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        "title": "On Visualization and Reconstruction from Non-uniform Point Sets",
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        "abstract": "Technological and research advances in both acquisition and simulation devices provide continuously increasing high-resolution volumetric data that by far exceed today's graphical and display capabilities. Non-uniform representations offer a way of balancing this deluge of data by adaptively measuring (sampling) according to the importance (variance) of the data. Also, in many real-life situations the data are known only on a non-uniform representation. \r\n\r\nProcessing of non-uniform data is a non-trivial task and hence more difficult when compared to processing of regular data. Transforming from non-uniform to uniform representations is a well-accepted paradigm in the signal processing community. In this thesis we advocate such a concept. The main motivation for adopting this paradigm is that most of the techniques and methods related to signal processing, data mining and data exploration are well-defined and stable for Cartesian data, but generally are non-trivial to apply to non-uniform data. Among other things, \r\nthis will allow us to better exploit the capabilities of modern GPUs.\r\n\r\nIn non-uniform representations sampling rates can vary drastically even by several orders of magnitude, making the decision on a target resolution a non-trivial trade-off between accuracy and efficiency. In several cases the points are spread non-uniformly with similar density across the volume, while in other cases the points have an enormous variance in distribution. In this thesis we present solutions to both cases. For the first case we suggest computing reconstructions of the same volume in different resolutions based on the level of detail we are interested in. The second case scenario is the main motivation for proposing a multi-resolution scheme, where the scale of reconstruction is decided adaptively based on the number of points in each subregion of the whole volume.\r\n\r\nWe introduce a novel framework for 3D reconstruction and visualization from non-uniform scalar and vector data. We adopt a variational reconstruction approach. In this method non-uniform point sets are transformed to a uniform representation consisting of B-spline coefficients that are attached to the grid. With these coefficients we can define a C2 continuous function across the whole volume. Several testings were performed in order to analyze and fine-tune our framework. All the testings and the results of this thesis offer a view from a new and different perspective to the visualization and reconstruction from non-uniform point sets.",
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        "title": "On Visualization and Reconstruction from Non-Uniform Point Sets using B-splines",
        "date": "2009-06",
        "abstract": "In this paper we present a novel framework for the visualization and reconstruction from non-uniform point sets.\r\nWe adopt a variational method for the reconstruction of 3D non-uniform data to a uniform grid of chosen resolution.\r\nWe will extend this reconstruction to an efficient multi-resolution uniform representation of the underlying\r\ndata. Our multi-resolution representation includes a traditional bottom-up multi-resolution approach and a novel\r\ntop-down hierarchy for adaptive hierarchical reconstruction. Using a hybrid regularization functional we can\r\nimprove the reconstruction results. Finally, we discuss further application scenarios and show rendering results\r\nto emphasize the effectiveness and quality of our proposed framework. By means of qualitative results and error\r\ncomparisons we demonstrate superiority of our method compared to competing methods",
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        "event": "Eurographics/IEEE Symposium on Visualization",
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        "id": "fuchs-2008-del",
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        "title": "Delocalized Unsteady Vortex Region Detectors",
        "date": "2008-10",
        "abstract": "In this paper we discuss generalizations of instantaneous, local vortex criteria.\r\nWe incorporate information on spatial context and temporal development into the\r\ndetection process. The presented method is generic in so far that it can extend\r\nany given Eulerian criterion to take the Lagrangian approach into account. Furthermore,\r\nwe present a visual aid to understand and steer the feature extraction process.\r\nWe show that the delocalized detectors are able to distinguish between connected vortices\r\nand help understanding regions of multiple interacting vortex structures.\r\nThe delocalized detectors extract smoother structures and reduce noise in the vortex detection result.",
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        "title": "The Visible Vortex - Interactive Analysis and Extraction of Vortices in Large Time-Dependent Flow Data Sets",
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        "abstract": "Computational simulation of physical and chemical processes has become an essential tool to tackle questions from the field of fluid dynamics.\nUsing current simulation packages it is possible to compute unsteady flow simulations for\nrealistic scenarios. The resulting solutions are stored in large to very large grids in 2D or 3D,\nfrequently time-dependent, with multi-variate results from the numeric simulation.\nWith increasing complexity of simulation results,\npowerful analysis and visualization tools are needed to make sense of the computed information and answer\nthe question at hand. To do this we need new approaches and algorithms to locate regions of\ninterest, find important structures in the flow and analyze the behavior of the\nflow interactively.\n\nThe main motives of this thesis are the extension of vortex detection criteria to unsteady flow and\nthe combination of vortex detectors with interactive visual analysis.\nTo develop an understanding for the simulation results it is necessary to\ncompare attributes of the simulation to each other and to be able to\nrelate them to larger structures such as vortices. It is shown how automatic feature detection algorithms can be combined with interactive analysis techniques such that both detection and analysis benefit.\n\nBy extending and integrating vortex detectors into the process of visual analysis, it becomes possible\nto understand the impact of vortex structures on the development of\nthe flow. Using real-world examples from the field of engine design we discuss how vortex structures\ncan have critical impact on the performance of a prototype. We illustrate how interactive visual analysis\ncan support prototype design and evaluation.\nFurthermore, we show that taking the unsteady nature of the flow into account improves the quality of the extracted structures.",
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        "title": "Efficient Reconstruction from Non-uniform Point Sets",
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        "abstract": "We propose a method for non-uniform reconstruction of 3D scalar data. Typically, radial basis functions, trigonometric polynomials or shift-invariant functions are used in the functional approximation of 3D data. We adopt a variational approach for the reconstruction and rendering of 3D data. The principle idea is based on data fitting via thin-plate splines. An approximation by B-splines offers more compact support for fast reconstruction. We adopt this method for large datasets by introducing a block-based reconstruction approach. This makes the method practical for large data sets. Our reconstruction will be smooth across blocks. We give reconstruction measurements as error estimations based on different parameter settings and also an insight on the computational effort. We show that the block size used in reconstruction has a negligible effect on the reconstruction error. Finally we show rendering results to emphasize the quality of this 3D reconstruction technique.",
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        "title": "Parallel Vectors Criteria for Unsteady Flow Vortices",
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        "abstract": "Feature-based flow visualization is naturally dependent\r\n  on feature extraction. To extract flow features, often higher-order\r\n  properties of the flow data are used such as the Jacobian or\r\n  curvature properties, implicitly describing the flow features in\r\n  terms of their inherent flow characteristics (e.g., collinear flow\r\n  and vorticity vectors). In this paper we present recent research\r\n  which leads to the (not really surprising) conclusion that feature extraction algorithms\r\n  need to be extended to a time-dependent analysis framework (in terms\r\n  of time derivatives) when dealing with unsteady flow data.\r\n  Accordingly, we present two extensions of the parallel vectors based vortex\r\n  extraction criteria to the time-dependent domain and show the improvements of\r\n  feature-based flow visualization in comparison to the\r\n  steady versions of this extraction algorithm both in the context of\r\n  a high-resolution dataset, i.e., a simulation specifically designed\r\n  to evaluate our new approach, as well as for a real-world dataset\r\n  from a concrete application.",
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                "description": "We compare the computed corelines with respect to lambda2 and equivalence ratio. (a) The modified algorithm detects two vortex core lines (red) whereas the original version only detects the main vortex core line (white). (b) An isosurface of equivalence ratio at 0.7 containing the region of optimal mixing. (c) The surface containing the region of equivalence ratio of 0.5 and lambda2< -1000$.",
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        "title": "N-dimensional Data-Dependent Reconstruction Using Topological Changes",
        "date": "2007-09",
        "abstract": "We introduce a new concept for a geometrically based feature preserving reconstruction\r\ntechnique of n-dimensional scattered data. Our goal is to generate\r\nan n-dimensional triangulation, which preserves the high frequency regions via\r\nlocal topology changes. It is the generalization of a 2D reconstruction approach\r\nbased on data-dependent triangulation and Lawson‘s optimization procedure.\r\nThe definition of the mathematic optimum of the reconstruction is given. We\r\ndiscuss an original cost function and a generalization of known functions for\r\nthe n-dimensional case.",
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        "abstract": "This paper describes a novel method for creating surface\r\nmodels of multi-material components using dual energy\r\ncomputed tomography (DECT). Application scenario\r\nfor the presented work is metrology and dimensional\r\nmeasurement of multi-material components in industrial\r\nhigh resolution 3D X-Ray computed tomography\r\n(3DCT). The basis of this method is the dual source\r\n/ dual exposure technology using the different X-Ray\r\nimaging modalities of a high precision micro-focus and\r\na high energy macro-focus X-Ray source.\r\nThe presented work aims at combining the advantages\r\nof both X-Ray modalities in order to facilitate dimensional\r\nmeasurement of multi-material components with\r\nhigh density material within low density material. We\r\npropose a pipeline model using image fusion and local\r\nsurface extraction technologies: A prefiltering step reduces\r\ndata inherent noise. For image fusion purposes\r\nthe datasets have to be registered to each other. In the fusion\r\nstep the benefits of each modality are combined. So\r\nthe structure of the specimen is taken from the low precision,\r\nblurry, high energy dataset while the sharp edges\r\nare adopted and fused into the resulting image from the\r\nhigh precision, crisp, low energy dataset. In the final\r\nstep a reliable surface model is calculated of the fused\r\ndataset, which locally adapts the surface model by moving\r\nsurface vertices in the direction of the corresponding\r\npoint normal to a position with maximum gradient magnitude.\r\nThe major contribution of this paper is the development\r\nof a specific workflow for dimensional measurement of multi-material industrial components from high resolution\r\nindustrial CT data. Several algorithms are extended\r\nto take two data sources with complementary strengths\r\nand weaknesses into account. The presented workflow\r\nis crucial for the following visual inspection of deviations.",
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        "abstract": "This paper describes a robust method for creating surface models from volume datasets with distorted density\r\nvalues due to artefacts and noise. Application scenario for the presented work is variance comparison and\r\ndimensional measurement of homogeneous industrial components in industrial high resolution 3D computed\r\ntomography (3D-CT). We propose a pipeline which uses common 3D image processing filters for pre-processing\r\nand segmentation of 3D-CT datasets in order to create the surface model. In particular, a pre-filtering step\r\nreduces noise and artefacts without blurring edges in the dataset. A watershed filter is applied on the gradient\r\ninformation of the smoothed data to create a binary dataset. Finally the surface model is constructed, using\r\nconstrained elastic-surface nets to generate a smooth but feature preserving mesh of a binary volume. The major\r\ncontribution of this paper is the development of the specific processing pipeline for homogeneous industrial\r\ncomponents to handle large resolution data of industrial CT scanners. The pipeline is crucial for the following\r\nvisual inspection of deviations.",
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