Fractal Analysis and Chaos in Geosciences

The fractal analysis is becoming a very useful tool to process obtained data from chaotic systems in geosciences. It can be used to resolve many ambiguities in this domain. This book contains eight chapters showing the recent applications of the fractal/mutifractal analysis in geosciences. Two chapters are devoted to applications of the fractal analysis in climatology, two of them to data of cosmic and solar geomagnetic data from observatories. Four chapters of the book contain some applications of the (multi-) fractal analysis in exploration geophysics. I believe that the current book is an important source for researchers and students from universities

Sampling Strategy and Accuracy Assessment for Digital Terrain Modelling

In this thesis, investigations into some of the problems related to three of the main concerns (i. e. accuracy, cost and efficiency) of digital terrain modelling have been carried out. Special attention has been given to two main issues - the establishment of a family of mathematical models which is comprehensive in theory and reliable in practice, and the development of a procedure for the determination of an optimum sampling interval for a DTM project with a specified accuracy requirement. Concretely, the following discussions or investigations have been carried out:- i). First of all, a discussion of the theoretical background to digital terrain modelling has been conducted and an insight into the complex matter of digital terrain surface modelling has been obtained. ii). Some investigations into the improvement of the quality of DTM source data have been carried out. In this respect, algorithms for gross error detection have been developed and a procedure for random noise filtering implemented. iii). Experimental tests of the accuracy of DTMs derived from various data sources (i. e. aerial photography, space photography and existing contour maps) have been carried out. In the case of the DTMs derived from photogrammetrically measured data, the tests were designed deliberately to investigate the relationship between DTM accuracy and sampling interval, terrain slope and data pattern. In the case of DTMs derived from digital contour data, the tests were designed to investigate the relationship between DTM accuracy and contour interval, terrain slope and the characteristics of the data set. iv). The problems related to the reliability of the DTM accuracy figures obtained from the results of the experimental tests have also been investigated. Some criteria have also been set for the accuracy, number and distribution of check points. v). A family of mathematical models has been developed for the prediction of DTM accuracy. These models have been validated by experimental test data and evaluated from a theoretical standpoint. Some of the existing accuracy models have also been evaluated for comparison purposes. vi). A procedure for the determination of the optimum sampling interval for a DTM project with a specified accuracy requirement has also been proposed. Based on this procedure, a potential sampling strategy has also been investigated

Information Extraction and Modeling from Remote Sensing Images: Application to the Enhancement of Digital Elevation Models

To deal with high complexity data such as remote sensing images presenting metric resolution over large areas, an innovative, fast and robust image processing system is presented. The modeling of increasing level of information is used to extract, represent and link image features to semantic content. The potential of the proposed techniques is demonstrated with an application to enhance and regularize digital elevation models based on information collected from RS images

Fractal analyses of some natural systems

Fractal dimensions are estimated by the box-counting method for real world data sets and for mathematical models of three natural systems. 1 he natural systems are nearshore sea wave profiles, the topography of Shei-pa National Park in Taiwan, and the normalised difference vegetation index (NDV1) image of a fresh fern. I he mathematical models which represent the natural systems utilise multi-frequency sinusoids for the sea waves, a synthetic digital elevation model constructed by the mid-point displacement method for the topography and the Iterated Function System (IFS) codes for the fern leaf. The results show that similar fractal dimensions are obtained for discrete sub-sections of the real and synthetic one-dimensional wave data, whilst different fractal dimensions are obtained for discrete sections of the real and synthetic topographical and fern data. The similarities and differences are interpreted in the context of system evolution which was introduced by Mandelbrot (1977). Finally, the results for the fern images show that use of fractal dimensions can successfully separate void and filled elements of the two-dimensional series

Characterization of the spectral distribution of hyperspectral imagery for improved exploitation

Widely used methods of target, anomaly, and change detection when applied to spectral imagery provide less than desirable results due to the complex nature of the data. In the case of hyperspectral data, dimension reduction techniques are employed to reduce the amount of data used in the detection algorithms in order to produce better results and/or decreased computation time. This essentially ignores a significant amount of the data collected in k unique spectral bands. Methods presented in this work explore using the distribution of the collected data in the full k dimensions in order to identify regions of interest contained in spatial tiles of the scene. Here, interest is defined as small and large scale manmade activity. The algorithms developed in this research are primarily data driven with a limited number of assumptions. These algorithms will individually be applied to spatial subsets or tiles of the full scene to indicate the amount of interest contained. Each tile is put through a series of tests using the algorithms based on the full distribution of the data in the hyperspace. The scores from each test will be combined in such a way that each tile is labeled as either interesting or not interesting. This provides a cueing mechanism for image analysts to visually inspect locations within a hyperspectral scene with a high likelihood of containing manmade activity

The scale free and scale - bound properties of land surfaces: fractal analysis and specific geomorphometry from digital terrain models

The scale-bound view of landsurfaces, being an assemblage of certain landforms, occurring within limited scale ranges, has been challenged by the scale-free characteristics of fractal geometry. This thesis assesses the fractal model by examining the irregularity of landsurface form, for the self-affine behaviour present in fractional Brownian surfaces. Different methods for detecting self-affine behaviour in surfaces are considered and of these the variogram technique is shown to be the most effective. It produces the best results of two methods tested on simulated surfaces, with known fractal properties. The algorithm used has been adapted to consider log (altitude variance) over a sample of log (distances) for: complete surfaces; subareas within surfaces; separate directions within surfaces. Twenty seven digital elevation models of landsurfaces arc re-examined for self- affine behaviour. The variogram results for complete surfaces show that none of these are self-affine over the scale range considered. This is because of dominant slope lengths and regular valley, spacing within areas. For similar reasons subarea analysis produces the non-fractal behaviour of markedly different variograms for separate subareas. The linearity of landforms in many areas, is detected by the variograms for separate directions. This indicates that the roughness of landsurfaces is anisotropic, unlike that of fractal surfaces. Because of difficulties in extracting particular landforms from their landsurfaces, no clear links between fractal behaviour, and landform size distribution could be established. A comparative study shows the geomorphometric parameters of fractal surfaces to vary with fractal dimension, while the geomorphometry of landsurfaces varies with the landforms present. Fractal dimensions estimated from landsurfaces do not correlate with geomorphometric parameters. From the results of this study, real landsurfaces would not appear to be scale- free. Therefore, a scale-bound approach towards landsurfaces would seem to be more appropriate to geomorphology than the fractal alternative