This thesis investigates the feasibility of establishing a generalised approach for defining similarity metrics between 3D shapes for the casting design problem in Case-Based Reasoning (CBR). This research investigates a new approach for improving the quality of casting design advice achieved from a CBR system using casting design knowledge associated with past cases. The new approach uses enhanced similarity metrics to those used in previous research in this area to achieve improvements in the advice given. The new similarity metrics proposed here are based on the decomposition of casting shape cases into a set of components. The research into metrics defines and uses the Component Type Similarity Metric (CTM) and Maximum Common Subgraph (MCS) metric between graph representations of the case shapes and are focused on the definition of partial similarity between the components of the same type that take into account the geometrical features and proportions of each single shape component. Additionally, the investigation extends the scope of the research to 3D shapes by defining and evaluating a new metric for the overall similarity between 3D shapes. Additionally, this research investigates a methodology for the integration of the CBR cycle and automation of the feature extraction from target and source case shapes. The ShapeCBR system has been developed to demonstrate the feasibility of integrating the CBR approach for retrieving and reusing casting design advice. The ShapeCBR system automates the decomposition process, the classification process and the shape matching process and is used to evaluate the new similarity metrics proposed in this research and the extension of the approach to 3D shapes. Evaluation of the new similarity metrics show that the efficiency of the system is enhanced using the new similarity metrics and that the new approach provides useful casting design information for 3D casting shapes. Additionally, ShapeCBR shows that it is possible to automate the decomposition and classification of components that allow a case shape to be represented in graph form and thus provide the basis for automating the overall CBR cycle. The thesis concludes with new research questions that emerge from this research and an agenda for further work to be pursued in further research in the area.

Estimating the size of an insect pest population in an agricultural field is an integral part of insect pest monitoring. An abundance estimate can be used to decide if action is needed to bring the population size under control, and accuracy is important in ensuring that the correct decision is made. Conventionally, statistical techniques are used to formulate an estimate from population density data obtained via sampling. This thesis thoroughly investigates an alternative approach of applying numerical integration techniques. We show that when the pest population is spread over the entire field, numerical integration methods provide more accurate results than the statistical counterpart. Meanwhile, when the spatial distribution is more aggregated, the error behaves as a random variable and the conventional error estimates do not hold. We thus present a new probabilistic approach to assessing integration accuracy for such functions, and formulate a mathematically rigorous estimate of the minimum number of sample units required for accurate abundance evaluation in terms of the species diffusion rate. We show that the integration error dominates the error introduced by noise in the density data and thus demonstrate the importance of formulating numerical integration techniques which provide accurate results for sparse spatial data.