Crease surfaces: from theory to extraction and application to diffusion tensor MRI

Crease surfaces are two-dimensional manifolds along which a scalar field assumes a local maximum (ridge) or a local minimum (valley) in a constrained space. Unlike isosurfaces, they are able to capture extremal structures in the data. Creases have a long tradition in image processing and computer vision, and have recently become a popular tool for visualization. When extracting crease surfaces, degeneracies of the Hessian (i.e., lines along which two eigenvalues are equal), have so far been ignored. We show that these loci, however, have two important consequences for the topology of crease surfaces: First, creases are bounded not only by a side constraint on eigenvalue sign, but also by Hessian degeneracies. Second, crease surfaces are not in general orientable. We describe an efficient algorithm for the extraction of crease surfaces which takes these insights into account and demonstrate that it produces more accurate results than previous approaches. Finally, we show that DT-MRI streamsurfaces, which were previously used for the analysis of planar regions in diffusion tensor MRI data, are mathematically ill-defined. As an example application of our method, creases in a measure of planarity are presented as a viable substitute

Hybrid Sample-based Surface Rendering

The performance of rasterization-based rendering on current GPUs strongly depends on the abilities to avoid overdraw and to prevent rendering triangles smaller than the pixel size. Otherwise, the rates at which highresolution polygon models can be displayed are affected significantly. Instead of trying to build these abilities into the rasterization-based rendering pipeline, we propose an alternative rendering pipeline implementation that uses rasterization and ray-casting in every frame simultaneously to determine eye-ray intersections. To make ray-casting competitive with rasterization, we introduce a memory-efficient sample-based data structure which gives rise to an efficient ray traversal procedure. In combination with a regular model subdivision, the most optimal rendering technique can be selected at run-time for each part. For very large triangle meshes our method can outperform pure rasterization and requires a considerably smaller memory budget on the GPU. Since the proposed data structure can be constructed from any renderable surface representation, it can also be used to efficiently render isosurfaces in scalar volume fields. The compactness of the data structure allows rendering from GPU memory when alternative techniques already require exhaustive paging

Description of induced nuclear fission with Skyrme energy functionals: static potential energy surfaces and fission fragment properties

Eighty years after its experimental discovery, a description of induced nuclear fission based solely on the interactions between neutrons and protons and quantum many-body methods still poses formidable challenges. The goal of this paper is to contribute to the development of a predictive microscopic framework for the accurate calculation of static properties of fission fragments for hot fission and thermal or slow neutrons. To this end, we focus on the Pu239(n,f) reaction and employ nuclear density functional theory with Skyrme energy densities. Potential energy surfaces are computed at the Hartree-Fock-Bogoliubov approximation with up to five collective variables. We find that the triaxial degree of freedom plays an important role, both near the fission barrier and at scission. The impact of the parametrization of the Skyrme energy density and the role of pairing correlations on deformation properties from the ground state up to scission are also quantified. We introduce a general template for the quantitative description of fission fragment properties. It is based on the careful analysis of scission configurations, using both advanced topological methods and recently proposed quantum many-body techniques. We conclude that an accurate prediction of fission fragment properties at low incident neutron energies, although technologically demanding, should be within the reach of current nuclear density functional theory

Consistent Approximation of Local Flow Behavior for 2D Vector Fields Using Edge Maps

Abstract not provide

Designing 2D Vector Fields of Arbitrary Topology

We introduce a scheme of control polygons to design topological skeletons for vector fields of arbitrary topology. Based on this we construct piecewise linear vector fields of exactly the topology specified by the control polygons. This way a controlled construction of vector fields of any topology is possible. Finally we apply this method for topology-preserving compression of vector fields consisting of a simple topology