Abstract:We present a new method to visualize from an ensemble of flow fields the statistical properties of streamlines passing through a selected location. We use principal component analysis to transform the set of streamlines into a low-dimensional Euclidean space. In this space the streamlines are clustered into major trends, and each cluster is in turn approximated by a multivariate Gaussian distribution. This yields a probabilistic mixture model for the streamline distribution, from which confidence regions can b… Show more
“…Djurcilov et al [DKLP01] directly visualize scalar field uncertainty in direct volume rendering. For vector fields, curve boxplots [MWK14] and streamline variability plots [FBW16] focus on the variation of features extracted from the field, rather than the field itself. Botchen et.…”
A Diffusion Tensor Imaging (DTI) group study consists of a collection of volumetric diffusion tensor datasets (i.e., an ensemble) acquired from a group of subjects. The multivariate nature of the diffusion tensor imposes challenges on the analysis and the visualization. These challenges are commonly tackled by reducing the diffusion tensors to scalar‐valued quantities that can be analyzed with common statistical tools. However, reducing tensors to scalars poses the risk of losing intrinsic information about the tensor. Visualization of tensor ensemble data without loss of information is still a largely unsolved problem. In this work, we propose an overview + detail visualization to facilitate the tensor ensemble exploration. We define an ensemble representative tensor and variations in terms of the three intrinsic tensor properties (i.e., scale, shape, and orientation) separately. The ensemble summary information is visually encoded into the newly designed aggregate tensor glyph which, in a spatial layout, functions as the overview. The aggregate tensor glyph guides the analyst to interesting areas that would need further detailed inspection. The detail views reveal the original information that is lost during aggregation. It helps the analyst to further understand the sources of variation and formulate hypotheses. To illustrate the applicability of our prototype, we compare with most relevant previous work through a user study and we present a case study on the analysis of a brain diffusion tensor dataset ensemble from healthy volunteers.
“…Djurcilov et al [DKLP01] directly visualize scalar field uncertainty in direct volume rendering. For vector fields, curve boxplots [MWK14] and streamline variability plots [FBW16] focus on the variation of features extracted from the field, rather than the field itself. Botchen et.…”
A Diffusion Tensor Imaging (DTI) group study consists of a collection of volumetric diffusion tensor datasets (i.e., an ensemble) acquired from a group of subjects. The multivariate nature of the diffusion tensor imposes challenges on the analysis and the visualization. These challenges are commonly tackled by reducing the diffusion tensors to scalar‐valued quantities that can be analyzed with common statistical tools. However, reducing tensors to scalars poses the risk of losing intrinsic information about the tensor. Visualization of tensor ensemble data without loss of information is still a largely unsolved problem. In this work, we propose an overview + detail visualization to facilitate the tensor ensemble exploration. We define an ensemble representative tensor and variations in terms of the three intrinsic tensor properties (i.e., scale, shape, and orientation) separately. The ensemble summary information is visually encoded into the newly designed aggregate tensor glyph which, in a spatial layout, functions as the overview. The aggregate tensor glyph guides the analyst to interesting areas that would need further detailed inspection. The detail views reveal the original information that is lost during aggregation. It helps the analyst to further understand the sources of variation and formulate hypotheses. To illustrate the applicability of our prototype, we compare with most relevant previous work through a user study and we present a case study on the analysis of a brain diffusion tensor dataset ensemble from healthy volunteers.
“…Examples from the field of weather forecast can be found in Sanyal et al [29] or Wilson et al [30]. Ferstl et al [31] use a clustering of flow lines, which are then visualized using variability plots representing the distribution of each cluster. These variability plots have some similarity with our charge coverage visualization.…”
Abstract:We present a visualization system for analyzing stochastic particle trajectory ensembles, resulting from Kinetic Monte-Carlo simulations on charge transport in organic solar cells. The system supports the analysis of such trajectories in relation to complex material morphologies. It supports the inspection of individual trajectories or the entire ensemble on different levels of abstraction. Characteristic measures quantify the efficiency of the charge transport. Hence, our system led to better understanding of ensemble trajectories by: (i) Capturing individual trajectory behavior and providing an ensemble overview; (ii) Enabling exploration through linked interaction between 3D representations and plots of characteristics measures; (iii) Discovering potential traps in the material morphology; (iv) Studying preferential paths. The visualization system became a central part of the research process. As such, it continuously develops further along with the development of new hypothesis and questions from the application. Findings derived from the first visualizations, e.g., new efficiency measures, became new features of the system. Most of these features arose from discussions combining the data-perspective view from visualization with the physical background knowledge of the underlying processes. While our system has been built for a specific application, the concepts translate to data sets for other stochastic particle simulations.
“…Theoretically, they both leverage the mathematical notion of data depth, which can help reveal how central a line instance is within the distribution of the ensemble members. Based on the contour boxplot and curve boxplot, a novel technique named streamline variability plots [5] has been proposed to show the clustering trends of the ensemble streamlines.…”
Section: Visualizations Of Vector Field Ensemblesmentioning
We propose a longest common subsequence (LCSS)-based approach to compute the distance among vector field ensembles. By measuring how many common blocks the ensemble pathlines pass through, the LCSS distance defines the similarity among vector field ensembles by counting the number of shared domain data blocks. Compared with traditional methods (e.g., pointwise Euclidean distance or dynamic time warping distance), the proposed approach is robust to outliers, missing data, and the sampling rate of the pathline timesteps. Taking advantage of smaller and reusable intermediate output, visualization based on the proposed LCSS approach reveals temporal trends in the data at low storage cost and avoids tracing pathlines repeatedly. We evaluate our method on both synthetic data and simulation data, demonstrating the robustness of the proposed approach.
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