The boundaries of the cities are not immutable, they can be changed. With the development of the economies and societies, the population and pollution of cities are increasing. Some urban areas are expanding with more population or other dynamics of urbanization, while other urban areas are reducing with the changing of the dynamics. Therefore, detecting urban areas or delineating the boundaries of the cities is one of the most important steps for urban studies, which is closely related to human settlements and human activities. Remote sensing data (RS) is widely used to monitor and detect land use and land cover on the surface of the earth. But the extraction of urban areas from the ordinary RS data is not easy work. The Operational Linescan System (OLS) is the sensors of the Defense Meteorological Satellite Program (DMSP). The nighttime lights from the DMSP/OLS provide worldwide remotely sensed data to analyze long-term light emissions which are closely related to human activities. But the nighttime lights imagery data contains inherent errors. Therefore, the approaches to calibrate the data and extract the urban areas from the data are complicated. The long-term objective of this thesis is to delineate the boundaries of the natural cities of the continental United States of America (USA) from 1992 to 2010 of nightlight imagery data with all the different satellites. In this thesis, the coefficients for the intercalibration of the nightlight imagery data have been calculated based on the method developed by Elvidge, et al. (2009), but the coefficients are new and available. The approach used to determine the most appropriate threshold value is very important to eliminate the possible data error. The method to offset this possible error and delineate the boundaries of the cities from nightlight imagery data is the head/tail breaks classification, which is proposed by Jiang (2012b). The head/tail breaks classification is also useful for finding the ht-index of the extracted natural cities which is developed by Jiang and Yin (2013). The ht-index is an indicator of the underlying hierarchy of the data. The results of this study can be divided into two categories. In the first, the achieved coefficients for the intercalibration of nightlight images of the continental USA are shown in a table, and the achieved data of the urban areas are stored in a data archive. In the second, the different threshold values of the uncalibrated images and the individual threshold value of the calibrated images are shown in tables, and the results of the head/tail breaks classification and power law test are also drawn. The results show that the acquired natural cities obey the power law distribution. And the results also confirm that the head/tail breaks classification is available for finding a suitable threshold value for the nightlight imagery data. Key words: cities’ boundaries; DMSP/OLS; head/tail breaks classification; nighttime lights; power law; urban areas

A city consists of many elements such as humans, buildings, and roads. The complexity of cities is difficult to measure using Euclidean geometry. In this study, we use fractal geometry (scaling analysis) to measure the complexity of urban areas. We observe urban development from different perspectives using the bottom-up approach. In a bottom-up approach, we observe an urban region from a basic to higher level from our daily life perspective to an overall view. Furthermore, an urban environment is not constant, but it is complex; cities with greater complexity are more prosperous. There are many disciplines that analyze changes in the Earth’s surface, such as urban planning, detection of melting ice, and deforestation management. Moreover, these disciplines can take advantage of remote sensing for research. This study not only uses satellite imaging to analyze urban areas but also uses check-in and points of interest (POI) data. It uses straightforward means to observe an urban environment using the bottom-up approach and measure its complexity using fractal geometry.   Web 2.0, which has many volunteers who share their information on different platforms, was one of the most important tools in this study. We can easily obtain rough data from various platforms such as the Stanford Large Network Dataset Collection (SLNDC), the Earth Observation Group (EOG), and CloudMade. The check-in data in this thesis were downloaded from SLNDC, the POI data were obtained from CloudMade, and the nighttime lights imaging data were collected from EOG. In this study, we used these three types of data to derive natural cities representing city regions using a bottom-up approach. Natural cities were derived from open geographic data without human manipulation. After refining data, we used rough data to derive natural cities. This study used a triangulated irregular network to derive natural cities from check-in and POI data.   In this study, we focus on the four largest US natural cities regions: Chicago, New York, San Francisco, and Los Angeles. The result is that the New York City region is the most complex area in the United States. Box-counting fractal dimension, lacunarity, and ht-index (head/tail breaks index) can be used to explain this. Box-counting fractal dimension is used to represent the New York City region as the most prosperous of the four city regions. Lacunarity indicates the New York City region as the most compact area in the United States. Ht-index shows the New York City region having the highest hierarchy of the four city regions. This conforms to central place theory: higher-level cities have better service than lower-level cities. In addition, ht-index cannot represent hierarchy clearly when data distribution does not fit a long-tail distribution exactly. However, the ht-index is the only method that can analyze the complexity of natural cities without using images.