Point cloud representation

Reconstructing a surface out of a three-dimensional set of points, which is obtained by sampling an object\u27s boundary, is done by generating an arbitrary triangular mesh. Our approach is to obviate the computation of such a mesh connectivity and to represent the object\u27s surface only by the point cloud. We discuss how such a point cloud representation can be visualized and present processing steps like coarsifying and smoothing, which are important for dealing with the objects. Further we apply a multiresolution method to point cloud representations and use this technique as well as others for modelling purposes

Fan Clouds - An Alternative To Meshes

A fan cloud is a set of triangles that can be used to visualize and work with point clouds. It is fast to compute and can replace a triangular mesh representation: We discuss visualization,multiresolution reduction, refinement, and selective refinement. Algorithms for triangular meshes can also be applied to fan clouds. They become even simpler, because fans are not interrelated. This localness of fan clouds is one of their main advantages. No remeshing is necessary for local or adaptive refinement and reduction

Variational Level-Set Detection of Local Isosurfaces from Unstructured Point-based Volume Data

A standard approach for visualizing scalar volume data is the extraction of isosurfaces. The most efficient methods for surface extraction operate on regular grids. When data is given on unstructured point-based samples, regularization can be applied but may introduce interpolation errors. We propose a method for smooth isosurface visualization that operates directly on unstructured point-based volume data avoiding any resampling. We derive a variational formulation for smooth local isosurface extraction using an implicit surface representation in form of a level-set approach, deploying Moving Least Squares (MLS) approximation, and operating on a kd-tree. The locality of our approach has two aspects: first, our algorithm extracts only those components of the isosurface, which intersect a subdomain of interest; second, the action of the main term in the governing equation is concentrated near the current isosurface position. Both aspects reduce the computation times per level-set iteration. As for most level-set methods a reinitialization procedure is needed, but we also consider a modified algorithm where this step is eliminated. The final isosurface is extracted in form of a point cloud representation. We present a novel point completion scheme that allows us to handle highly adaptive point sample distributions. Subsequently, splat-based or mere (shaded) point rendering is applied. We apply our method to several synthetic and real-world data sets to demonstrate its validity and efficiency

Hierarchical Large-scale Volume Representation with 3rd-root-of-2 Subdivision and Trivariate B-spline Wavelets

Multiresolution methods provide a means for representing data at multiple levels of detail. They are typically based on a hierarchical data organization scheme and update rules needed for data value computation. We use a data organization that is based on what we call $\sqrt[n]{2}$ subdivision. The main advantage of $\sqrt[n]{2}$ subdivision, compared to quadtree (n=2) or octree (n=3) organizations, is that the number of vertices is only doubled in each subdivision step instead of multiplied by a factor of four or eight, respectively. To update data values we use n-variate B-spline wavelets, which yield better approximations for each level of detail. We develop a lifting scheme for n=2 and n=3 based on the $\sqrt[n]{2}$-subdivision scheme. We obtain narrow masks that provide a basis for out-of-core techniques as well as view-dependent visualization and adaptive, localized refinement

An interactive visual analysis tool for investigating teleconnections in climate simulations

Teleconnections refer to links between regions that are distant to each other, but nevertheless exhibit some relation. The study of such teleconnections is a well-known task in climate research. Climate simulation shall model known teleconnections. Detecting teleconnections in climate simulations is a crucial aspect in judging the quality of the simulation output. It is common practice to run scripts to execute a sequence of analysis steps on the climate simulations to search for teleconnections. Such a scripting approach is not flexible and targeted towards one specific goal. It is desirable to have one tool that allows for a flexible analysis of all teleconnection patterns with a dataset. We present such a tool, where the extracted information is provided in an intuitive visual form to users, who then can interactively explore the data. We developed an analysis workflow that is modeled around four views showing different facets of the data with coordinated interaction. We present a teleconnection study with simulation ensembles and reanalysis data obtained by data assimilation to observe how well the teleconnectivity patterns match and to demonstrate the effectiveness of our tool

Time-resolved velocity mapping at high magnetic fields: A preclinical comparison between stack‐of‐stars and cartesian 4D-Flow

Purpose: Prospectively-gated Cartesian 4D-flow (referred to as Cartesian-4D-flow) imaging suffers from long TE and intensified flow-related intravoxel-dephasing especially in preclinical ultra-high field MRI. The ultra-short-echo (UTE) 4D-flow technique can resolve the signal loss in higher-order blood flows; however, the long scan time of the high resolution UTE-4D-flow is considered as a disadvantage for preclinical imaging. To compensate for prolonged acquisitions, an accelerated k0-navigated golden-angle center-out stack-of-stars 4D-flow sequence (referred to as SoS-4D-flow) was implemented at 9.4T and the results were compared to conventional Cartesian-4D-flow mapping in-vitro and in-vivo. Methods: The study was conducted in three steps (A) In-vitro evaluation in a static phantom: to quantify the background velocity bias. (B) In-vitro evaluation in a flowing water phantom: to investigate the effects of polar undersampling (US) on the measured velocities and to compare the spatial velocity profiles between both sequences. (C) In-vivo evaluations: 24 C57BL/6 mice were measured by SoS-4D-flow (n = 14) and Cartesian-4D-flow (n = 10). The peak systolic velocity in the ascending aorta and the background velocity in the anterior chest wall were analyzed for both techniques and were compared to each other. Results: According to the in-vitro analysis, the background velocity bias was significantly lower in SoS-4D-flow than in Cartesian-4D-flow (p < 0.05). Polar US in SoS-4D-flow influenced neither the measured velocity values nor the spatial velocity profiles in comparison to Cartesian-4D-flow. The in-vivo analysis showed significantly higher diastolic velocities in Cartesian-4D-flow than in SoS-4D-flow (p < 0.05). A systemic background bias was observed in the Cartesian velocity maps which influenced their streamline directions and magnitudes. Conclusion: The results of our study showed that at 9.4T SoS-4D-flow provided higher accuracy in slow flow imaging than Cartesian-4D-flow, while the same measurement time could be achieved