Cellular Urban Descriptors of Lowland Urban Model

Shape analysis of city growth is an essential means to develop a comprehensive city plan and the key elements of shape analysis are shape descriptors. Recently, many cellular urban models have been developed including the special models for lowland cities. Shape descriptors are the indices used for output of such urban models. Shape descriptors play a very important role in model fitness, calibration, validation as well as interpretation of the model outcome. This paper proposes the usage of image features that are commonly used in the field of image processing and computer vision as urban shape descriptors. The cellular urban descriptors can be classified into geometric and multi-scale features. The geometric urban descriptors related with the shape of the city or development cluster of the city can be computed based on connected component or boundary of the cluster. Multi-scale urban descriptors take into account the role of development index of each cell. Determination of each cellular urban descriptor is described using urban development terminology. Special urban model for lowland cities is clarified and relationships of urban descriptor are investigated. Introduction Shape analysis has a broad range of applications in urban planning and design, from urban spatial pattern, urban form and sprawl until landscape configuration. Evolution of the physical growth of cities has been shaped by geography, environment, socio-economic and political power of society. Classification of cities according to their various urban forms has always been an important influence on the way cities are planned and conserved. Similar types of urban forms may have similar characteristics that can be used for planning. Shape analysis of city growth is also an essential means to develop a comprehensive city plan and the key elements of shape analysis are shape descriptors. To measure the urban sprawl and urban development, shape analysis is one of the main factors. For example, a bigger city may increase the average travel time to work for the residents and lower the quality of life of the city population in general. The measurement of the average travel time is directly related to the diameter of the city and the city development. Most of denser city populations and high land values happen in the city center rather than in other areas. The density and land value may be represented roughly by an urban development index. City diameter and urban development indices are few examples of urban descriptors. Aside from common descriptors of development index and city diameter, fractal dimension has been proposed as urban descriptors in several papers [Batty (1991)]. Recently many urban models have been developed including the special models for lowland cities. All of these models have characteristics of using cellular grid array as the spatial basis. Shape descriptors play very important role in model fitness, calibration, validation as well as interpretation of the model outcome. The operation of a cellular grid array is reminiscent of a well-defined field in computer vision and image processing. In all of shape analysis models, shape descriptors are the indices used for output of such urban models. Each model proposed one or two descriptors separately without any integration. Additional descriptors may be added at the cost of reliability and computational cost since they may come from different sets of data or defined separately from the original descriptors. In addition, the reason to select those descriptors is simply due to common practices. This paper proposes the usage of image features that are commonly used in the field of image processing and computer vision as urban shape descriptors. The significant contribution of this paper is the integration approach of the determination of the cellular urban descriptors. Only a single assessment is needed to obtain all the descriptors. The proposed approach does not only reduce the computational cost of the descriptors such that all the cellular urban descriptors can be computed at each simulation time. It also improves the reliability and validity of the descriptors since they all come from a single source of data. The paper is organized as follows. The next section describes the heart of this paper on determination of the urban cellular features which is divided into geometric and multi-scale features. After that a special urban model for lowland cities is explained briefly. The relationships of urban cellular descriptor were investigated from the Proceedings of International Symposium of Lowland Technology, Bangkok, September 2004, pp. 297-302 298 numerical experiments and reported for demonstration purposes. Finally conclusions are drawn in last section Urban Cellular Descriptors We suggest the usage of image features that are commonly used in the field of image processing and computer vision as urban shape descriptors. Since we are dealing with a cellular urban model, it may be better to call them cellular urban descriptors. Determination of each cellular urban descriptor is described using urban development terminology. The cellular features can be classified into two types: geometric features, and multi-scale features. The geometric features are related with the city shape characteristics (the connected component), while the multi-scale features are associated with the development index of the city. Each of these features can be measured over time. Geometric Features The geometric features are related with the shape of the city or development cluster of the city. The explanation below is related to the way the features are calculated. Except for the fractal dimension which is calculated for the whole city, the cellular features below are calculated for each development cluster of the city. Connected component Based on the development cluster, the number of clusters and area of each development cluster are used as cellular features. The area of a development cluster A is the total number of developed cells in the cluster. Neighbor is defined as the adjacent cells, which are only at the first layer. Since development cluster is defined based on the adjacent neighbors, and urban simulation may have several clusters and some clusters may join up together (or split up under a negative development index). Newly developed cell which is not adjacent from its center of consideration will create a new development cluster consisting of a single cell. After some time, this single cell cluster may grow or be connected with other clusters and make a greater area. Contour Following The boundary of a development cluster is an internal digital contour which can be extracted using the contour following method. The boundary of a development cluster is the active zone of a growing cluster. Consequently, measurement toward the contour boundary of development cluster is a very important task. Several cellular features are measured based on the contour boundary of a development cluster. Measuring the length of the contour boundary of a development cluster gives the perimeter of the cluster, P . Scanning the city matrix to look for the developed cell and tracking the boundary of the development cluster will give the contour boundary. The tracking boundary of the cluster is called contour following. It is done by finding any cell on the edge of the development cluster and then track around successive cells on the edge, store the directional change (quantified at single cell step) required to follow the edge until the original starting cell is reached. The directional change of the contour is called chain code. Using the chain code, many cellular features can be computed directly, without necessity to reconvert the development cluster into an array format. Contour representation of development cluster is also fast to compute and reduces the amount of storage to represent the cluster boundary if we encode the directional change as a single array of chain code. The directional change is stored as number 0-7. Each code represents one step change in direction between adjacent developed cells. Example of a chain code for a simple object is given in the figure below. We call the edge of the development cluster the perimeter or surface of this cluster. Representing the edge of development cluster as a close curve, we can measure the length of this boundary curve. The Perimeter of the development cluster can be acquired faster by chain code from the contour following, as suggested by Fairhurst (1988) as 2 odd event CCode CCode P + = Where event CCode and odd CCode is the summation of event and odd chain code respectively. Change in step in direction 0, 2, 4, 6 are called even direction, while direction 1, 3, 5, 7 are the odd directions. Transition one unit of an even direction has 1 unit distance, while transition of 1 unit in odd direction corresponds to ◊2-unit distance. Knowing the coordinate of the contour boundary, we can also compute the center of gravity of the development cluster as A x g c x ∑ = . and A y g c y ∑ = . The center of gravity is the basis to compute the radius of the development cluster. Taking the development cluster as part of city cluster (or even the city as a whole), the center of gravity is a point representative of the cluster center. Proceedings of International Symposium of Lowland Technology, Bangkok, September 2004, pp. 297-302 299 Area and Perimeter There are two approaches to derive the cellular features. One is based on a circular shape and another is based on a rectangular shape. Both approaches are presented in this section. Based on the area and perimeter of the development cluster, several cellular features can be derived. A P ratio area to Perimeter = measures the compactness of the city. For a circle, the value is 1 4 − D . In later chapters we can see that this ratio has a very important role to measure the city growth. 2 4π A Thinness ratio P = is the index to measure the circularity of city shape. For a circle, the value of thinness ratio is one. Another similar way to measure circularity of city shape is through index A P y Circularit 2 = , which is equal to 4 for a circle. Still another index for measuring thinness and circularity is called