Thesis (D. Phil.(Computer Science))--University of Pretoria, 2008. / Includes bibliographical references (leaves 166-183).

In the field of spatial statistics, it is often desirable to generate a smooth surface for a region over which only noisy observations of the surface are available at some locations, or even across time. Kriging and kernel estimations are two of the most popular methods. However, these two methods become problematic when the domain is not regular, such as when it is rectangular or convex. Bivariate B-splines developed by mathematicians provide a useful nonparametric tool in bivariate surface modeling. They inherit several appealing properties of univariate B-splines and are applicable in various modeling problems. More importantly, bivariate B-splines have advantages over kriging and kernel estimation when dealing with complicated domains. The purpose of this dissertation is to develop a nonparametric surface fitting method by using bivariate B-splines that can handle complex spatial domains. The dissertation consists of four parts. The first part of this dissertation explains the challenges of smoothing over complicated domains and reviews existing methods. The second part introduces bivariate B-splines and explains its properties and implementation techniques. The third and fourth parts discuss application of the bivariate B-splines in two nonparametric spatial surface fitting problems. In particular, the third part develops a penalized B-splines method to reconstruct a smooth surface from noisy observations. A numerical algorithm is derived, implemented, and applied to simulated and real data. The fourth part develops a reduced rank mixed-effects model for functional principal components analysis of sparsely observed spatial data. A numerical algorithm is used to implement the method and tested on simulated and real data.

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An increasing amount of freely available Geographic Information System (GIS) data on the Internet has stimulated recent research into Spatial Information Retrieval (SIR). Typically, SIR looks at the problem of retrieving spatial data on a dataset by dataset basis. However in practice, GIS datasets are generally not analysed in isolation. More often than not multiple datasets are required to create a map for a particular analysis task. To do this using the current SIR techniques, each dataset is retrieved one by one using traditional retrieval methods and manually added to the map. To automate map creation the traditional SIR paradigm of matching a query to a single dataset type must be extended to include discovering relationships between different dataset types. This thesis presents a Bayesian inference retrieval framework that will incorporate expert knowledge in order to retrieve all relevant datasets and automatically create a map given an initial user query. The framework consists of a Bayesian network that utilises causal relationships between GIS datasets. A series of Bayesian learning algorithms are presented that automatically discover these causal linkages from historic expert knowledge about GIS datasets. This new retrieval model improves support for complex and vague queries through the discovered dataset relationships. In addition, the framework will learn which datasets are best suited for particular query input through feedback supplied by the user. This thesis evaluates the new Bayesian Framework for SIR. This was achieved by utilising a test set of queries and responses and measuring the performance of the respective new algorithms against conventional algorithms. This contribution will increase the performance and efficiency of knowledge extraction from GIS by allowing users to focus on interpreting data, instead of focusing on finding which data is relevant to their analysis. In addition, they will allow GIS to reach non-technical people.

This thesis aims to define the concept of a marine cadastre through an analysis of institutional and legal aspects of Australia’s current marine based management system. It also aims to investigate the applicability of current legal, institutional and administrative land based spatial management arrangements, including the Australian Spatial Data Infrastructure (ASDI) and cadastre, to the administration of current spatial rights, restrictions and responsibilities in the marine environment. (For complete abstract open document)

The fragmentation of administrative boundaries is a serious problem in the analysis of social, environmental and economic data. This research focuses on the development of a coordinated approach to the design of administrative boundaries that endeavours to support accurate decision making. Around the world, administrative boundaries have been structured in an uncoordinated manner, limiting data exchange and integration between organisations. The solution proposed in this research adopts the hierarchical reorganisation of administrative boundaries to enhance data integration and data exchange within the spatial data infrastructure (SDI) framework.The SDI is an initiative intended to facilitate access to complete and consistent data sets. One of the most fundamental problems restricting the objectives of the SDI is the fragmentation of data between non-coterminous boundary systems. The majority of administrative boundaries have been constructed by individual agencies to meet individual needs. Examples of the proliferation of different boundary systems include postcodes, census-collector districts, health districts and police districts. Due to the lack of coordination between boundary systems, current technologies for analysing spatial data, such as geographic information systems (GIS), are not reaching their full potential. A review of the current literature reveals that, until now, little has been done to solve this problem.The prototype developed within this research provides a new mechanism for the design of administrative boundaries. The prototype incorporates two algorithms. These are based on HSR theory and administrative-agency constraints and are implemented within the GIS environment. Such an approach is an example of the potential that is available when we link spatial information theory with the SDI framework and disciplinary knowledge.

The process of decision making is best undertaken with the consideration of as much information as possible. One way to maximise the amount of information that is being used in the process is to use metadata engines. Metadata engines can be used to create virtual databases which are a collection of individual datasets located over a network. Virtual databases allow decisions to be made using data from many different data bases at many different locations on a network. They shield the user from this fact. From the users point of view they are only using data from the one location. This thesis investigates some of the concepts behind metadata engines for Internet based Spatial Data Infrastructures. The thesis has a particular emphasis on how metadata engines can be used to create virtual databases that could be of use in the planning and decision making processes. The thesis also investigates some current spatial data technologies such as SDIs, data warehouses, data marts and clearing houses, their interoperability and their relationship to metadata engines. It also explores some of the more recent spatial data applications that have been developed in the context of metadata engines and Spatial Data Infrastructures.

The primary aim of this research is to develop and assess the innovative methods and techniques which are used to augment GPS using a variety of digital spatial data. It is well known that the use of GPS can be severely compromised by various error sources such as signal obstructions, multipath and poor satellite geometry etc., especially in highly built-up areas. In order to improve the accuracy and reliability of GPS, complementary data is often combined with GPS data for enhancing the performance of a standalone GPS receiver. Spatial data is one type of complementary data that can be used to augment GPS. However, the potential of using various types of existing and newly acquired spatial data for enhancing GPS performance has not been fully realised. This is particularly true due to the fact that higher accuracy digital surface models (DSMs), which include buildings and vegetation, and digital maps, have only been made widely available in recent years. This thesis will report on a number of experiments that used spatial data of various complexity and accuracy for enhancing GPS performance. These experiments include height aiding with different scale digital terrain models (DTMs); map-matching using odometer data, DTM and road centrelines; modelling and prediction of GPS satellite visibility using DSMs; and prediction of GPS multipath effect using DSMs and building footprints. These experiments are closely related to each other in the sense that GPS and spatial data are combined to provide value-added information for improved modelling and prediction of GPS positioning accuracy and reliability, for applications such as transport navigation and tracking ... Extensive fieldwork has been carried out to verify the developed techniques and methods. The results show that the accuracy of a standalone GPS receiver can be improved by height aiding using a higher resolution DTM and map-matching especially when the satellite geometry is poor. The mean error of single receiver GPS positioning for one particular dataset, on which the described map-matching algorithm was developed, is 8.8m compared with 53.7m for GPS alone. This work was carried out in collaboration with London Transport. In terms of satellite visibility analysis, the results obtained from the fieldwork indicate that greater modelling accuracy has been achieved when using higher resolution DSMs. Furthermore, a ray tracing model was implemented in a 3D GIS environment in order to model reflected and diffracted GPS signals. The Double Differencing (DD) residuals were used to give an indication of the magnitude of the possible pseudorange multipath error caused by diffraction. A single-knife diffraction model was first implemented on 1m Light Detection And Ranging (LiDAR) DSMs, and verified by post-processing (i.e. large DD residuals occurred when the satellites are partially masked and unmasked by buildings), which indicate that GPS multipath prediction with LiDAR data and building footprints is feasible, and has the potential to offer greater modelling accuracy.

Spatial data (e.g., points) have extensive applications in practice, such as spatial databases, Location-Based Services, spatial computing, social analyses, computational geometry, graph design, medical imaging, etc. Geometric queries, such as geometric range queries (i.e., finding points inside a geometric range) and nearest neighbor queries (i.e., finding the closest point to a given point), are fundamental primitives to analyze and retrieve information over spatial data. For example, a medical researcher can query a spatial dataset to collect information about patients in a certain geometric area to predict whether there will be a dangerous outbreak of a particular disease (e.g., Ebola or Zika). With the dramatic increase on the scale and size of data, many companies and organizations are outsourcing significant amounts of data, including significant amounts of spatial data, to public cloud data services in order to minimize data storage and query processing costs. For instance, major companies and organizations, such as Yelp, Foursquare and NASA, are using Amazon Web Services as their public cloud data services, which can save billions of dollars per year for those companies and organizations. However, due to the existence of attackers (e.g., a curious administrator or a hacker) on remote servers, users are worried about the leakage of their private data while storing and querying those data on public clouds. Searchable Encryption (SE) is an innovative technique to protect the data privacy of users on public clouds without losing search functionalities on the server side. Specifically, a user can encrypt its data with SE before outsourcing data to a public server, and this public server is able to search encrypted data without decryption. Many SE schemes have been proposed to support simple queries, such as keyword search. Unfortunately, how to efficiently and securely support geometric queries over encrypted spatial data remains open. In this dissertation, to protect the privacy of spatial data in public clouds while still maintaining search functions without decryption, we propose a set of new SE solutions to support geometric queries, including geometric range queries and nearest neighbor queries, over encrypted spatial data. The major contributions of this dissertation focus on two aspects. First, we enrich search functionalities by designing new solutions to carry out secure fundamental geometric search queries, which were not supported in previous works. Second, we minimize the performance gap between theory and practice by building novel schemes to perform geometric queries with highly efficient search time and updates over large-scale encrypted spatial data. Specifically, we first design a scheme supporting circular range queries (i.e., retrieving points inside a circle) over encrypted spatial data. Instead of directly evaluating compute-then-compare operations, which are inefficient over encrypted data, we use a set of concentric circles to represent a circular range query, and then verify whether a data point is on any of those concentric circles by securely evaluating inner products over encrypted data. Next, to enrich search functionalities, we propose a new scheme, which can support arbitrary geometric range queries, such as circles, triangles and polygons in general, over encrypted spatial data. By leveraging the properties of Bloom filters, we convert a geometric range search problem to a membership testing problem, which can be securely evaluated with inner products. Moving a step forward, we also build another new scheme, which not only supports arbitrary geometric range queries and sub-linear search time but also enables highly efficient updates. Finally, we address the problem of secure nearest neighbor search on encrypted large-scale datasets. Specifically, we modify the algorithm of nearest neighbor search in advanced tree structures (e.g., R-trees) by simplifying operations, where evaluating comparisons alone on encrypted data is sufficient to efficiently and correctly find nearest neighbors over datasets with millions of tuples.

Cartography is the science and art of making maps and thematic cartography is a subsection that deals with the production of thematic maps. A thematic map portrays the distribution of features, incidents or classifications related to a specific topic. With the rapidly increasing volumes of data, thematic maps allow users to efficiently analyse data and identify trends quicker. A spatial data infrastructure (SDI) focuses on making data available and ensures data interoperability through a geoportal and associated web services for discovery, display, editing, and analysis. Implementations of web service standards by the Open Geospatial Consortium (OGC), and the ISO/TC211, Geographic information/Geomatics enable the display, query and custom visualisation of spatial data in a geoportal. In the past, sophisticated cartographic methods have been mainly available on desktop applications, but with the advances in web mapping technology these methods have become increasingly popular on the Web. Currently, producing thematic maps using web services is a manual process that requires quite a lot of custom programming. The orchestrations of standard web services automate the process to produce thematic maps in a geoportal. It is preferable to use standard web services as opposed to customised programming; the standards provide flexibility, interoperability, and standard protocols, to name a few benefits. The goal of this research was to determine how standard OGC web services could be orchestrated to produce thematic maps within the geoportal of an SDI. To achieve this goal, an orchestrated thematic web service, named ThematicWS, was constructed from existing implementations of individual standard OGC web services, which are monolithic and interchangeable. The thematic cartographic process for producing choropleth and proportional symbol maps was investigated to model the process and obtain a set of steps. Experiments were performed to determine which existing web service standards could be used in the process. ThematicWS was developed using existing implementations of the following standards: WFS to retrieve the attribute data, WPS for the wrapping of custom functionalities (statistical processing and SLD generation), and a WMS to produce the thematic map image. The 52° North and ZOO project frameworks’ orchestration capabilities were evaluated for to determine the suitability for producing thematic maps. The evaluation showed that orchestration is possible in both frameworks. However, there are limitations in both frameworks for automatic orchestration such as the lack of semantic information and poor usability of the framework. The use of WPS services to wrap custom functionalities and to provide a standard interface has proved to be useful for the orchestration of standard web services. ThematicWS was successfully implemented based on standard web service implementations using both workflow scripting and workflow modelling. The orchestrated ThematicWS can be called and consumed by a geoportal of an SDI to produce thematic maps according to user defined parameters. / Dissertation (MSc)--University of Pretoria, 2013. / Geography, Geoinformatics and Meteorology / Unrestricted