On the Geometry of IFS Fractals and its Applications

Visually complex objects with infinitesimally fine features, naturally call for mathematical representations. The geometrical property of self-similarity - the whole similar to its parts - when iterated to infinity generates such features. Finite sets of affine contractions called Iterated Function Systems (IFS), with their compact attractors IFS fractals, can be applied to represent detailed self-similar shapes, such as trees or mountains. The fine local features of such attractors prevent their straightforward geometrical handling, and often imply a non-integer Hausdorff dimension. The main goal of the thesis is to develop an alternative approach to the geometry of IFS fractals in the classical sense via bounding sets. The results are obtained with the objective of practical applicability. The thesis thus revolves around the central problem of determining bounding sets to IFS fractals - and the convex hull in particular - emphasizing the fundamental role of such sets in their geometry. This emphasis is supported throughout the thesis, from real-life and theoretical applications to numerical algorithms crucially dependent on bounding

Basics of Modelling and Visualization

This textbook presents basic concepts related to modelling and visualization tasks. Chapters 1-4 describe transformations in the plane and in the space, and geometrical forms of graphical objects such as curves, patches and fractals. Chapter 5 is about lights, materials, textures, colours that all are needed to enrich a severe appearance of pure geometrical objects leading to their photorealistic visualizations. In Chapter 6 freeware software such as POV Ray, MayaVi and Deep View are described. Using those software one can obtain photorealistic renderings and visualizations. The textbook was prepared for students of the specialization ,,Modelling and Visualization in Bioinformatics'' but it should be helpful to anyone who is interested in computer graphics, modelling techniques, animation and visualization of data. Authors of this textbook believe that information presented in the book will be useful for students and will inspire their imagination in creation of photorealistic static 3D scenes and also will be helpful in creation of animations and visualization of data in an effective and professional way

Optimal use of computing equipment in an automated industrial inspection context

This thesis deals with automatic defect detection. The objective was to develop the techniques required by a small manufacturing business to make cost-efficient use of inspection technology. In our work on inspection techniques we discuss image acquisition and the choice between custom and general-purpose processing hardware. We examine the classes of general-purpose computer available and study popular operating systems in detail. We highlight the advantages of a hybrid system interconnected via a local area network and develop a sophisticated suite of image-processing software based on it. We quantitatively study the performance of elements of the TCP/IP networking protocol suite and comment on appropriate protocol selection for parallel distributed applications. We implement our own distributed application based on these findings. In our work on inspection algorithms we investigate the potential uses of iterated function series and Fourier transform operators when preprocessing images of defects in aluminium plate acquired using a linescan camera. We employ a multi-layer perceptron neural network trained by backpropagation as a classifier. We examine the effect on the training process of the number of nodes in the hidden layer and the ability of the network to identify faults in images of aluminium plate. We investigate techniques for introducing positional independence into the network's behaviour. We analyse the pattern of weights induced in the network after training in order to gain insight into the logic of its internal representation. We conclude that the backpropagation training process is sufficiently computationally intensive so as to present a real barrier to further development in practical neural network techniques and seek ways to achieve a speed-up. Weconsider the training process as a search problem and arrive at a process involving multiple, parallel search "vectors" and aspects of genetic algorithms. We implement the system as the mentioned distributed application and comment on its performance

Fractal Analysis of Microstructural and Fractograpghic Images for Evaluation of Materials

Materials have hierarchically organized complex structures at different length scales. Quantitative description of material behaviour is dependent on four fundamental length scales [1], which are of concern to materials scientists. These are (1) nano scale, 1-103 nm, (2)micro scale, 1-10 3 μm, (3) macro scale, 1-103mm, and (4) global size scale, 1-106 m. While the nano scale corresponds to, often, highly ordered atomic structures, the global size scale relates geophysical phenomena and large man made engineering structures. Micro scale and macro scale correspond to size of material samples used in laboratories, for designing and for fabrication of miniature to small machineries

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