Functional Decomposition for Bundled Simplification of Trail Sets

Integral Curve Clustering and Simplification for Flow Visualization: A Comparative Evaluation

Unsupervised clustering techniques have been widely applied to flow simulation data to alleviate clutter and occlusion in the resulting visualization. However, there is an absence of systematic guidelines for users to evaluate (both quantitatively and visually) the appropriate clustering technique and similarity measures for streamline and pathline curves. In this work, we provide an overview of a number of prevailing curve clustering techniques. We then perform a comprehensive experimental study to qualitatively and quantitatively compare these clustering techniques coupled with popular similarity measures used in the flow visualization literature. Based on our experimental results, we derive empirical guidelines for selecting the appropriate clustering technique and similarity measure given the requirements of the visualization task. We believe our work will inform the task of generating meaningful reduced representations for large-scale flow data and inspire the continuous investigation of a more refined guidance on clustering technique selection.

Interactive Structure-aware Blending of Diverse Edge Bundling Visualizations

Many edge bundling techniques (i.e., data simplification as a support for data visualization and decision making) exist but they are not directly applicable to any kind of dataset and their parameters are often too abstract and difficult to set up. As a result, this hinders the user ability to create efficient aggregated visualizations. To address these issues, we investigated a novel way of handling visual aggregation with a task-driven and user-centered approach. Given a graph, our approach produces a decluttered view as follows: first, the user investigates different edge bundling results and specifies areas, where certain edge bundling techniques would provide user-desired results. Second, our system then computes a smooth and structural preserving transition between these specified areas. Lastly, the user can further fine-tune the global visualization with a direct manipulation technique to remove the local ambiguity and to apply different visual deformations. In this paper, we provide details for our design rationale and implementation. Also, we show how our algorithm gives more suitable results compared to current edge bundling techniques, and in the end, we provide concrete instances of usages, where the algorithm combines various edge bundling results to support diverse data exploration and visualizations.

OD Morphing: Balancing Simplicity with Faithfulness for OD Bundling

OD bundling is a promising method to identify key origin-destination (OD) patterns, but the bundling can mislead the interpretation of actual trajectories traveled. We present OD Morphing, an interactive OD bundling technique that improves geographical faithfulness to actual trajectories while preserving visual simplicity for OD patterns. OD Morphing iteratively identifies critical waypoints from the actual trajectory network with a min-cut algorithm and transitions OD bundles to pass through the identified waypoints with a smooth morphing method. Furthermore, we extend OD Morphing to support bundling at interaction speeds to enable users to interactively transition between degrees of faithfulness to aid sensemaking. We introduce metrics for faithfulness and simplicity to evaluate their trade-off achieved by OD morphed bundling. We demonstrate OD Morphing on real-world city-scale taxi trajectory and USA domestic planned flight datasets.

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.

FiberClay: Sculpting Three Dimensional Trajectories to Reveal Structural Insights

Visualizing 3D trajectories to extract insights about their similarities and spatial configuration is a critical task in several domains. Air traffic controllers for example deal with large quantities of aircrafts routes to optimize safety in airspace and neuroscientists attempt to understand neuronal pathways in the human brain by visualizing bundles of fibers from DTI images. Extracting insights from masses of 3D trajectories is challenging as the multiple three dimensional lines have complex geometries, may overlap, cross or even merge with each other, making it impossible to follow individual ones in dense areas. As trajectories are inherently spatial and three dimensional, we propose FiberClay: a system to display and interact with 3D trajectories in immersive environments. FiberClay renders a large quantity of trajectories in real time using GP-GPU techniques. FiberClay also introduces a new set of interactive techniques for composing complex queries in 3D space leveraging immersive environment controllers and user position. These techniques enable an analyst to select and compare sets of trajectories with specific geometries and data properties. We conclude by discussing insights found using FiberClay with domain experts in air traffic control and neurology.