This thesis investigates the segmentation of data in 2D and 3D by texture analysis using Fourier domain filtering. The field of texture analysis is a well-trodden one in 2D, but many applications, such as Medical Imaging, Stratigraphy or Crystallography, would benefit from 3D analysis instead of the traditional, slice-by-slice approach. With the intention of contributing to texture analysis and segmentation in 3D, a multiresolution volumetric texture segmentation (M-VTS) algorithm is presented. The method extracts textural measurements from the Fourier domain of the data via sub-band filtering using a Second Orientation Pyramid. A novel Bhattacharyya space, based on the Bhattacharyya distance is proposed for selecting of the most discriminant measurements and produces a compact feature space. Each dimension of the feature space is used to form a Quad Tree. At the highest level of the tree, new positional features are added to improve the contiguity of the classification. The classified space is then projected to lower levels of the tree where a boundary refinement procedure is performed with a 3D equivalent of butterfly filters. The performance of M-VTS is tested in 2D by classifying a set of standard texture images. The figures contain different textures that are visually stationary. M-VTS yields lower misclassification rates than reported elsewhere ([104, 111, 124]). The algorithm was tested in 3D with artificial isotropic data and three Magnetic Resonance Imaging sets of human knees with satisfactory results. The regions segmented from the knees correspond to anatomical structures that could be used as a starting point for other measurements. By way of example, we demonstrate successful cartilage extraction using our approach.

Negative Poisson’s ratio, or auxetic, materials present the possibility of designing structures and components with tailored or enhanced mechanical properties. This thesis explores the phenomenon of auxetic behaviour in cubic crystals using classical and quantum modelling techniques and assesses the validity of these techniques when predicting auxetic behaviour in cubic elemental metals. These techniques are then used to explore the mechanism of this behaviour. The findings of the atomistic modelling are then used as a template to create networks of bending beams with tailored Poisson’s ratio behaviour.