Applications of fractals to image data compression

Digital image processing is exploited in many diverse applications but the size of digital images places excessive demands on current storage and transmission technology. Image data compression is required to permit further use of digital image processing. Conventional image compression techniques based on statistical analysis have reached a saturation level so it is necessary to explore more radical methods. This thesis is concerned with novel methods, based on the use of fractals, for achieving significant compression of image data within reasonable processing time without introducing excessive distortion. Images are modelled as fractal data and this model is exploited directly by compression schemes. The validity of this is demonstrated by showing that the fractal complexity measure of fractal dimension is an excellent predictor of image compressibility. A method of fractal waveform coding is developed which has low computational demands and performs better than conventional waveform coding methods such as PCM and DPCM. Fractal techniques based on the use of space-filling curves are developed as a mechanism for hierarchical application of conventional techniques. Two particular applications are highlighted: the re-ordering of data during image scanning and the mapping of multi-dimensional data to one dimension. It is shown that there are many possible space-filling curves which may be used to scan images and that selection of an optimum curve leads to significantly improved data compression. The multi-dimensional mapping property of space-filling curves is used to speed up substantially the lookup process in vector quantisation. Iterated function systems are compared with vector quantisers and the computational complexity or iterated function system encoding is also reduced by using the efficient matching algcnithms identified for vector quantisers.

Visual data mining: integrating machine learning with information visualization

Today, the data available to tackle many scientific challenges is vast in quantity and diverse in nature. The exploration of heterogeneous information spaces requires suitable mining algorithms as well as effective visual interfaces. Most existing systems concentrate either on mining algorithms or on visualization techniques. Though visual methods developed in information visualization have been helpful, for improved understanding of a complex large high-dimensional dataset, there is a need for an effective projection of such a dataset onto a lower-dimension (2D or 3D) manifold. This paper introduces a flexible visual data mining framework which combines advanced projection algorithms developed in the machine learning domain and visual techniques developed in the information visualization domain. The framework follows Shneiderman’s mantra to provide an effective user interface. The advantage of such an interface is that the user is directly involved in the data mining process. We integrate principled projection methods, such as Generative Topographic Mapping (GTM) and Hierarchical GTM (HGTM), with powerful visual techniques, such as magnification factors, directional curvatures, parallel coordinates, billboarding, and user interaction facilities, to provide an integrated visual data mining framework. Results on a real life high-dimensional dataset from the chemoinformatics domain are also reported and discussed. Projection results of GTM are analytically compared with the projection results from other traditional projection methods, and it is also shown that the HGTM algorithm provides additional value for large datasets. The computational complexity of these algorithms is discussed to demonstrate their suitability for the visual data mining framework.

Spatially structured cognitve models of semantic information:the implications for computerised databases

Existing theories of semantic cognition propose models of cognitive processing occurring in a conceptual space, where ‘meaning’ is derived from the spatial relationships between concepts’ mapped locations within the space. Information visualisation is a growing area of research within the field of information retrieval, and methods for presenting database contents visually in the form of spatial data management systems (SDMSs) are being developed. This thesis combined these two areas of research to investigate the benefits associated with employing spatial-semantic mapping (documents represented as objects in two- and three-dimensional virtual environments are proximally mapped dependent on the semantic similarity of their content) as a tool for improving retrieval performance and navigational efficiency when browsing for information within such systems. Positive effects associated with the quality of document mapping were observed; improved retrieval performance and browsing behaviour were witnessed when mapping was optimal. It was also shown using a third dimension for virtual environment (VE) presentation provides sufficient additional information regarding the semantic structure of the environment that performance is increased in comparison to using two-dimensions for mapping. A model that describes the relationship between retrieval performance and browsing behaviour was proposed on the basis of findings. Individual differences were not found to have any observable influence on retrieval performance or browsing behaviour when mapping quality was good. The findings from this work have implications for both cognitive modelling of semantic information, and for designing and testing information visualisation systems. These implications are discussed in the conclusions of this work.

Reduced dimension models for weather forecasting

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