With the high development of economic and demand for city research, an issue of detecting city boundaries plays an extremely important role in urbanization that promotes the progress of human civilization. Some critical applications such as land use, urban planning and city sprawl have been constantly discussed, which rely on the acquisition of city areas. For the better acquisition of city areas, choosing a proper method to capture city boundaries becomes significant where it greatly improves the value of city study. Although conventional data can be used to define the city boundaries, some drawbacks still exist when measuring the city boundaries in a global scale. Remote sensing (RS) data of nightlight imagery (2010) by Defense Meteorological Satellite Program’s Operational Linescan System (DMSP/OLS) acquired from National oceanic and atmospheric administration's National Geoscience Data Center (NOAA/NOGA) is applied to extract the city boundaries in fifty countries, of which these countries are chosen followed by the Gross Domestic Product that are ranked in top 50. In this case, the data distribution of nightlight imagery followed by heavy-tailed distribution. Head/tail break algorithm poses a possibility of calculating reasonable threshold and extracting the natural cities with the help of software based on the Geomatics information system (GIS). An extended study of power law is made by using of power law estimator from previous studies to check whether the extracted natural cities can match the power law distribution. Result shows that combination of the nightlight imagery data and the head/tail break is capable of extracting the city boundaries and a set of possible thresholds with visual inspection by using the head/tail break are executed. There is only one country, namely Belgium, cannot be processed due to its data properties. Result also address how well the natural cities of the fifty countries can be extracted in terms of visual inspection, among the chosen cities, 33 of countries boundaries can be better matched and 13 countries can fundamentally match the city boundaries. Meanwhile, an extended study of power law is provided and four countries have to be found that do not follow the power law distribution. From the result obtained, the study expects that integration of support data will efficiently increase the accuracy of extraction and more useful information can be acquired in further study. On the other hand, a comparative study of threshold decision needs to be verified, put it differently, whether using head/tail break with visual inspection on extracted city boundaries is helpful or not.

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.

Zipf’s law is one of the empirical statistical regularities found within many natural systems, ranging from protein sequences of immune receptors in cells to the intensity of solar flares from the sun. Verifying the universality of Zipf’s law can provide many opportunities for us to further seek the commonalities of phenomena that possess the power law behavior. Since power law-like phenomena, as many studies have previously indicated, is often interpreted as evidence for studying complex systems, exploring the universality of Zipf’s law is also of potential capability in explaining underlying generative mechanisms and endogenous processes, i.e. self-organization and chaos theory. The main purpose of this study was to verify whether Zipf’s law is valid for city sizes, city numbers and population extracted from natural cities. Unlike traditional city boundaries extracted by applying census-imposed and top-down imposed data, which are arbitrary and subjective, the study established the new kind of boundaries of cities, namely, natural cities through using four location-based social media data from Twitter, Brightkite, Gowalla and Freebase and head/tail breaks rule. In order to capture and quantify the hierarchical level for studying heterogeneous scales of cities, ht-index derived from head/tail breaks rule was employed. Furthermore, the validation of Zipf’s law was examined. The result revealed that the natural cities had deviations in subtle patterns when different social media data were examined. By employing head/tail breaks method, the result calculated the ht-index and detected that hierarchy levels were not largely influenced by spatial-temporal changes but rather data itself. On the other hand, the study found that Zipf’s law is not universal in the case of using location-based social media data. Compared to city numbers extracted from nightlight imagery, the study found out the reason why Zipf’s law does not hold for location-based social media data, i.e. due to bias of customer behavior. The bias mainly resulted in the emergence of natural cities were much more frequent than others in certain regions and countries so that making the emergence of natural cities was not exhibited objectively. Furthermore, the study showed whether Zipf’s law could be well observed depends not only on the data itself and man-made limitations but also on calculation methods, data precisions and scales and the idealized status of observed data.

Geographic space is not neutral or lifeless, but an intricate living structure composed of numerous small features and a few large ones across all scales. The living structure is crucial for comprehending how geographic space shapes human activities. With the emerging geospatial big data, researchers now have unprecedented opportunities to study the relationship between geographic space and human behaviour at a finer spatial resolution. This thesis leverages multisource geospatial big data, including Twitter check-in locations, street networks from OpenStreetMap, building footprints, and night-time light images, to explore the fundamental mechanisms of human activities that underlie geographic space. To overcome the limitations of conventional analytics in this era of big data, we propose the topological representation and living structure based on Christopher Alexander's conception of space. We utilize scaling and topological analyses to reveal the underlying living structure of geographic space with various big datasets. Our results demonstrate that tweet locations or human activities at different scales can be accurately predicted by the underlying living structure of street nodes. We also capture and characterize human activities using big data and find that building footprints and tweets show similar scaling patterns in terms of sizes of their spatial clusters. We also propose an improved spatial clustering method to increase the processing speed of geospatial big data. Finally, we adopt topological representation to identify urban centres by the fusion of multi-source geospatial big data. The living structure, together with its topological representation can help us better understand human activities patterns in the geographic space at both city and country levels.