@phdthesis{Prohaska2007, author = {Prohaska, Steffen}, title = {Skeleton-based visualization of massive voxel objects with network-like architecture}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14888}, year = {2007}, abstract = {This work introduces novel internal and external memory algorithms for computing voxel skeletons of massive voxel objects with complex network-like architecture and for converting these voxel skeletons to piecewise linear geometry, that is triangle meshes and piecewise straight lines. The presented techniques help to tackle the challenge of visualizing and analyzing 3d images of increasing size and complexity, which are becoming more and more important in, for example, biological and medical research. Section 2.3.1 contributes to the theoretical foundations of thinning algorithms with a discussion of homotopic thinning in the grid cell model. The grid cell model explicitly represents a cell complex built of faces, edges, and vertices shared between voxels. A characterization of pairs of cells to be deleted is much simpler than characterizations of simple voxels were before. The grid cell model resolves topologically unclear voxel configurations at junctions and locked voxel configurations causing, for example, interior voxels in sets of non-simple voxels. A general conclusion is that the grid cell model is superior to indecomposable voxels for algorithms that need detailed control of topology. Section 2.3.2 introduces a noise-insensitive measure based on the geodesic distance along the boundary to compute two-dimensional skeletons. The measure is able to retain thin object structures if they are geometrically important while ignoring noise on the object's boundary. This combination of properties is not known of other measures. The measure is also used to guide erosion in a thinning process from the boundary towards lines centered within plate-like structures. Geodesic distance based quantities seem to be well suited to robustly identify one- and two-dimensional skeletons. Chapter 6 applies the method to visualization of bone micro-architecture. Chapter 3 describes a novel geometry generation scheme for representing voxel skeletons, which retracts voxel skeletons to piecewise linear geometry per dual cube. The generated triangle meshes and graphs provide a link to geometry processing and efficient rendering of voxel skeletons. The scheme creates non-closed surfaces with boundaries, which contain fewer triangles than a representation of voxel skeletons using closed surfaces like small cubes or iso-surfaces. A conclusion is that thinking specifically about voxel skeleton configurations instead of generic voxel configurations helps to deal with the topological implications. The geometry generation is one foundation of the applications presented in Chapter 6. Chapter 5 presents a novel external memory algorithm for distance ordered homotopic thinning. The presented method extends known algorithms for computing chamfer distance transformations and thinning to execute I/O-efficiently when input is larger than the available main memory. The applied block-wise decomposition schemes are quite simple. Yet it was necessary to carefully analyze effects of block boundaries to devise globally correct external memory variants of known algorithms. In general, doing so is superior to naive block-wise processing ignoring boundary effects. Chapter 6 applies the algorithms in a novel method based on confocal microscopy for quantitative study of micro-vascular networks in the field of microcirculation.}, language = {en} } @phdthesis{Lamecker2008, author = {Lamecker, Hans}, title = {Variational and statistical shape modeling for 3D geometry reconstruction}, year = {2008}, abstract = {The reconstruction of geometric shapes plays an important role in many biomedical applications. One example is the patient-specific, computer-aided planning of complex interventions, which requires the generation of explicitly represented geometric models of anatomical structures from medical image data. Only solutions that require minimal interaction by medical personnel are likely to enter clinical routine. Another example is the planning of surgical corrections of deformities where the target shape is unknown. Surgeons are often forced to resort to subjective criteria. These applications still pose highly challenging reconstruction problems, which are addressed in this thesis. The fundamental hypothesis, pursued in this thesis, is that the problems can be solved by incorporating a-priori knowledge about shape and other application-specific characteristics. Here, we focus mainly on the aspect of geometric shape analysis. The basic idea is to capture the most essential variations of a certain class of geometric objects via statistical shape models, which model typical features contained in a given population, and restrict the outcome of a reconstruction algorithm (more or less) to the space spanned by such models. A fundamental prerequisite for performing statistical shape analysis on a set of different objects is the identification of corresponding points on their associated surfaces. This problem is particularly difficult to solve if the shapes stem from different individuals. The reason lies in the basic difficulty of defining suitable measures of similarity. In this thesis, we divide the correspondence problem into feature and non-feature matching. The feature part depends on the application, while the non-feature part can be characterized by a purely geometric description. We propose two different approaches. The first approach has proved useful in many applications. Yet, it suffers from some practical limitations and does not yield a measure of similarity. Our second, variational, approach is designed to overcome these limitations. In it, we propose to minimize an invariant stretching measure, constrained by previously computed features. An important property, which sets our method apart from previous work, is that it does not require the computation of a global surface parameterization.}, language = {en} } @phdthesis{Zachow2005, author = {Zachow, Stefan}, title = {Computer assisted osteotomy planning in cranio-maxillofacial surgery under consideration of facial soft tissue changes}, year = {2005}, language = {en} } @phdthesis{Benger2004, author = {Benger, Werner}, title = {Visualization of General Relativistic Tensor Fields via a Fiber Bundle Data Model}, year = {2004}, language = {en} } @phdthesis{neeZoeckler2003, author = {(n{\´e}e Z{\"o}ckler), Malte}, title = {Efficient Visualization and Reconstruction of 3D Geometric from Neuro-Biological Confocal Microscope Scans}, year = {2003}, language = {en} } @phdthesis{Kasten2012, author = {Kasten, Jens}, title = {Lagrangian feature extraction in two-dimensional unsteady flows}, year = {2012}, language = {en} } @phdthesis{Reininghaus2012, author = {Reininghaus, Jan}, title = {Computational discrete Morse theory}, year = {2012}, language = {en} } @phdthesis{Sahner2009, author = {Sahner, Jan}, title = {Extraction of Vortex Structures in 3D Flow Fields}, year = {2009}, language = {en} } @phdthesis{Weinkauf2008, author = {Weinkauf, Tino}, title = {Extraction of Topological Structures in 2D and 3D Vector Fields}, year = {2008}, language = {en} } @phdthesis{SchmidtEhrenberg2008, author = {Schmidt-Ehrenberg, Johannes}, title = {Analysis and Visualization of Molecular Conformations}, year = {2008}, language = {en} } @phdthesis{Kratz2013, author = {Kratz, Andrea}, title = {Three-Dimensional Second-Order Tensor Fields: Exploratory Visualization and Anisotropic Sampling}, school = {Freie Universit{\"a}t Berlin}, pages = {XIV, 157 S.}, year = {2013}, abstract = {Tensors provide a powerful mathematical language to describe physical phenomena. Consequently, they have a long tradition in physics and appear in various application areas, either as intermediate product or as output of simulations or measurements. The potential of tensors to describe complex anisotropic behavior, however, concurrently complicates their interpretation. The central research question of this thesis is how three-dimensional tensor fields of second order are visualized effectively so that, as a long term goal, their interpretation becomes easier. The focus of this thesis lies on the class of indefinite tensors. The methods that are proposed in this thesis fall into two main categories: (1.) the interactive exploration of the three-dimensional tensor data, and (2.) the geometric reduction of the data to two-dimensional planes or triangulated surfaces. In both cases, possible visualization approaches are presented. For interactive exploration of the data, we propose to combine diagram views with three-dimensional hybrid visualizations. We show that this facilitates familiarizing with the data and leads to exciting analytic queries. If a geometric data reduction is possible, we focus on glyph- and texture-based methods. In this context, the thesis is concerned with methods to improve their quality. Therefore, we propose two algorithms for the efficient creation of anisotropic sample distributions. Moreover, we present a novel visualization method that works on planar slices as well as on triangulated surfaces. The basic idea of this method is to use anisotropic sample distributions for the efficient computation of anisotropic Voronoi cells, which then are used as base elements for texture mapping. Hence, the usage of textures to encode the tensor's various degrees of freedom becomes possible. We evaluate our methods for the interactive exploration on stress tensor fields from structure simulations. To show the ffectiveness of novel visualization methods, various datasets are presented.}, language = {en} }