This thesis is concerned with the development of two-dimensional spectral analysis as a technique for investigating spatial pattern, and the stochastic processes which generate pattern. The technique is discussed for two types of data: first, quantitative measurements associated with a rectangular grid, or lattice; secondly, analysis of spatial point patterns using the coordinates which describe the locations of events. Spectral analysis of lattice data is applied to two examples of remotely sensed digital imagery. The first example consists of digitised aerial photographs of glaciated terrain in Canada. Spectral analysis is used to detect geological lineations which are visible in the photographs, and to study the structure of the land surface beneath the lineations. The second example is meteorological satellite imagery. Spectral analysis is used to develop a system for discrimination between different cloud types. Point spectral analysis is used as the basis of formal tests for randomness, against alternatives such as clustering or inhibition. Spectral theory for univariate spatial point patterns is extended to cross-spectral analysis of bivariate point patterns. In particular, we show how cross-spectral functions indicate the type of interaction between the events of two patterns. A test for independent components is composed, and the application of the test is demonstrated using a variety of real and artificial patterns. A further extension, to bispectral analysis of third-order properties of spatial point patterns, is also discussed. This type of analysis is used to distinguish between processes which have the same first- and second-order properties, but different third-order properties. Finally, we show how Greig-Smith analysis of quadrant count data can be interpreted as a type of two-dimensional spectral analysis based on a set of orthogonal square waves known as Walsh functions. This representation indicates why Greig Smith's method is entirely dependent on the starting point of the grid.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:659705 |
| Date | January 1990 |
| Creators | Mugglestone, Moira A. |
| Publisher | University of Edinburgh |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/1842/15450 |
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