GIS Based Studies in the Humanities and Social Sciences - Chpater 20 (end)

20 Visualization of the Mental Image of a City Using GIS Yukio Sadahiro and Yoshio Igarashi CONTENTS 20.1 Introduction................................................................................................299 20.2 Methodology ..............................................................................................301 20.2.1 Representation of the Image of a City.......................................301 20.2.2 Model Description.........................................................................301 20.2.3 Visualization of the Image of a City..........................................302 20.3. A Prototype System...................................................................................304 20.3.1 Spatial Data....................................................................................304 20.3.2 Model of the Image of Shibuya..................................................305 20.3.3 Visualization of the Image of Shibuya ......................................306 20.3.4 System Evaluation.........................................................................306 20.4 Conclusion ..................................................................................................309 Literature Cited...................................................................................................313 References.............................................................................................................313 20.1 Introduction Visualization is one of the essential functions of Geographical Information System (GIS) (Cromley, 1992; MacEachren and Taylor, 1994; Nielson et al., 1997; Slocum, 1998). As a tool of spatial analysis, it is an efficient way to explore spatial phenomena. We often grasp the structure of a spatial phe-nomenon by only looking at the picture indicating the phenomenon. Chang-ing the scale of visualization, we detect spatial patterns at various scales from local to global. Visualization is also useful for making a decision on spatial phenomena. In sightseeing, for instance, tourist maps help us finding good places to visit and stay. Bus-route maps tell us which routes we need 299 Copyright © 2006 Taylor & Francis Group, LLC 300 GIS-based Studies in the Humanities and Socail Sciences in order to reach our destinations. Crime maps show us the regional variation of crime rate — how dangerous it is to visit a certain place. Weather maps are indispensable in making plans for a field trip. As well as physical and concrete objects, abstract information can also be visualized in GIS if represented as a computational model. To explore a wider application of GIS, this paper discusses the visualization of an abstract concept, the mental image of a city, with a focus on its spatial variation. The image of a city is usually communicated by text information, typically a sentence characterizing a location by adjectives. We may say, “That square is lively and often bustling,” “The art galleries and antique shops create an artistic atmosphere on the street,” and “The downtown area is very calm, so I sometimes feel it is dangerous.” The objective of this paper is to incorporate these literal representations into GIS to visualize the image of a city. In academics the mental image of a city is often discussed in architecture and environmental psychology (Bell et al., 1990; Bechtel and Churchman, 2002). Psychologists are interested in the relationship between the image of a space and its physical elements, such as buildings, roadways, and pavements, to understand the structure and formation of mental image. Architects look at this relationship from a more practical viewpoint, that is, how to give a good impression to visitors of a space. Visualization of the image of a city would help in studying the relationship between phys-ical and mental spaces. Image visualization is also useful in marketing and traveling. Image is critical in apparel industries. When locating a new store, a company exam-ines the image of a city in detail to seek the best location for not only selling its products, but also improving the image of the company and its brands. When we visit a new city, we often wish to stroll around the city rather than visit certain places. In such a case, it is useful to know the image of streets and regions of a city rather than detailed information of individual facilities. Individual regions in New York, say, SOHO, East Village, and Harlem, are characterized by their own images, which helps visitors of New York understand the urban structure of New York and make a trip plan. As mentioned above, the image of a city is usually represented as text information, which cannot be directly treated in GIS. To incorporate such information into GIS, we first describe the formal representation of the image in the following section. We then discuss how the image is created by spatial objects, which leads to a mathematical model of the image. The section ends with discussion on the visualization methods of the image in GIS. Section 20.3 shows a prototype system that visualizes the image of a city, taking Shibuya in Tokyo, Japan, as an example. Source data, a model of the image, and a visualization method are described in turn, which is followed by the system evaluation by users. Section 20.4 summarizes the features of the system with discussion for further research. Copyright © 2006 Taylor & Francis Group, LLC Visualization of the Mental Image of a City Using GIS 301 20.2 Methodology 20.2.1 Representation of the Image of a City The image of a city is usually described by adjectives, say, lively, bustling, busy, sophisticated, calm, lonely, and dangerous, often with adverbs, such as extremely, considerably, very, moderately, and slightly. This implies that the image consists of numerous elements represented by adjectives. We thus define the image of a city as a set of elements, each of which is a function of location, time, and individual. Take, for instance, the liveliness of a city. Since the liveliness varies from place to place and changes over time, it is reasonable to assume a function of location and time. It also varies among individuals because it happens that some feel lively while others do not in the same situation. The above definition is described mathematically as follows. Assume that the image of a city of region S consists of m elements, such as the liveliness, calmness, and dangerousness. Given a location x and a time t, we denote the perceptual degree of element i by an individual j as f (x, t). The image of a city is then represented as a set of functions F = {f (x, t), i = 1, …, m, j = 1, …, n}. This representation allows variations in three dimensions, that is, loca-tion, time, and individual. This high flexibility, though it seems quite reasonable, makes it difficult to visualize the image of a city as it is in GIS. Even if we fix the time at t, we still have m¢n distributions to visualize. It is difficult to understand the structure of the image if we visualize them in GIS as they convey too much information about the image. To reduce the amount of information, we summarize the variation among individuals by their mean and variance. We replace F = {f (x, t), j = 1, …, n}, the set of functions of element i, by their mean m (x, t) and variance s2 (x, t). The image of a city is then represented by a set of functions I = {m(x, t), s2 (x, t), i = 1, …, m}. 20.2.2 Model Description Having defined the representation of the image of a city, we then propose its mathematical model. The image of a city at a certain location depends on the properties of its surrounding spatial objects. For instance, the image of a square is determined by buildings, streets, sidewalk stands, and so forth. The effect of a spatial object usually decreases with the distance from its location. A beautiful building greatly improves the image of its sur-rounding area, while it rarely affects the image of a distant place. These observations naturally give a mathematical model of the image defined as follows. Copyright © 2006 Taylor & Francis Group, LLC 302 GIS-based Studies in the Humanities and Socail Sciences Suppose K spatial objects with L properties distributed in S. The location of spatial object k is denoted by z . The property l of spatial object k at time t is akl (t). The mean of image element i at (x, t) is given by mi (x,t)= 1 ååril (x − zk )gi (akl (t)) (20.1) k l where g (a (t)) is the effect of property l of spatial object k on element i, and r (|x – z |) is its distance-decay function. The variance of the image among individuals also depends on the prop-erties of surrounding spatial objects. This paper assumes that it is a function of the variance in the effect of spatial objects and that it decreases with the number of spatial objects: s2 (x,t)= ån(x − zk )×h k 1 å åril (x − zk )gi (akl (t))− mi (x,t) 2 k l (20.2) where n(|x – z |) is a distance-decay function. The latter assumption implies that the image is consistent among individuals where many spatial objects are clustered; individuals receive more information with an increase of spatial objects, which makes the image clearer. Specifying the functions r (|x – z |), g (a (t)), n(|x – z |), and h(x t), we obtain a mathematical model of the image of a city with some unknown parameters. These parameters are usually estimated through a questionnaire survey. A typical method is to ask subjects to rate each element of the image at sample locations and fit the model to the result obtained. An example of model estimation will be shown later. 20.2.3 Visualization of the Image of a City Once a model is estimated, the image of a city is visualized in GIS. A direct and straightforward method is to build computational models of the func-tion set I in GIS, such as Triangular Irregular Networks (TINs) and lattices, and visualize them as three-dimensional surfaces. Along with this ordinary method, this paper proposes smoothing of the functions. When interests lie only in the outline of the image, details are not necessary or even redundant, because they conceal the global structure of the image and their Copyright © 2006 Taylor & Francis Group, LLC Visualization of the Mental Image of a City Using GIS 303 visualization takes considerable time even if a high-performance computer is employed. The smoothing operation used in visualization is spatially inhomoge-neous, that is, it depends on the density of spatial objects. The smoothing function keeps the details of functions where spatial objects are densely distributed, while it makes them smooth where spatial objects are sparse. This is because we are interested in the local variation of the image where spatial objects are clustered. The smoothing operation on f(x) is mathemat-ically defined by s(x)= exp − y∈S g + kån(x − zk ) x − y f (y)dy (20.3) k Parameters g and k determine the scale of smoothing. The former g is an ordinary smoothing parameter; a large g yields smooth surfaces. The latter k, on the other hand, gives the spatial variation of smoothing by using the term ån(x − zk ), k the density of spatial objects around location x. A large k gives more details where spatial objects are clustered; if k is zero, smoothing operation is homo-geneous in S. Consequently, the mean and variance of image element i at (x, t) are visualized as surfaces defined by mi `(x,t)= òy∈ exp − = òy∈Sexp − g + k k n(x − zk ) g + k k n(x − zk ) x − y mi (y,t)dy x − y ååril (y − zk )gi (akl (t)dy = åå gi (akl (t))òy∈ exp − g + k k n(x − zk ) x − y ril (y − zk )dy (20.4) and Copyright © 2006 Taylor & Francis Group, LLC ... - tailieumienphi.vn