art map comparison analysis tools that could serve to quantify accuracy of a single map. However, accuracy assessment objectives generally extend beyond describing accuracy of a single map to comparing accuracy of several maps. Consequently, interest focuses on comparing map comparison measures when these measures are used to represent accuracy. The virtual workshop emphasizes the analysis component of map comparisons, but it is also important to examine the underlying study designs generating the data input into these analyses. The study designs for accuracy comparisons implemented in remote sensing practice often investigate only a single test site, thus limiting our ability to generalize the results of these accuracy comparisons. Map accuracy comparison studies can be designed to provide stronger generalizations by incorporating experimental design principles such as replication and blocking, and identifying an experimental unit appropriate for the application. It is also important to recognize the role of statistical hypothesis testing and inference for different objectives that motivate map accuracy comparisons. Deciding which of two maps to use for a particular site can be addressed by enumerative inference and does not require hypothesis testing. For the objective of a more general comparison of classification procedures, analytic inference is appropriate and hypothesis testing plays a more prominent role.     

Quantitative relations between spatial similarity degree and map scale change of individual linear objects in multi-scale map spaces

Quantitative relations between spatial similarity degree and map scale change in multi-scale map spaces play important roles in map generalization and construction of spatial data infrastructure. Nevertheless, no achievements have been made regarding this issue. To fill the gap, this paper firstly proposes a model for calculating spatial similarity degrees between an individual linear object at one scale and its generalized counterpart at the other scale. Then psychological experiments are designed to validate the new model, taking four different individual linear objects at five different scales as test samples. The experiments have shown that spatial similarity degrees calculated by the new model can be accepted by a majority of the subjects. After this, it constructs a formula that can calculate spatial similarity degree using map scale change (and vice versa) for individual linear objects in multi-scale map spaces by the curve fitting method using the point data from the psychological experiments. Both the formula and the model can calculate quantitative relations between spatial similarity degree and map scale change of individual linear objects in multi-scale map spaces, which facilitates automation of map generalization algorithms for linear features.     

Updating land cover automatically based on change detection using satellite images: case study of national forests in Southern California

Observing dynamic change patterns and higher-order complexities from remotely sensed images is warranted, but the main challenges include image inconsistency, plant phenological differences, weather variations, and difficulties of incorporating natural conditions into automatic image processing. In this study, we proposed a new algorithm and demonstrated it by producing 2002–2008 and 2010 land-cover maps in heterogeneous Southern California based on an existing 2009 land-cover map. The new algorithm improves the baseline land-cover map quality by discarding potential bad land-cover pixels and dividing each land-cover type into several subclasses. Time series Landsat images were used to detect changed and unchanged areas between baseline year and target year t. Subsequently, for each individual year t, each pixel that was identified as unchanged inherited the baseline classification. Otherwise, each pixel in the changed areas was classified by a similar surrogate majority classifier. The demonstration results in Southern California showed that the land-cover temporal pattern captured the observed successional stages of the ecosystem very well. The accuracy assessment had an overall classification accuracies ranging from 81% to 86% and overall kappa coefficients ranging from 0.79 to 0.83.     

跨媒介的地图色域映射方法研究

颜色设备相关性的特点导致地图在跨媒介再现时容易出现丢色、偏色等现象,影响地图视觉效果,甚至传输错误的属性、数量等信息。从地图色域特征出发,将地图色域映射问题转换为目标设备色域约束下的地图色域离散点云形变问题。进一步引入Delaunay剖分和几何矩,定义CIE1976LAB色空间下地图色域形变的目标函数,给出全局最优解的求解流程。将算法结果与ICC再现意图结果进行对比,结果表明该方法能够很好保持地图整体的色貌特征以及局部图斑之间的色彩对比、连续等色彩特征,能够显著提高地图跨媒介地图颜色复制精度。     

A TEST OF AUTO-COLLIMATION

Abstract

In the July 1940 issue of the Empire Survey Review Mr A. V. Lawes contributes a valuable article, “The Application of the Gauss Method of Collimation to the Adjustment of Survey Instruments”. One section of the article describes four methods of adjusting collimators at solar focus, in other words of assuring that the emitted rays are parallel or that the target appears at an infinite distance. Mr Lawes rightly claims that auto-collimation is the most accurate of the four methods, and he warns readers that “the reflector used in this method must be as perfect optically as the objective”. However, he fails to give any method of testing the result obtained by following his directions, and experience suggests that auto-collimation may give a result considerably in error even though the reflector may with some justification be presumed to be good.     

基于小波变换的栅格数字地图水印算法

本文提出了一种基于小波变换的栅格数字地图水印算法。算法基于栅格数字地图相比自然图像具有较高亮度,低频分量具有更高感觉容量的特点,在栅格数字地图经小波变换后的低频分量部分依据其亮度调节强度嵌入周期性扩展水印;同时为提高算法鲁棒性,在细节分量部分嵌入相同水印,水印嵌入位置根据人类视觉系统特性和小波系数间内在联系确定。实验分析表明,该算法能较好抵抗诸如JPEG压缩、锐化、剪裁等各种攻击,具有好的鲁棒性。     

多媒体电子地图集中超媒体结构的语言学机制

通过对现有多媒体电子地图多种信息主体及其关系的分析,阐述了多媒体电子地图集中超媒体结构的语言学机制,并就该理论的实际应用给出了一个实例。     

On the Mátern covariance family: a proposal for modeling temporal correlations based on turbulence theory

Current variance models for GPS carrier phases that take correlation due to tropospheric turbulence into account are mathematically difficult to handle due to numerical integrations. In this paper, a new model for temporal correlations of GPS phase measurements based on turbulence theory is proposed that overcomes this issue. Moreover, we show that the obtained model belongs to the Mátern covariance family with a smoothness of 5/6 as well as a correlation time between 125–175 s. For this purpose, the concept of separation distance between two lines-of-sight introduced by Schön and Brunner (J Geod 1:47–57, 2008a) is extended. The approximations made are highlighted as well as the turbulence parameters that should be taken into account in our modeling. Subsequently, fully populated covariance matrices are easily computed and integrated in the weighted least-squares model. Batch solutions of coordinates are derived to show the impact of fully populated covariance matrices on the least-squares adjustments as well as to study the influence of the smoothness and correlation time. Results for a specially designed network with weak multipath are presented by means of the coordinate scatter and the a posteriori coordinate precision. It is shown that the known overestimation of the coordinate precision is significantly reduced and the coordinate scatter slightly improved in the sub-millimeter level compared to solutions obtained with diagonal, elevation-dependent covariance matrices. Even if the variations are small, turbulence-based values for the smoothness and correlation time yield best results for the coordinate scatter.     

Digitized global land-sea map and access software

A computer-efficient global data file, which contains digitized information that enables identification of a given latitude/longitude defined point as over land or over water, was generated from a data base which defines the world's shoreline. The method used in the generation of this land-sea boundary data map and its data structure are discussed. The data file was originally generated on a Control Data Corporation(CDC) computer, but it has been transported to other computer systems, includingIBM, DEC/VAX, UNIVAC and Cray computers. The land-sea boundary map also includes information on islands and inland lakes. The resolution of this map is 5′×5′ or an equivalent of9 km square surface blocks at the equator. The software to access this data base is structured to be easily transportable to different computers. This data base was used in the generation of the Seasat Geophysical Data Record(GDR) to identify whether a spaceborne radar altimeter measurement was over-land or over-ocean.     

Approach to calculating spatial similarity degrees of the same river basin networks on multi-scale maps

Obtaining spatial similarity degrees among the same objects on multi-scale maps is of importance in map generalization. This paper firstly defines the concepts of ‘map scale change’ and ‘spatial similarity degree’; then it proposes a model for calculating the spatial similarity degree between a river basin network at one scale and its generalized version at another scale. After this, it validates the new model and gets 16 points in the model validation process. The x-coordinate and y-coordinate of each point are map scale change and spatial similarity degree, respectively. Last, a formula for calculating spatial similarity degree taking map scale change as the only variable is obtained by the curve fitting method. The formula along with the model can be used to automate the algorithms for simplifying river basin networks.     

An Automated System for Image-to-Vector Georeferencing

Although modern imagery usually has latitude and longitude or similar coordinates to provide true world location, much potentially useful imagery lacks this information. This includes historical imagery, as well as modern imagery that may have lost its locational information through inappropriate processing. Its provision through the process of georeferencing is still primarily a manual procedure. This paper proposes an efficient, fully- automated solution for massively asymmetric image-to-vector georeferencing whereby an image of a relatively small geographic area is automatically located relative to a substantially larger vector map base. For control points, road intersections are automatically extracted from high resolution aerial or satellite imagery using the new concepts of reference circles and central pixels. For automated control point pair identification between image and vector map, an invariant point pattern matching approach is proposed based on shape invariance for similarity transforms and invariant area ratios for affine transforms. The matching algorithm necessitates only a small subset of image points and requires no additional information beyond pixel and map coordinates. Further, it tolerates inaccurate, missing and spurious points, and provides high performance with linear scalability. A final step performs transformation verification, globalization and optimization based upon an Iterative Closest Point Greedy algorithm. Experimentation shows that images covering a few city blocks with as few as 6 to 17 extracted road intersection points can be efficiently and correctly located using the road network of Dallas County, Texas, with over 80,000 intersections.     

地图学四面体--数字化时代地图学的诠释

传统地图学研究3个关系:实地-地图,读者-地图,读者-实地.这个学科的框架可以称为"地图学三角形".对这三种关系的研究随学科和行业的不同而各有侧重.数字地图的出现扩大了传统地图学的视野和服务面.现代地图学需要面对6个关系的探讨.除了上述3个关系外,还要增加数字地图-地图,数字地图-实地,数字地图-读者3个关系.新的学科框架变成了"地图学四面体".从"三角形"到"四面体"反映了信息时代地图学的发展与变革.地图学的存在取决于人类对地图永恒的需求和地图本身的科学价值.