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Saddle Connectors - An Approach to Visualizing the Topological Skeleton of Complex 3D Vector Fields
(2003)
Ancient Egyptian papyri are often folded, rolled up or kept as small packages, sometimes even sealed. Physically unrolling or unfolding these packages might severely damage them. We demonstrate a way to get access to the hidden script without physical unfolding by employing computed tomography and mathematical algorithms for virtual unrolling and unfolding. Our algorithmic approaches are combined with manual interaction. This provides the necessary flexibility to enable the unfolding of even complicated and partly damaged papyrus packages. In addition, it allows us to cope with challenges posed by the structure of ancient papyrus, which is rather irregular, compared to other writing substrates like metallic foils or parchment. Unfolding of packages is done in two stages. In the first stage, we virtually invert the physical folding process step by step until the partially unfolded package is topologically equivalent to a scroll or a papyrus sheet folded only along one fold line. To minimize distortions at this stage, we apply the method of moving least squares. In the second stage, the papyrus is simply flattened, which requires the definition of a medial surface. We have applied our software framework to several papyri. In this work, we present the results of applying our approaches to mockup papyri that were either rolled or folded along perpendicular fold lines. In the case of the folded papyrus, our approach represents the first attempt to address the unfolding of such complicated folds.
Ancient Egyptian papyri are often folded, rolled up or kept as small packages, sometimes even sealed. Physically unrolling or unfolding these packages might severely damage them. We demonstrate a way to get access to the hidden script without physical unfolding by employing computed tomography and mathematical algorithms for virtual unrolling and unfolding. Our algorithmic approaches are combined with manual interaction. This provides the necessary flexibility to enable the unfolding of even complicated and partly damaged papyrus packages. In addition, it allows us to cope with challenges posed by the structure of ancient papyrus, which is rather irregular, compared to other writing substrates like metallic foils or parchment. Unfolding of packages is done in two stages. In the first stage, we virtually invert the physical folding process step by step until the partially unfolded package is topologically equivalent to a scroll or a papyrus sheet folded only along one fold line. To minimize distortions at this stage, we apply the method of moving least squares. In the second stage, the papyrus is simply flattened, which requires the definition of a medial surface. We have applied our software framework to several papyri. In this work, we present the results of applying our approaches to mockup papyri that were either rolled or folded along perpendicular fold lines. In the case of the folded papyrus, our approach represents the first attempt to address the unfolding of such complicated folds.
Purpose/Aims of the Study: Bone’s hierarchical structure can be visualized using a variety of methods. Many techniques, such as light and electron microscopy generate two-dimensional (2D) images, while micro computed tomography (μCT) allows a direct representation of the three-dimensional (3D) structure. In addition, different methods provide complementary structural information, such as the arrangement of organic or inorganic compounds. The overall aim of the present study is to answer bone research questions by linking information of different 2D and 3D imaging techniques. A great challenge in combining different methods arises from the fact that they usually reflect different characteristics of the real structure.
Materials and Methods: We investigated bone during healing by means of μCT and a couple of 2D methods. Backscattered electron images were used to qualitatively evaluate the tissue’s calcium content and served as a position map for other experimental data. Nanoindentation and X-ray scattering experiments were performed to visualize mechanical and structural properties. Results: We present an approach for the registration of 2D data in a 3D μCT reference frame, where scanning electron microscopies serve as a methodic link. Backscattered electron images are perfectly suited for registration into μCT reference frames, since both show structures based on the same physical principles. We introduce specific registration tools that have been developed to perform the registration process in a semi-automatic way.
Conclusions: By applying this routine, we were able to exactly locate structural information (e.g. mineral particle properties) in the 3D bone volume. In bone healing studies this will help to better understand basic formation, remodeling and mineralization processes.
Realistic prediction of individual facial emotion expressions for craniofacial surgery simulations
(2003)
Real-time rendering of complex photorealistic landscapes using hybrid level-of-detail approaches
(2005)
Einführung: Die Tiefenwirkung dreidimensionaler Räume in einem zweidimensionalen Bild einzufangen, ist ein Faszinosum nahezu aller Kulturen der Menschheitsgeschichte. Der vorliegende Aufsatz folgt den Spuren dieses Faszinosums, vergleichend in der Malerei und der mathematisierten Computergrafik. Die Entdeckung der Zentralperspektive in der italienischen Renaissance zeigt bereits den engen Zusammenhang von Malerei und Mathematik. Auf der Suche nach Maltechniken, mit denen Raumtiefe bildnerisch dargestellt werden kann, beginnen wir in Kap. 2 mit einem chronologischen Gang durch verschiedene Epochen der europäischen Malerei. Hieraus abgeleitete Prinzipien, soweit sie im Rechner realisierbar scheinen, stellen wir in Kap. 3 am Beispiel moderner Methoden der mathematischen Visualisierung vor.
Visualization grammars are gaining popularity as they allow visualization specialists and experienced users to quickly create static and interactive views. Existing grammars, however, mostly focus on abstract views, ignoring three-dimensional (3D) views, which are very important in fields such as natural sciences. We propose a generalized interaction grammar for the problem of coordinating heterogeneous view types, such as standard charts (e.g., based on Vega-Lite) and 3D anatomical views. An important aspect of our web-based framework is that user interactions with data items at various levels of detail can be systematically integrated and used to control the overall layout of the application workspace. With the help of a concise JSON-based specification of the intended workflow, we can handle complex interactive visual analysis scenarios. This enables rapid prototyping and iterative refinement of the visual analysis tool in collaboration with domain experts. We illustrate the usefulness of our framework in two real-world case studies from the field of neuroscience. Since the logic of the presented grammar-based approach for handling interactions between heterogeneous web-based views is free of any application specifics, it can also serve as a template for applications beyond biological research.