published_or_final_version / Comparative Literature / Master / Master of Philosophy

A numerical study of two classes of neural network models is presented. The performance of Ising spin neural networks as content-addressable memories for the storage of bit patterns is analysed. By studying systems of increasing sizes, behaviour consistent with fintite-size scaling, characteristic of a first-order phase transition, is shown to be exhibited by the basins of attraction of the stored patterns in the Hopfield model. A local iterative learning algorithm is then developed for these models which is shown to achieve perfect storage of nominated patterns with near-optimal content-addressability. Similar scaling behaviour of the associated basins of attraction is observed. For both this learning algorithm and the Hopfield model, by extrapolating to the thermodynamic limit, estimates are obtained for the critical minimum overlap which an input pattern must have with a stored pattern in order to successfully retrieve it. The role of a neural network as a tool for optimising cost functions of binary valued variables is also studied. The particular application considered is that of restoring binary images which have become corrupted by noise. Image restorations are achieved by representing the array of pixel intensities as a network of analogue neurons. The performance of the network is shown to compare favourably with two other deterministic methods-a gradient descent on the same cost function and a majority-rule scheme-both in terms of restoring images and in terms of minimising the cost function. All of the computationally intensive simulations exploit the inherent parallelism in the models: both SIMD (the ICL DAP) and MIMD (the Meiko Computing Surface) machines are used.

abstract / Computer Science / Doctoral / Doctor of Philosophy

abstract / Electrical and Electronic Engineering / Doctoral / Doctor of Philosophy

<p>Digital image analysis is the field of extracting relevant information from digital images. Recent developments in imaging techniques have made 3-dimensional volume images more common. This has created a need to extend existing 2D image analysis tools to handle images of higher dimensions. Such extensions are usually not straightforward. In many cases, the theoretical and computational complexity of a problem increases dramatically when an extra dimension is added.</p><p>A fundamental problem in image analysis is image segmentation, i.e., identifying and separating relevant objects and structures in an image. Accurate segmentation is often required for further processing and analysis of the image can be applied. Despite years of active research, general image segmentation is still seen as an unsolved problem. This mainly due to the fact that it is hard to identify objects from image data only. Often, some high-level knowledge about the objects in the image is needed. This high-level knowledge may be provided in different ways. For fully automatic segmentation, the high-level knowledge must be incorporated in the segmentation algorithm itself. In interactive applications, a human user may provide high-level knowledge by guiding the segmentation process in various ways.</p><p>The aim of the work presented here is to develop segmentation and analysistools for volume images. To limit the scope, the focus has been on two specic capplications of volume image analysis: analysis of volume images of fibrousmaterials and interactive segmentation of medical images. The respective image analysis challenges of these two applications will be discussed. While the work has been focused on these two applications, many of the results presented here are applicable to other image analysis problems.</p>

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This dissertation describes the application of maximum entropy image restoration to envelope-detected ultrasonic sector scans. The maximum entropy restoration of the image of a point target (phantom) test object is shown to be superior to results obtained from the more familiar Wiener filter. The subsequent application of maximum entropy to an in-vivo clinical ultrasound image, however, illustrates the pitfalls associated with determining the relative merit of an ultrasonic image restoration technique from test object results alone. Since the resolution of sector scan images is substantially worse in the lateral (azimuthal) scan direction than the axial scan direction, the deconvolution filters described in this thesis were applied in the lateral direction only. The maximum entropy method is shown to have certain inherent advantages over linear frequency-domain techniques for the restoration of ultrasonic sector scan images. The positivity constraint inherent in the maximum entropy method is shown to produce restorations with substantially fewer oscillatory artifacts than those produced by Wiener filtering. In addition, the iterative nature of the maximum entropy algorithm is shown to be compatible with the restoration of the undersampled regions in the far field of sector scan images. The restoration of sector scan images is complicated by the spatially varying degradation associated with such images. A novel approach to the restoration of this class of image degradation is presented in this thesis. The widespread use of maximum entropy image restoration has been inhibited by the technique's demanding computational requirements. This problem can be alleviated by the use of high speed computer hardware, and the final chapters of this thesis describe the design and construction of a microcomputer-based array processor. The advantages inherent in the use of such hardware are demonstrated with reference to the maximum entropy restoration of ultrasonic images.

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