We consider moving objects as multivariate time-series. By visually analyzing the attributes, patterns may appear that explain why certain movements have occurred. Density maps as proposed by Scheepens et al. [25] are a way to reveal these patterns by means of aggregations of filtered subsets of trajectories. Since filtering is often not sufficient for analysts to express their domain knowledge, we propose to use expressions instead. We present a flexible architecture for density maps to enable custom, versatile exploration using multiple density fields. The flexibility comes from a script, depicted in this paper as a block diagram, which defines an advanced computation of a density field. We define six different types of blocks to create, compose, and enhance trajectories or density fields. Blocks are customized by means of expressions that allow the analyst to model domain knowledge. The versatility of our architecture is demonstrated with several maritime use cases developed with domain experts. Our approach is expected to be useful for the analysis of objects in other domains.

Figure 1: A density map of vessel traffic in front of Rotterdam during a single day. The density map is a combination of four density fields each covering a quarter of the day. The following manually defined color map is used: night is dark blue, morning is bright yellow, afternoon is dark yellow, and evening is bright blue. Furthermore, the saturation of the color represents the density field contribution and the hue is given by the period with the highest density. To discriminate daylight patterns from nighttime, the night and evening use half the kernel radius of the other periods. This figure shows that the main routes are the most used during daylight, while in the night deviations from these routes occur. ABSTRACTWe present a method to interactively explore multiple attributes in trajectory data using density maps, i.e., images that show an aggregate overview of massive amounts of data. So far, density maps have mainly been used to visualize single attributes. Density maps are created in a two-way procedure; first smoothed trajectories are aggregated in a density field, and then the density field is visualized. In our approach, the user can explore attributes along trajectories by calculating a density field for multiple subsets of the data. These density fields are then either combined into a new density field or first visualized and then combined. Using a widget, called a distribution map, the user can interactively define subsets in an effective and intuitive way, and, supported by high-end graphics hardware the user gets fast feedback for these computationally expensive density field calculations. We show the versatility of our method with use cases in the maritime domain: to distinguish between periods in the temporal aggregation, to find anomalously behaving vessels, to solve ambiguities in density maps via drill down in the data, and for risk assessments. Given the generic framework and the lack of domain-specific assumptions, we expect our concept to be applicable for trajectories in other domains as well.

Visualization of the trajectories of moving objects leads to dense and cluttered images, which hinders exploration and understanding. It also hinders adding additional visual information, such as direction, and makes it difficult to interactively extract traffic flows, i.e., subsets of trajectories. In this paper we present our approach to visualize traffic flows and provide interaction tools to support their exploration. We show an overview of the traffic using a density map. The directions of traffic flows are visualized using a particle system on top of the density map. The user can extract traffic flows using a novel selection widget that allows for the intuitive selection of an area, and filtering on a range of directions and any additional attributes. Using simple, visual set expressions, the user can construct more complicated selections. The dynamic behaviors of selected flows may then be shown in annotation windows in which they can be interactively explored and compared. We validate our approach through use cases where we explore and analyze the temporal behavior of aircraft and vessel trajectories, e.g., landing and takeoff sequences, or the evolution of flight route density. The aircraft use cases have been developed and validated in collaboration with domain experts.

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