Computational Geometry-Based Kinematic Morphology for Urban Growth

The present study presents a novel approach for studying the dynamic boundary evolution of an urban area. It uses the satellite remote sensing-derived urban growth maps of the study area. The derived urban maps are used to extract the boundaries of study areas for three time intervals, 1999, 2009 and 2019. Using the centroid of urban boundary of 1999, the urban boundaries are discretized into 36 parts at 10 degree interval. Thus, each line emanating from the centroid towards the boundaries thus intersects the boundaries at three points indicating the position of boundary at three durations. Since there are three points, a second order polynomial equation is constructed and differentiated with time to obtain the growth rates of 36 points. The growth rates are then related to various potential driver variables using a linear regression analysis. The results show that the urban boundary expansion is predominant in areas closer the roads and airports, having milder slopes and towards North and East directions of Mumbai Metropolitan Region. However, the growth is occurring away from the urban centres and suburban railway stations because of lack of spaces for further development in close proximity of these areas. The present study thus solves the inverse evolution problem and can be helpful for the planners for effective planning of the resources. It uses the geometric kinematics to study the boundary growth rates and then relates it with potential driver variables using a linear regression model.