We introduce relaxed dot plots as an improvement of nonlinear dot plots for unit visualization. Our plots produce more faithful data representations and reduce moiré effects. Their contour is based on a customized kernel frequency estimation to match the shape of the distribution of underlying data values. Previous nonlinear layouts introduce column-centric nonlinear scaling of dot diameters for visualization of high-dynamic-range data with high peaks. We provide a mathematical approach to convert that column-centric scaling to our smooth envelope shape. This formalism allows us to use linear, root, and logarithmic scaling to find ideal dot sizes. Our method iteratively relaxes the dot layout for more correct and aesthetically pleasing results. To achieve this, we modified Lloyd's algorithm with additional constraints and heuristics. We evaluate the layouts of relaxed dot plots against a previously existing nonlinear variant and show that our algorithm produces less error regarding the underlying data while establishing the blue noise property that works against moiré effects. Further, we analyze the readability of our relaxed plots in three crowd-sourced experiments. The results indicate that our proposed technique surpasses traditional dot plots.

Abstract We present an approach for visual analysis of high‐dimensional measurement data with varying sampling rates as routinely recorded in intensive care units. In intensive care, most assessments not only depend on one single measurement but a plethora of mixed measurements over time. Even for trained experts, efficient and accurate analysis of such multivariate data remains a challenging task. We present a linked‐view post hoc visual analytics application that reduces data complexity by combining projection‐based time curves for overview with small multiples for details on demand. Our approach supports not only the analysis of individual patients but also of ensembles by adapting existing techniques using non‐parametric statistics. We evaluated the effectiveness and acceptance of our approach through expert feedback with domain scientists from the surgical department using real‐world data: a post‐surgery study performed on a porcine surrogate model to identify parameters suitable for diagnosing and prognosticating the volume state, and clinical data from a public database. The results show that our approach allows for detailed analysis of changes in patient state while also summarizing the temporal development of the overall condition.

We introduce inverted stippling , a method to mimic an inversion technique used by artists when performing stippling. To this end, we extend Linde-Buzo-Gray (LBG) stippling to multi-class LBG (MLBG) stippling with multiple layers. MLBG stippling couples the layers stochastically to optimize for per-layer and overall blue-noise properties. We propose a stipple-based filling method to generate solid color backgrounds for inverting areas. Our experiments demonstrate the effectiveness of MLBG in terms of reducing overlapping and intensity accuracy. In addition, we showcase MLBG with color stippling and dynamic multi-class blue-noise sampling, which is possible due to its support for temporal coherence.

Rectangular treemaps visualize hierarchical numerical data by recursively partitioning an input rectangle into smaller rectangles whose areas match the data. Numerical data often has uncertainty associated with it. To visualize uncertainty in a rectangular treemap, we identify two conflicting key requirements: (i) to assess the data value of a node in the hierarchy, the area of its rectangle should directly match its data value, and (ii) to facilitate comparison between data and uncertainty, uncertainty should be encoded using the same visual variable as the data, that is, area. We present Uncertainty Treemaps, which meet both requirements simultaneously by introducing the concept of hierarchical uncertainty masks. First, we define a new cost function that measures the quality of Uncertainty Treemaps. Then, we show how to adapt existing treemapping algorithms to support uncertainty masks. Finally, we demonstrate the usefulness and quality of our technique through an expert review and a computational experiment on real-world datasets.

We present a novel variant of parallel coordinates plots (PCPs) in which we show clusters in 2D subspaces of multivariate data and emphasize flow between them. We achieve this by duplicating and stacking individual axes vertically. On a high level, our clusterflow layout shows how data points move from one cluster to another in different subspaces. We achieve cluster-based bundling and limit plot growth through the reduction of available vertical space for each duplicated axis. Although we introduce space between clusters, we preserve the readability of intra-cluster correlations by starting and ending with the original slopes from regular PCPs and drawing Hermite spline segments in between. Moreover, our rendering technique enables the visualization of small and large data sets alike. Cluster-flow PCPs can even propagate the uncertainty inherent to fuzzy clustering through the layout and rendering stages of our pipeline. Our layout algorithm is based on A*. It achieves an optimal result with regard to a novel set of cost functions that allow us to arrange axes horizontally (dimension ordering) and vertically (cluster ordering).

We present a framework for rapid prototyping of pervasive visual deficiency simulation in the context of graphical interfaces, virtual reality, and augmented reality. Our framework facilitates the emulation of various visual deficiencies for a wide range of applications, which allows users with normal vision to experience combinations of conditions such as myopia, hyperopia, presbyopia, cataract, nyctalopia, protanopia, deuteranopia, tritanopia, and achromatopsia. Our framework provides an infrastructure to encourage researchers to evaluate visualization and other display techniques regarding visual deficiencies, and opens up the field of visual disease simulation to a broader audience. The benefits of our framework are easy integration, configuration, fast prototyping, and portability to new emerging hardware. To demonstrate the applicability of our framework, we showcase a desktop application and an Android application that transform commodity hardware into glasses for visual deficiency simulation. We expect that this work promotes a greater understanding of visual impairments, leads to better product design for the visually impaired, and forms a basis for research to compensate for these impairments as everyday help.

We propose a technique to represent two-dimensional data using stipples. While stippling is often regarded as an illustrative method, we argue that it is worth investigating its suitability for the visualization domain. For this purpose, we generalize the Linde-Buzo-Gray stippling algorithm for information visualization purposes to encode continuous and discrete 2D data. Our proposed modifications provide more control over the resulting distribution of stipples for encoding additional information into the representation, such as contours. We show different approaches to depict contours in stipple drawings based on locally adjusting the stipple distribution. Combining stipple-based gradients and contours allows for simultaneous assessment of the overall structure of the data while preserving important local details. We discuss the applicability of our technique using datasets from different domains and conduct observation-validating studies to assess the perception of stippled representations.

We present a technique that conveys the uncertainty in the secondary structure of proteins-an abstraction model based on atomic coordinates. While protein data inherently contains uncertainty due to the acquisition method or the simulation algorithm, we argue that it is also worth investigating uncertainty induced by analysis algorithms that precede visualization. Our technique helps researchers investigate differences between multiple secondary structure assignment methods. We modify established algorithms for fuzzy classification and introduce a discrepancy-based approach to project an ensemble of sequences to a single importance-weighted sequence. In 2D, we depict the aggregated secondary structure assignments based on the per-residue deviation in a collapsible sequence diagram. In 3D, we extend the ribbon diagram using visual variables such as transparency, wave form, frequency, or amplitude to facilitate qualitative analysis of uncertainty. We evaluated the effectiveness and acceptance of our technique through expert reviews using two example applications: the combined assignment against established algorithms and time-dependent structural changes originating from simulated protein dynamics.

We propose a tree visualization technique for comparison of structures and attributes across multiple hierarchies. Many software systems are structured hierarchically by design. For example, developers subdivide source code into libraries, modules, and functions. This design propagates to software configuration and business processes, rendering software hierarchies even more important. Often these structural elements are attributed with reference counts, code quality metrics, and the like. Throughout the entire software life cycle, these hierarchies are reviewed, integrated, debugged, and changed many times by different people so that the identity of a structural element and its attributes is not clearly traceable. We argue that pairwise comparison of similar trees is a tedious task due to the lack of overview, especially when applied to a large number of hierarchies. Therefore, we strive to visualize multiple similar trees as a whole by merging them into one supertree. To merge structures and combine attributes from different trees, we leverage the Jaccard similarity and solve a matching problem while keeping track of the origin of a structure element and its attributes. Our visualization approach allows users to inspect these supertrees using node-link diagrams and indented tree plots. The nodes in these plots depict aggregated attributes and, using word-sized line plots, detailed data. We demonstrate the usefulness of our method by exploring the evolution of software repositories and debugging data processing pipelines using provenance data.

We present a novel type of circular treemap, where we intentionally allocate extra space for additional visual variables. With this extended visual design space, we encode hierarchically structured data along with their uncertainties in a combined diagram. We introduce a hierarchical and force-based circle-packing algorithm to compute Bubble Treemaps, where each node is visualized using nested contour arcs. Bubble Treemaps do not require any color or shading, which offers additional design choices. We explore uncertainty visualization as an application of our treemaps using standard error and Monte Carlo-based statistical models. To this end, we discuss how uncertainty propagates within hierarchies. Furthermore, we show the effectiveness of our visualization using three different examples: the package structure of Flare, the S&P 500 index, and the US consumer expenditure survey.

Analysis of software performance typically takes into account clock cycles and memory consumption at each sampling point in time. Although this is a valid strategy, we argue that it is also worth investigating data and control flow structures, as observed using memory traces and call stacks, because of their importance for performance engineering. In this work, we present a visual approach to memory profiling that supports analysis of memory layout, access patterns, and aliasing in correlation to program execution. Our method leverages language-agnostic dynamic code instrumentation to minimize the impact of tracing on performance, i.e., the application remains usable on commodity hardware. The profiled data is then clustered and visualized using a density-based scatter plot. If debug symbols are available, the scatter plot is augmented by a flame graph to ease linking to the high-level source code. Our visualization helps software engineers to identify runtime behavior by relating memory addresses to instruction execution. We demonstrate our approach using a set of examples revealing different memory access patterns and discuss their influence on software performance.

We present a novel uncertain network visualization technique based on node-link diagrams. Nodes expand spatially in our probabilistic graph layout, depending on the underlying probability distributions of edges. The visualization is created by computing a two-dimensional graph embedding that combines samples from the probabilistic graph. A Monte Carlo process is used to decompose a probabilistic graph into its possible instances and to continue with our graph layout technique. Splatting and edge bundling are used to visualize point clouds and network topology. The results provide insights into probability distributions for the entire network-not only for individual nodes and edges. We validate our approach using three data sets that represent a wide range of network types: synthetic data, protein-protein interactions from the STRING database, and travel times extracted from Google Maps. Our approach reveals general limitations of the force-directed layout and allows the user to recognize that some nodes of the graph are at a specific position just by chance.

Abstract We present a coordinated‐view application for the analysis of molecular surface features like cavities, channels and pockets. Our tool employs object‐space ambient occlusion for the detection of such features and tracks them over time. It offers time‐dependent graphs of metrics concerning those features and allows analyzing the temporal relationship of the features, i.e. when they (dis)appear, split or merge and which features participate in each of these events. The automated analysis process is performed in real time while the user interactively explores a dynamic data set. The system supports linking and brushing to allow for a user‐guided visual analysis based on different aspects of the data. We demonstrate the effectiveness of our approach by applying it to data sets from biochemistry and report the insights that can be gained. We also evaluate the benefits of our method with respect to recent advancements in the field. The algorithmic pipeline leverages the computing power of modern GPUs, thus achieving interactive frame rates without any precomputation for fully dynamic data sets.