Curve boxplot: Generalization of boxplot for ensembles of curves

pre-printIn simulation science, computational scientists often study the behavior of their simulations by repeated solutions with variations in parameters and/or boundary values or initial conditions. Through such simulation ensembles, one can try to understand or quantify the variability or uncertainty in a solution as a function of the various inputs or model assumptions. In response to a growing interest in simulation ensembles, the visualization community has developed a suite of methods for allowing users to observe and understand the properties of these ensembles in an efficient and effective manner. An important aspect of visualizing simulations is the analysis of derived features, often represented as points, surfaces, or curves. In this paper, we present a novel, nonparametric method for summarizing ensembles of 2D and 3D curves. We propose an extension of a method from descriptive statistics, data depth, to curves. We also demonstrate a set of rendering and visualization strategies for showing rank statistics of an ensemble of curves, which is a generalization of traditional whisker plots or boxplots to multidimensional curves. Results are presented for applications in neuroimaging, hurricane forecasting and fluid dynamics

An Information-Theoretic Framework for Evaluating Edge Bundling Visualization

Edge bundling is a promising graph visualization approach to simplifying the visual result of a graph drawing. Plenty of edge bundling methods have been developed to generate diverse graph layouts. However, it is difficult to defend an edge bundling method with its resulting layout against other edge bundling methods as a clear theoretic evaluation framework is absent in the literature. In this paper, we propose an information-theoretic framework to evaluate the visual results of edge bundling techniques. We first illustrate the advantage of edge bundling visualizations for large graphs, and pinpoint the ambiguity resulting from drawing results. Second, we define and quantify the amount of information delivered by edge bundling visualization from the underlying network using information theory. Third, we propose a new algorithm to evaluate the resulting layouts of edge bundling using the amount of the mutual information between a raw network dataset and its edge bundling visualization. Comparison examples based on the proposed framework between different edge bundling techniques are presented

Magnitude-based streamlines seed point selection for unsteady flow visualization

Flow visualization is a method utilized to obtain information from flow data sets. Proper blood flow visualization can assist surgeons in treating the patients. However, the main problem in visualizing the blood flow inside the aorta is the unsteady blood flow rate. Thus, an unsteady flow visualization method is required to show the blood flow clearly. Unfortunately, streamlines cannot be used by time-dependent flow visualization. This research aims to propose an improvement for the current streamline visualization technique and appearance by implementing an improved streamline generation method based on structured grid vector data to visualize the unsteady flow. The research methodology follows a comparative study method with the Evenly-Spaced Seed Point placement (ESSP) method as the benchmark. Magnitude-Based Seed Point placement (MBSP) and selective streamlines enhancement are introduced to produce longer, uniform, and clutter-free streamlines output. A total of 20 visualization results are produced with different streamlines separation distance. Results are then evaluated by comparing streamlines count and uniformity score. Subsequently, survey and expert reviews are carried out to strengthen the analysis. Survey questions are distributed to respondents that have data visualization knowledge background in order to get feedback related to streamlines uniformity and enhancement. In addition, experts review is conducted to get feedback based on current researches and techniques utilized in the related fields. Results indicate that streamlines count for MBSP are higher, but the differences are neglectable. Uniformity analysis shows good performance; with 80% of the MBSP results have better uniformity. Survey responses show 65% of respondents agreed MBSP results have better uniformity compared to ESSP. Majority of the respondents (92%) agreed that selective streamlines is a better approach. Experts review highlights that MBSP can distribute streamlines better in 3-dimension space compared to ESSP. Two significant findings are identified in this research: magnitude is proven to be an important input to locate seed points; and selective streamlines enhancement is a more effective approach as compared to global streamlines enhancement

ENABLING TECHNIQUES FOR EXPRESSIVE FLOW FIELD VISUALIZATION AND EXPLORATION

Flow visualization plays an important role in many scientific and engineering disciplines such as climate modeling, turbulent combustion, and automobile design. The most common method for flow visualization is to display integral flow lines such as streamlines computed from particle tracing. Effective streamline visualization should capture flow patterns and display them with appropriate density, so that critical flow information can be visually acquired. In this dissertation, we present several approaches that facilitate expressive flow field visualization and exploration. First, we design a unified information-theoretic framework to model streamline selection and viewpoint selection as symmetric problems. Two interrelated information channels are constructed between a pool of candidate streamlines and a set of sample viewpoints. Based on these information channels, we define streamline information and viewpoint information to select best streamlines and viewpoints, respectively. Second, we present a focus+context framework to magnify small features and reduce occlusion around them while compacting the context region in a full view. This framework parititions the volume into blocks and deforms them to guide streamline repositioning. The desired deformation is formulated into energy terms and achieved by minimizing the energy function. Third, measuring the similarity of integral curves is fundamental to many tasks such as feature detection, pattern querying, streamline clustering and hierarchical exploration. We introduce FlowString that extracts shape invariant features from streamlines to form an alphabet of characters, and encodes each streamline into a string. The similarity of two streamline segments then becomes a specially designed edit distance between two strings. Leveraging the suffix tree, FlowString provides a string-based method for exploratory streamline analysis and visualization. A universal alphabet is learned from multiple data sets to capture basic flow patterns that exist in a variety of flow fields. This allows easy comparison and efficient query across data sets. Fourth, for exploration of vascular data sets, which contain a series of vector fields together with multiple scalar fields, we design a web-based approach for users to investigate the relationship among different properties guided by histograms. The vessel structure is mapped from the 3D volume space to a 2D graph, which allow more efficient interaction and effective visualization on websites. A segmentation scheme is proposed to divide the vessel structure based on a user specified property to further explore the distribution of that property over space

EXTRACTING FLOW FEATURES USING BAG-OF-FEATURES AND SUPERVISED LEARNING TECHNIQUES

Measuring the similarity between two streamlines is fundamental to many important flow data analysis and visualization tasks such as feature detection, pattern querying and streamline clustering. This dissertation presents a novel streamline similarity measure inspired by the bag-of-features concept from computer vision. Different from other streamline similarity measures, the proposed one considers both the distribution of and the distances among features along a streamline. The proposed measure is tested in two common tasks in vector field exploration: streamline similarity query and streamline clustering. Compared with a recent streamline similarity measure, the proposed measure allows users to see the interesting features more clearly in a complicated vector field. In addition to focusing on similar streamlines through streamline similarity query or clustering, users sometimes want to group and see similar features from different streamlines. For example, it is useful to find all the spirals contained in different streamlines and present them to users. To this end, this dissertation proposes to segment each streamline into different features. This problem has not been studied extensively in flow visualization. For instance, many flow feature extraction techniques segment streamline based on simple heuristics such as accumulative curvature or arc length, and, as a result, the segments they found usually do not directly correspond to complete flow features. This dissertation proposes a machine learning-based streamline segmentation algorithm to segment each streamline into distinct features. It is shown that the proposed method can locate interesting features (e.g., a spiral in a streamline) more accurately than some other flow feature extraction methods. Since streamlines are space curves, the proposed method also serves as a general curve segmentation method and may be applied in other fields such as computer vision. Besides flow visualization, a pedagogical visualization tool DTEvisual for teaching access control is also discussed in this dissertation. Domain Type Enforcement (DTE) is a powerful abstraction for teaching students about modern models of access control in operating systems. With DTEvisual, students have an environment for visualizing a DTE-based policy using graphs, visually modifying the policy, and animating the common DTE queries in real time. A user study of DTEvisual suggests that the tool is helpful for students to understand DTE

A stable tensor-based deflection model for controlled fluid simulations

The association between fluids and tensors can be observed in some practical situations, such as diffusion tensor imaging and permeable flow. For simulation purposes, tensors may be used to constrain the fluid flow along specific directions. This work seeks to explore this tensor-fluid relationship and to propose a method to control fluid flow with an orientation tensor field. To achieve our purposes, we expand the mathematical formulation governing fluid dynamics to locally change momentum, deflecting the fluid along intended paths. Building upon classical computer graphics approaches for fluid simulation, the numerical method is altered to accomodate the new formulation. Gaining control over fluid diffusion can also aid on visualization of tensor fields, where the detection and highlighting of paths of interest is often desired. Experiments show that the fluid adequately follows meaningful paths induced by the underlying tensor field, resulting in a method that is numerically stable and suitable for visualization and animation purposes.A associação entre fluidos e tensores pode ser observada em algumas situações práticas, como em ressonância magnética por tensores de difusão ou em escoamento permeável. Para fins de simulação, tensores podem ser usados para restringir o escoamento do fluido ao longo de direções específicas. Este trabalho visa explorar esta relação tensor-fluido e propor um método para controlar o escoamento usando um campo de tensores de orientação. Para atingir nossos objetivos, nós expandimos a formulação matemática que governa a dinâmica de fluidos para alterar localmente o momento, defletindo o fluido para trajetórias desejadas. Tomando como base abordagens clássicas para simulação de fluidos em computação gráfica, o método numérico é alterado para acomodar a nova formulação. Controlar o processo de difusão pode também ajudar na visualização de campos tensoriais, onde frequentemente busca-se detectar e realçar caminhos de interesse. Os experimentos realizados mostram que o fluido, induzido pelo campo tensorial subjacente, percorre trajetórias significativas, resultando em um método que é numericamente estável e adequado para fins de visualização e animação

DEPLOYING, IMPROVING AND EVALUATING EDGE BUNDLING METHODS FOR VISUALIZING LARGE GRAPHS

A tremendous increase in the scale of graphs has been witnessed in a wide range of fields, which demands efficient and effective visualization techniques to assist users in better understandings of large graphs. Conventional node-link diagrams are often used to visualize graphs, whereas excessive edge crossings can easily incur severe visual clutter in the node-link diagram of a large graph. Edge bundling can effectively remedy visual clutter and reveal high-level graph structures. Although significant efforts have been devoted to developing edge bundling, three challenging problems remain. First, edge bundling techniques are often computationally expensive and are not easy to deploy for web-based applications. The state-of-the-art edge bundling methods often require special system supports and techniques such as high-end GPU acceleration for large graphs, which makes these methods less portable, especially for ubiquitous mobile devices. Second, the quantitative quality of edge bundling results is barely assessed in the literature. Currently, the comparison of edge bundling mainly focuses on computational performance and perceptual results. Third, although the family of edge bundling techniques has a rich set of bundling layout, there is a lack of a generic method to generate different styles of edge bundling. In this research, I aim to address these problems and have made the following contributions. First, I provide an efficient framework to deploy edge bundling for web-based platforms by exploiting standard graphics hardware functions and libraries. My framework can generate high-quality edge bundling results on web-based platforms, and achieve a speedup of 50X compared to the previous state-of-the-art edge bundling method on a graph with half of a million edges. Second, I propose a new moving least squares based approach to lower the algorithm complexity of edge bundling. In addition, my approach can generate better bundling results compared to other methods based on a quality metric. Third, I provide an information-theoretic metric to evaluate the edge bundling methods. I leverage information theory in this metric. With my information-theoretic metric, domain users can choose appropriate edge bundling methods with proper parameters for their applications. Last but not least, I present a deep learning framework for edge bundling visualizations. Through a training process that learns the results of a specific edge bundling method, my deep learning framework can infer the final layout of the edge bundling method. My deep learning framework is a generic framework that can generate the corresponding results of different edge bundling methods. Adviser: Hongfeng Y