No / The complex formation of Islamic geometric Patterns (IGP) is one of the distinctive features in Islamic art and architecture. Many have attempted to reproduce these patterns in digital form, using various pattern generation techniques. Shape grammars are an effective pattern generation method, providing good aesthetic results. In this paper we present a novel approach in generating 3D IGP using an extended shape grammar: Parametrized Shape Grammar (PSG). PSG allows a user to generate both original and novel forms of Islamic geometric motifs (a repeated unit of a pattern). PSG is generalized to generate n-fold Islamic geometric motifs in a 3D environment, practically implemented as a 3D modeling tool within Autodesk Maya. The parametrization within each grammar rule is the key to generating numerous original and novel Islamic geometric motifs.

The method of Continuum Sensitivity Analysis (CSA) with Spatial Gradient Reconstruction (SGR) is presented for calculating the sensitivity of fluid, structural, and coupled fluid-structure (aeroelastic) response with respect to shape design parameters. One of the novelties of this work is the derivation of local CSA with SGR for obtaining flow derivatives using finite volume formulation and its nonintrusive implementation (i.e. without accessing the analysis source code). Examples of a NACA0012 airfoil and a lid-driven cavity highlight the effect of the accuracy of the sensitivity boundary conditions on the flow derivatives. It is shown that the spatial gradients of flow velocities, calculated using SGR, contribute significantly to the sensitivity transpiration boundary condition and affect the accuracy of flow derivatives. The effect of using an inconsistent flow solution and Jacobian matrix during the nonintrusive sensitivity analysis is also studied. Another novel contribution is derivation of a hybrid adjoint formulation of CSA, which enables efficient calculation of design derivatives of a few performance functions with respect to many design variables. This method is demonstrated with applications to 1-D, 2-D and 3-D structural problems. The hybrid adjoint CSA method computes the same values for shape derivatives as direct CSA. Therefore accuracy and convergence properties are the same as for the direct local CSA. Finally, we demonstrate implementation of CSA for computing aeroelastic response shape derivatives. We derive the sensitivity equations for the structural and fluid systems, identify the sources of the coupling between the structural and fluid derivatives, and implement CSA nonintrusively to obtain the aeroelastic response derivatives. Particularly for the example of a flexible airfoil, the interface that separates the fluid and structural domains is chosen to be flexible. This leads to coupling terms in the sensitivity analysis which are highlighted. The integration of the geometric sensitivity with the aeroelastic response for obtaining shape derivatives using CSA is demonstrated. / Ph. D. / Many natural and man-made systems exhibit behavior which is a combination of the structural elastic response, such as bending or twisting, and aerodynamic or fluid response, such as pressure; for example, flow of blood in arteries, flapping of a bird’s wings, fluttering of a flag, and flight of a hot-air balloon. Such a coupled fluid-structure response is defined as aeroelastic response. Flight of an aircraft through turbulent weather is another example of an aeroelastic response. In this work, a novel method is proposed for calculating the sensitivity of an aircraft’s aeroelastic response to changes in the shape of the aircraft. These sensitivities are numbers that indicate how sensitive the aircraft’s responses are to changes in the shape of the aircraft. Such sensitivities are essential for aircraft design. The method presented in this work is called Continuum Sensitivity Analysis (CSA). The main goal is to accurately and efficiently calculate the sensitivities which are used by optimization tools to compute the best aircraft shape that suits the customers needs. The key advantages of CSA, as compared to the other methods, are that it is more efficient and it can be used effectively with commercially available (nonintrusive) tools. A unique contribution is that the proposed method can be used to calculate sensitivities with respect to a few or many shape design variables, without much effort. Integration of structural and fluid sensitivities is carried out first by applying CSA individually for structural and fluid systems, followed by connecting these together to obtain the coupled aeroelastic sensitivity. We present the first application of local formulation of CSA for nonintrusive implementation of high-fidelity aeroelastic sensitivities. The following challenging tasks are tackled in this research: (a) deriving the sensitivity equations and boundary conditions, (b) developing and linking computer codes written in different languages (C++, MATLAB, FORTRAN) for solving these equations, and (c) implementing CSA using commercially available tools such as NASTRAN, FLUENT, and SU2. CSA can improve the design process of complex aircraft and spacecraft. Owing to its modularity, CSA is also applicable to multidisciplinary areas such as biomedical, automotive, ocean engineering, space science, etc.

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The field of computer vision studies the computational tools and methods required for computers to be able to process visual information, for example images and video. Shape descriptors are one of the tools commonly used in image processing applications. Shape descriptors are mathematical functions which are applied to an image and produce numerical values which are representative of a particular characteristic of the image. These numerical values can then be processed in order to provide some information about the image. For example, these values can be fed to a classifier in order to assign a class label to the image. There are a number of shape descriptors already existing in the literature for 2D and 3D images. The aim of this thesis is to develop additional shape descriptors which provide an improvement over (or an alternative to) those already existing in the literature. A large majority of the existing 2D shape descriptors use surface information to produce a measure. However, in some applications surface information is not present and only partially extracted contours are available. In such cases, boundary based shape descriptors must be used. A new boundary based shape descriptor called Linearity is introduced. This measure can be applied to open or closed curve segments. In general the availability of 3D images is comparatively smaller than that of 2D images. As a consequence, the number of existing 3D shape descriptors is also relatively smaller. However, there is an increasing interest in the development of 3D descriptors. In this thesis we present two basic 3D measures which afterwards are modified to produce a range of new shape descriptors. All of these descriptors are similar in their behaviour, however they can be combined and applied in different image processing applications such as image retrieval and classification. This simple fact is demonstrated through several examples.

"Patients with repaired tetralogy of Fallot (TOF) account for the majority of cases with late onset right ventricle (RV) failure. The current surgical approach, which includes pulmonary valve replacement/insertion (PVR), has yielded mixed results in terms of RV functional recovery. Therefore, it is of great interest for clinicians to identify parameters, which may be used to predict post-PVR outcome. Pre- and post-PVR cardiac magnetic resonance (CMR) data were obtained from 60 repaired TOF patients with consent obtained for analysis. RV ejection fraction (RVEF) change (post-PVR RVEF minus pre-PVR RVEF) was used to measure post-PVR improvement. The patients were divided into Group 1(optimal outcome) and Group 2 (poor outcome) for comparison. RV wall thickness (WT) and curvature were obtained from CMR data for statistical analysis. Using mean quarter values (one CMR slice = 4 quarters), statistically significant differences in circumferential curvature (C-curvature) and longitudinal curvature (L-curvature) at end-diastole (maximum RV volume) and WT and C-curvature at end-systole (minimum RV volume) between Group 1 and Group 2 were found. Correlations between average WT at systole and between L-curvature at diastole and the change of RVEF were statistically significant. Specifically, the correlation coefficient between average WT at systole and change of RVEF was – 0.2715, (p = 0.036) and between L-curvature at diastole and change of RVEF 0.3297 (p = 0.01). This initial study suggests that the RV longitudinal curvature and wall thickness may be used as a marker/predictor for PVR surgical outcome. "

Master of Science in Engineering - Electrical and Information Engineering / With the increase in complexity of modern software systems, there is a great demand for software engineering techniques. Calculation processes are becoming more and more complex, especially in the field of machine vision and computational intelligence. A suitable object oriented calculation process framework is developed in order to address this problem. To demonstrate the effectiveness of the framework, a simple shape classification system is implemented in C#. A suitable method for representing shapes of images is developed and it is used for classification by a neural network. Sets of real-world images of hands and automobiles are used to test the system. The performance of the object oriented system in C# is compared to a functional paradigm system in Matlab and it is found that object orientation is well suited to the later stages of machine vision while the functional approach is well suited to low level image processing tasks.