Analysis of the appearance and disappearance of point objects over time

The appearance and disappearance of immovable points are important spatiotemporal events in geographical information science. They represent phenomena such as the birth and death of trees in forests, construction and destruction of buildings in cities and openings and closures of shops and restaurants. This paper proposes a new method for analyzing the appearance and disappearance of points. The method helps analysts capture the overall picture and regional variation of event pattern and detecting significant local patterns. Four measures are defined that indicate the intensity of spatial and temporal patterns of events. The measures are visualized as grid maps. A statistical test is used to evaluate the significance of the measures to extract the regions of significant patterns. The proposed method is applied in an analysis of shops and restaurants in Shibuya, Tokyo. Technical soundness of the method is discussed along with empirical findings.     

Statistical methods for analyzing the distribution of spatial objects in relation to a surface

This paper develops statistical methods for analyzing the distribution of spatial objects—points, convex polygons, and line segments—in relation to a surface. We propose statistics for measuring the relationship between the distribution of these objects and a surface and derive their expectations and variances under the null hypothesis that the objects are independently and randomly distributed. The statistics are approximately distributed according to the normal distribution under the null hypothesis, which enables us to test the significance of the spatial relationships statistically. Using the proposed methods, we empirically analyze the distribution of convenience stores in relation to the distribution of population in a suburb of Osaka, Japan. Some empirical findings are shown.     

Analysis of surface changes using primitive events

This paper develops a method for analysing changes in a surface, a scalar function defined over a two-dimensional region. The method is based on the topological method for static surfaces that uses critical points (peaks, bottoms, and cols) and their connecting lines. To extend the topological method to spatiotemporal domain, four types of primitive events are proposed: (1) generation, (2) disappearance, (3) movement, and (4) switch. The change of a surface is described by a combination of these primitives. From surfaces of two times a set of primitive events that cause the change is deduced. They are stored in GIS as spatial objects with attributes, and their spatio-temporal pattern is visually analysed. To test the validity of the method, the change of a retail cluster in Shinjuku and Shibuya area in Tokyo is analysed. The empirical study yielded some interesting findings that help us understand changes in the spatial structure of retailing.     

Analysis of the spatial relations among point distributions on a discrete space

This paper proposes a method of analyzing spatial relations among point distributions on a discrete space. Spatial topology and proximity are discussed in an integrated framework at both local and global scales. Local relations are described by geographical representations, whereas global relations are visualized by graph representations. The latter also provide a means of classifying the point distributions. The proposed method is applied to school location planning in Japan. The results reveal the appealing properties of the method and provide empirical findings.     

Buffer Operation on Spatial Data with Limited Accuracy

The quality of spatial data is limited by the accuracy of their sources such as paper maps and satellite images. It is also reduced by errors in map digitization and photo interpretation. Spatial operations performed on spatial data such as map overlay, buffer operations and spatial smoothing, do not always work correctly because their accuracy depends on the quality of spatial data. The present paper evaluates the accuracy of the buffer operation on a point and a line segment in relation to the positional accuracy of spatial data. Two quantitative measures are introduced to assess the accuracy of the buffer operation. Their explicit forms are derived for a point, and a condition is presented where the measures can be evaluated efficiently by numerical calculation. Applications provide empirical findings that deepen our understanding of the relationship between the accuracy of spatial data and that of the buffer operation.     

A computational approach for the analysis of changes in polygon distributions

 This paper develops a computational method for analyzing changes in polygon distributions. Unmovable polygons that change discontinuously without explicit functional linkage information are discussed. Six types of primitive events are used to describe the change: 1) generation, 2) disappearance, 3) expansion, 4) shrinkage, 5) union, and 6) division. The change of polygon distributions is decomposed into a combination of these events. A computational procedure for deducing a set of events from polygon distributions of two times is proposed. The method is applied to the analysis of the spatial competition between the major and small chains of convenience stores in Tokyo, Japan. Some empirical findings are shown. Received: 3 August 2000 / Accepted: 6 February 2001     

Number of Polygons Generated by Map Overlay: The Case of Convex Polygons

This paper analyzes the number of polygons generated by map overlay. Overlay of maps yields a number of small polygons, and often causes problems in computation, handling, and storage of derived polygons. One method to deal with these problems is to estimate the number of derived polygons before executing overlay operation. To this end, a stochastic model is proposed by which the expected number of derived polygons is calculated. The results are summarized as follows: (1) the number of polygons generated by map overlay depends on the number of original polygons and their perimeters; (2) the number of derived polygons increases with the perimeters of original polygons; (3) McAlpine and Cook's (1971) earlier method underestimated the number of derived polygons; and (4) the number of polygons generated by the overlay of maps having the same lattice system is proportional to the square of the number of overlaid maps and the number of polygons on the map, and inversely proportional to the area-perimeter ratio of the unit cell.     

GIS中地图注记尺寸和文字信息的损失

地图注记是地理信息系统中不可缺少的组成内容。它将与空间目标有关的各种属性联系起来,如目标的名称、面积、周长等。ＧＩＳ中都有将注记配置的功能。地图注记的可读性取决于多种因素。字符尺寸是其中最重要的影响因素之一,通常大字符往往比小字符易读。但当地图注记以...     

Measuring geographic segregation: a graph-based approach

Residential segregation is a multidimensional phenomenon that encompasses several conceptually distinct aspects of geographical separation between populations. While various indices have been developed as a response to different definitions of segregation, the reliance on such single-figure indices could oversimplify the complex, multidimensional phenomena. In this regard, this paper suggests an alternative graph-based approach that provides more detailed information than simple indices: The concentration profile graphically conveys information about how evenly a population group is distributed over the study region, and the spatial proximity profile depicts the degree of clustering across different threshold levels. These graphs can also be summarized into single numbers for comparative purposes, but the interpretation can be more accurate by inspecting the additional information. To demonstrate the use of these methods, the residential patterns of three major ethnic groups in Auckland, namely Māori, Pacific peoples, and Asians, are examined using the 2006 census data.