Hierarchical bounding structures for efficient virial computations: Towards a realistic molecular description of cholesterics

We detail the application of bounding volume hierarchies to accelerate second-virial evaluations for arbitrary complex particles interacting through hard and soft finite-range potentials. This procedure, based on the construction of neighbour lists through the combined use of recursive atom-decomposition techniques and binary overlap search schemes, is shown to scale sub-logarithmically with particle resolution in the case of molecular systems with high aspect ratios. Its implementation within an efficient numerical and theoretical framework based on classical density functional theory enables us to investigate the cholesteric self-assembly of a wide range of experimentally-relevant particle models. We illustrate the method through the determination of the cholesteric behaviour of hard, structurally-resolved twisted cuboids, and report quantitative evidence of the long-predicted phase handedness inversion with increasing particle thread angles near the phenomenological threshold value of $45^\circ$. Our results further highlight the complex relationship between microscopic structure and helical twisting power in such model systems, which may be attributed to subtle geometric variations of their chiral excluded-volume manifold

A novel model-based 3D+time left ventricular segmentation technique

A common approach to model-based segmentation is to assume a top-down modelling strategy. However, this is not feasible for complex 3D+time structures such as the cardiac left ventricle due to increased training requirements, aligning difficulties and local minima in resulting models. As our main contribution, we present an alternate bottom-up modelling approach. By combining the variation captured in multiple dimensionally-targeted models at segmentation-time we create a scalable segmentation framework that does not suffer from the ’curse of dimensionality’. Our second contribution involves a flexible contour coupling technique that allows our segmentation method to adapt to unseen contour configurations outside the training set. This is used to identify the endo- and epi-cardium contours of the left ventricle by coupling them at segmentationtime, instead of at model-time. We apply our approach to 33 3D+time MRI cardiac datasets and perform comprehensive evaluation against several state-of-the-art works. Quantitative evaluation illustrates that our method requires significantly less training than state-of-the-art model-based methods, while maintaining or improving segmentation accuracy

Curve-Based Shape Matching Methods and Applications

One of the main cues we use in our everyday life when interacting with the environment is shape. For example, we use shape information to recognise a chair, grasp a cup, perceive traffic signs and solve jigsaw puzzles. We also use shape when dealing with more sophisticated tasks, such as the medical diagnosis of radiographs or the restoration of archaeological artifacts. While the perception of shape and its use is a natural ability of human beings, endowing machines with such skills is not straightforward. However, the exploitation of shape cues is important for the development of competent computer methods that will automatically perform tasks such as those just mentioned. With this aim, the present work proposes computer methods which use shape to tackle two important tasks, namely packing and object recognition. The packing problem arises in a variety of applications in industry, where the placement of a set of two-dimensional shapes on a surface such that no shapes overlap and the uncovered surface area is minimised is important. Given that this problem is NP-complete, we propose a heuristic method which searches for a solution of good quality, though not necessarily the optimal one, within a reasonable computation time. The proposed method adopts a pictorial representation and employs a greedy algorithm which uses a shape matching module in order to dynamically select the order and the pose of the parts to be placed based on the “gaps” appearing in the layout during the execution. This thesis further investigates shape matching in the context of object recognition and first considers the case where the target object and the input scene are represented by their silhouettes. Two distinct methods are proposed; the first method follows a local string matching approach, while the second one adopts a global optimisation approach using dynamic programming. Their use of silhouettes, however, rules out the consideration of any internal contours that might appear in the input scene, and in order to address this limitation, we later propose a graph-based scheme that performs shape matching incorporating information from both internal and external contours. Finally, we lift the assumption made that input data are available in the form of closed curves, and present a method which can robustly perform object recognition using curve fragments (edges) as input evidence. Experiments conducted with synthetic and real images, involving rigid and deformable objects, show the robustness of the proposed methods with respect to geometrical transformations, heavy clutter and substantial occlusion