The visualization of numerical fluid flow datasets is essential to the engineering processes that motivate their computational simulation. To address the need for visual representations that convey meaningful relations and enable a deep understanding of flow structures, the discipline of Flow Visualization has produced many methods and schemes that are tailored to a variety of visualization tasks. The ever increasing complexity of modern flow simulations, however, puts an enormous demand on these methods. The study of vortex breakdown, for example, which is a highly transient and inherently three-dimensional flow pattern with substantial impact wherever it appears, has driven current techniques to their limits. In this thesis, we propose several novel visualization methods that significantly advance the state of the art in the visualization of complex flow structures. First, we propose a novel scheme for the construction of stream surfaces from the trajectories of particles embedded in a flow. These surfaces are extremely useful since they naturally exploit coherence between neighboring trajectories and are highly illustrative in nature. We overcome the limitations of existing stream surface algorithms that yield poor results in complex flows, and show how the resulting surfaces can be used a building blocks for advanced flow visualization techniques. Moreover, we present a visualization method that is based on moving section planes that travel through a dataset and sample the flow. By considering the changes to the flow topology on the plane as it moves, we obtain a method of visualizing topological structures in three-dimensional flows that are not accessible by conventional topological methods. On the same algorithmic basis, we construct an algorithm for the tracking of critical points in such flows, thereby enabling the treatment of time-dependent datasets. Last, we address some problems with the recently introduced Lagrangian techniques. While conceptually elegant and generally applicable, they suffer from an enormous computational cost that we significantly use by developing an adaptive approximation algorithm. This allows the application of such methods on very large and complex numerical simulations. Throughout this thesis, we will be concerned with flow visualization aspect of general practical significance but we will particularly emphasize the remarkably challenging visualization of the vortex breakdown phenomenon.
Modern digital imaging technologies, such as digital microscopy or micro-computed tomography, deliver such large amounts of 2D and 3D-image data that manual processing becomes infeasible. This leads to a need for robust, flexible and automatic image analysis tools in areas such as histology or materials science, where microstructures are being investigated (e.g. cells, fiber systems). General-purpose image processing methods can be used to analyze such microstructures. These methods usually rely on segmentation, i.e., a separation of areas of interest in digital images. As image segmentation algorithms rarely adapt well to changes in the imaging system or to different analysis problems, there is a demand for solutions that can easily be modified to analyze different microstructures, and that are more accurate than existing ones. To address these challenges, this thesis contributes a novel statistical model for objects in images and novel algorithms for the image-based analysis of microstructures. The first contribution is a novel statistical model for the locations of objects (e.g. tumor cells) in images. This model is fully trainable and can therefore be easily adapted to many different image analysis tasks, which is demonstrated by examples from histology and materials science. Using algorithms for fitting this statistical model to images results in a method for locating multiple objects in images that is more accurate and more robust to noise and background clutter than standard methods. On simulated data at high noise levels (peak signal-to-noise ratio below 10 dB), this method achieves detection rates up to 10% above those of a watershed-based alternative algorithm. While objects like tumor cells can be described well by their coordinates in the plane, the analysis of fiber systems in composite materials, for instance, requires a fully three dimensional treatment. Therefore, the second contribution of this thesis is a novel algorithm to determine the local fiber orientation in micro-tomographic reconstructions of fiber-reinforced polymers and other fibrous materials. Using simulated data, it will be demonstrated that the local orientations obtained from this novel method are more robust to noise and fiber overlap than those computed using an established alternative gradient-based algorithm, both in 2D and 3D. The property of robustness to noise of the proposed algorithm can be explained by the fact that a low-pass filter is used to detect local orientations. But even in the absence of noise, depending on fiber curvature and density, the average local 3D-orientation estimate can be about 9° more accurate compared to that alternative gradient-based method. Implementations of that novel orientation estimation method require repeated image filtering using anisotropic Gaussian convolution filters. These filter operations, which other authors have used for adaptive image smoothing, are computationally expensive when using standard implementations. Therefore, the third contribution of this thesis is a novel optimal non-orthogonal separation of the anisotropic Gaussian convolution kernel. This result generalizes a previous one reported elsewhere, and allows for efficient implementations of the corresponding convolution operation in any dimension. In 2D and 3D, these implementations achieve an average performance gain by factors of 3.8 and 3.5, respectively, compared to a fast Fourier transform-based implementation. The contributions made by this thesis represent improvements over state-of-the-art methods, especially in the 2D-analysis of cells in histological resections, and in the 2D and 3D-analysis of fibrous materials.
In its rather short history robotic research has come a long way in the half century since it started to exist as a noticeable scientic eld. Due to its roots in engineering, computer science, mathematics, and several other 'classical' scientic branches,a grand diversity of methodologies and approaches existed from the very beginning. Hence, the researchers in this eld are in particular used to adopting ideas that originate in other elds. As a fairly logical consequence of this, scientists tended to biology during the 1970s in order to nd approaches that are ideally adapted to the conditions of our natural environment. Doing so allows for introducing principles to robotics that have already shown their great potential by prevailing in a tough evolutionary selection process for millions of years. The variety of these approaches spans from efficient locomotion, to sensor processing methodologies and all the way to control architectures. Thus, the full spectrum of challenges for autonomous interaction with the surroundings while pursuing a task can be covered by such means. A feature that has proven to be amongst the most challenging to recreate is the human ability of biped locomotion. This is mainly caused by the fact that walking,running and so on are highly complex processes involving the need for energy efficient actuation, sophisticated control architectures and algorithms, and an elaborate mechanical design while at the same time posting restrictions concerning stability and weight. However, it is of special interest since our environment is favoring this specic kind of locomotion and thus promises to open up an enormous potential if mastered. More than the mere scientic interest, it is the fascination of understanding and recreating parts of oneself that drives the ongoing eorts in this area of research. The fact that this is not at all an easy task to tackle is not only caused by the highly dynamical processes but also has its roots in the challenging design process. That is because it cannot be limited to just one aspect like e.g. the control architecture, actuation, sensors, or mechanical design alone. Each aspect has to be incorporated into a sound general concept in order to allow for a successful outcome in the end. Since control is in this context inseparably coupled with the mechanics of the system, both has to be dealt with here.
In urban planning, both measuring and communicating sustainability are among the most recent concerns. Therefore, the primary emphasis of this thesis concerns establishing metrics and visualization techniques in order to deal with indicators of sustainability.
First, this thesis provides a novel approach for measuring and monitoring two indicators of sustainability - urban sprawl and carbon footprints – at the urban neighborhood scale. By designating different sectors of relevant carbon emissions as well as different household categories, this thesis provides detailed information about carbon emissions in order to estimate impacts of daily consumption decisions and travel behavior by household type. Regarding urban sprawl, a novel gridcell-based indicator model is established, based on different dimensions of urban sprawl.
Second, this thesis presents a three-step-based visualization method, addressing predefined requirements for geovisualizations and visualizing those indicator results, introduced above. This surface-visualization combines advantages from both common GIS representation and three-dimensional representation techniques within the field of urban planning, and is assisted by a web-based graphical user interface which allows for accessing the results by the public.
In addition, by focusing on local neighborhoods, this thesis provides an alternative approach in measuring and visualizing both indicators by utilizing a Neighborhood Relation Diagram (NRD), based on weighted Voronoi diagrams. Thus, the user is able to a) utilize original census data, b) compare direct impacts of indicator results on the neighboring cells, and c) compare both indicators of sustainability visually.