Visual Analysis of Trajectories in Multi‐Dimensional State Spaces

Multi‐dimensional data originate from many different sources and are relevant for many applications. One specific sub‐type of such data is continuous trajectory data in multi‐dimensional state spaces of complex systems. We adapt the concept of spatially continuous scatterplots and spatially continuous parallel coordinate plots to such trajectory data, leading to continuous‐time scatterplots and continuous‐time parallel coordinates. Together with a temporal heat map representation, we design coordinated views for visual analysis and interactive exploration. We demonstrate the usefulness of our visualization approach for three case studies that cover examples of complex dynamic systems: cyber‐physical systems consisting of heterogeneous sensors and actuators networks (the collection of time‐dependent sensor network data of an exemplary smart home environment), the dynamics of robot arm movement and motion characteristics of humanoids.     

Pathline glyphs

Visualization of pathlines is common and highly relevant for the analysis of unsteady flow. However, pathlines can intersect, leading to visual clutter and perceptual issues. This makes it intrinsically difficult to provide expressive visualizations of the entire domain by an arrangement of multiple pathlines, in contrast to well‐established streamline placement techniques. We present an approach to reduce these problems. It is inspired by glyph‐based visualization and small multiples: we partition the domain into cells, each corresponding to a downscaled version of the entire domain. Inside these cells, a single downscaled pathline is drawn. On the overview scale, our pathline glyphs lead to emergent visual patterns that provide insight into time‐dependent flow behavior. Zooming‐in allows us to analyze individual pathlines in detail and compare neighboring lines. The overall approach is complemented with a context‐preserving zoom lens and interactive pathline‐based exploration. While we primarily target the visualization of 2D flow, we also address the extension to 3D. Our evaluation includes several examples, comparison to other flow visualization techniques, and a user study with domain experts.     

Particle Level Set Advection for the Interactive Visualization of Unsteady 3D Flow

Typically, flow volumes are visualized by defining their boundary as iso‐surface of a level set function. Grid‐based level sets offer a good global representation but suffer from numerical diffusion of surface detail, whereas particle‐based methods preserve details more accurately but introduce the problem of unequal global representation. The particle level set (PLS) method combines the advantages of both approaches by interchanging the information between the grid and the particles. Our work demonstrates that the PLS technique can be adapted to volumetric dye advection via streak volumes, and to the visualization by time surfaces and path volumes. We achieve this with a modified and extended PLS, including a model for dye injection. A new algorithmic interpretation of PLS is introduced to exploit the efficiency of the GPU, leading to interactive visualization. Finally, we demonstrate the high quality and usefulness of PLS flow visualization by providing quantitative results on volume preservation and by discussing typical applications of 3D flow visualization.     

Visual comparability of 3D regular sampling and reconstruction

The Body-Centered Cubic (BCC) and Face-Centered Cubic (FCC) lattices have been analytically shown to be more efficient sampling lattices than the traditional Cartesian Cubic (CC) lattice, but there has been no estimate of their visual comparability. Two perceptual studies (each with N = 12 participants) compared the visual quality of images rendered from BCC and FCC lattices to images rendered from the CC lattice. Images were generated from two signals: the commonly used Marschner-Lobb synthetic function and a computed tomography scan of a fish tail. Observers found that BCC and FCC could produce images of comparable visual quality to CC, using 30-35 percent fewer samples. For the images used in our studies, the L(2) error metric shows high correlation with the judgement of human observers. Using the L(2) metric as a proxy, the results of the experiments appear to extend across a wide range of images and parameter choices.     

Information-based adaptive fast-forward for visual surveillance

Automated video analysis lacks reliability when searching for unknown events in video data. The practical approach is to watch all the recorded video data, if applicable in fast-forward mode. In this paper we present a method to adapt the playback velocity of the video to the temporal information density, so that the users can explore the video under controlled cognitive load. The proposed approach can cope with static changes and is robust to video noise. First, we formulate temporal information as symmetrized Rényi divergence, deriving this measure from signal coding theory. Further, we discuss the animated visualization of accelerated video sequences and propose a physiologically motivated blending approach to cope with arbitrary playback velocities. Finally, we compare the proposed method with the current approaches in this field by experiments and a qualitative user study, and show its advantages over motion-based measures.     

Visual signatures in video visualization

Video visualization is a computation process that extracts meaningful information from original video data sets and conveys the extracted information to users in appropriate visual representations. This paper presents a broad treatment of the subject, following a typical research pipeline involving concept formulation, system development, a path-finding user study, and a field trial with real application data. In particular, we have conducted a fundamental study on the visualization of motion events in videos. We have, for the first time, deployed flow visualization techniques in video visualization. We have compared the effectiveness of different abstract visual representations of videos. We have conducted a user study to examine whether users are able to learn to recognize visual signatures of motions, and to assist in the evaluation of different visualization techniques. We have applied our understanding and the developed techniques to a set of application video clips. Our study has demonstrated that video visualization is both technically feasible and cost-effective. It has provided the first set of evidence confirming that ordinary users can be accustomed to the visual features depicted in video visualizations, and can learn to recognize visual signatures of a variety of motion events.     

Volume-based large dynamic graph analysis supported by evolution provenance

We present an approach for the visualization and interactive analysis of dynamic graphs that contain a large number of time steps. A specific focus is put on the support of analyzing temporal aspects in the data. Central to our approach is a static, volumetric representation of the dynamic graph based on the concept of space-time cubes that we create by stacking the adjacency matrices of all time steps. The use of GPU-accelerated volume rendering techniques allows us to render this representation interactively. We identified four classes of analytics methods as being important for the analysis of large and complex graph data, which we discuss in detail: data views, aggregation and filtering, comparison, and evolution provenance. Implementations of the respective methods are presented in an integrated application, enabling interactive exploration and analysis of large graphs. We demonstrate the applicability, usefulness, and scalability of our approach by presenting two examples for analyzing dynamic graphs. Furthermore, we let visualization experts evaluate our analytics approach.