Selecting a good aspect ratio is crucial for effective 2D diagrams. There are several aspect ratio selection methods for function plots and line charts, but only few can handle general, discrete diagrams such as 2D scatter plots. However, these methods either lack a perceptual foundation or heavily rely on intermediate isoline representations, which depend on choosing the right isovalues and are time-consuming to compute. This paper introduces a general image-based approach for selecting aspect ratios for a wide variety of 2D diagrams, ranging from scatter plots and density function plots to line charts. Our approach is derived from Federer's co-area formula and a line integral representation that enable us to directly construct image-based versions of existing selection methods using density fields. In contrast to previous methods, our approach bypasses isoline computation, so it is faster to compute, while following the perceptual foundation to select aspect ratios. Furthermore, this approach is complemented by an anisotropic kernel density estimation to construct density fields, allowing us to more faithfully characterize data patterns, such as the subgroups in scatterplots or dense regions in time series. We demonstrate the effectiveness of our approach by quantitatively comparing to previous methods and revisiting a prior user study. Finally, we present extensions for ROI banking, multi-scale banking, and the application to image data.

In this paper we take a look into typical interaction scenarios when it comes to visualizing hierarchical data while we particularly focus on one specific candidate that is the visual depiction by generalized Pythagoras trees. Those are visualizations that benefit from their aesthetically appealing appearance since they come close to a visual model of trees growing in nature. Traditionally, those generalized Pythagoras trees are visualized on typical computer screens, clearly indicating the hierarchy, but negatively, the finer substructures are oftentimes not visible anymore due to the display space restriction and the low resolution. Hence, in this paper we describe the generalized Pythagoras trees displayed on largescale high-resolution displays and illustrate the challenges and perspectives when we have to interact with the visual representation by using the technique individually, but also in collaboration. To explore possible interactions we experimented with tablet computers combined with an optical tracking system. We evaluate the effectiveness and aesthetics by means of several modifiable visual parameters and by interacting with the visualization.

Visual search can be time-consuming, especially if the scene contains a large number of possibly relevant objects. An instance of this problem is present when using geographic or schematic maps with many different elements representing cities, streets, sights, and the like. Unless the map is well-known to the reader, the full map or at least large parts of it must be scanned to find the elements of interest. In this paper, we present a controlled eye-tracking study (30 participants) to compare four variants of map annotation with labels: within-image annotations, grid reference annotation, directional annotation, and miniature annotation. Within-image annotation places labels directly within the map without any further search support. Grid reference annotation corresponds to the traditional approach known from atlases. Directional annotation utilizes a label in combination with an arrow pointing in the direction of the label within the map. Miniature annotation shows a miniature grid to guide the reader to the area of the map in which the label is located. The study results show that within-image annotation is outperformed by all other annotation approaches. Best task completion times are achieved with miniature annotation. The analysis of eye-movement data reveals that participants applied significantly different visual task solution strategies for the different visual annotations.

Visualization by heat maps is a powerful technique for showing frequently visited areas in displayed stimuli. However, by aggregating the spatio-temporal data, heat maps lose the information about the transitions between fixations, i.e., the saccades. In gaze plots, instead, trajectories are shown as overplotted polylines, leading to much visual clutter, which makes those diagrams difficult to read. In this paper, we introduce Saccade Plots as a novel technique that combines the benefits of both approaches: it shows the gaze frequencies as a heat map and the saccades in the form of color-coded triangular matrices that surround the heat map. We illustrate the usefulness of our technique by applying it to a representative example from a previously conducted eye tracking study.

Partially drawn links in graph visualizations have been introduced as a concept for further reducing visual clutter caused by many link crossings in combination to a formerly applied layout algorithm focusing on aesthetic graph drawing criteria. Although this visualization strategy has been shown to be useful for a faster and more accurate visual exploration of node-link diagrams in some scenarios, it has not been integrated into a graph visualization tool as an interaction feature to this end. Apart from representing the entire displayed graph in the partially drawn link style we allow the viewer to apply this feature to several nodes, links, or regions of interest. To avoid possible ambiguities introduced by the disconnectedness of start and target nodes further interaction techniques can be applied to mitigate this situation by showing the complete link information for single selected vertices or edges again.

We introduce a technique for bundling edges in graphs where a hierarchical organization of the vertices is not available. Instead of applying time-complex force-directed edge bundling, we adopt the concept of Rapidly-Exploring Random Trees (RRTs). We use RRTs for fast computation of a hierarchical space organization that is independent of the spatial structure of the graph layout. Due to this independency, edge bundling can be applied to any graph layout and even allows us to define spatial obstacles through which no bundles may lead. Furthermore, when adding or removing graph nodes and edges on-the-fly, the bundling structure remains stable, which cannot be guaranteed for force-directed bundling. The main benefit of RRT bundling is its high efficiency, supporting interactive exploration. We rely on the low runtime complexity for a new interaction technique for visual clutter reduction in node-link diagrams that we refer to as the RRT edge bundling lens.

We propose a novel radial layered matrix visualization for dynamic directed weighted graphs in which the vertices can also be hierarchically organized. Edges are represented as color-coded arcs within the radial diagram. Their positions are defined by polar coordinates instead of Cartesian coordinates as in traditional adjacency matrix representations: the angular position of an edge within an annulus is given by the angle bisector of the two related vertices, the radial position depends linearly on the angular distance between these vertices. The exploration of time-varying relational data is facilitated by aligning graph patterns radially. Furthermore, our approach incorporates several interaction techniques to explore dynamic patterns such as trends and countertrends. The usefulness is illustrated by two case studies analyzing large dynamic call graphs acquired from open source software projects.

The vast amount of contents posted to microblogging services each day offers a rich source of information for analytical tasks. The aggregated posts provide a broad sense of the informal conversations complementing other media. However, analyzing the textual content is challenging due to its large volume, heterogeneity, and time-dependence. In this paper, we exploit the idea of tag clouds to visually analyze microblog content. As a major contribution, tag clouds are extended by an interactive visualization technique that we refer to as time-varying co-occurrence highlighting. It combines colored histograms with visual highlighting of co-occurrences, thus allowing for a time-dependent analysis of term relations. An example dataset of Twitter posts illustrates the applicability and usefulness of the approach.