Brushing techniques have a long history with the first interactive selection tools appearing in the 1990's. Since then, many additional techniques have been developed to address selection accuracy, scalability and flexibility issues. Selection is especially difficult in large datasets where many visual items tangle and create overlapping. This paper investigates a novel brushing technique which not only relies on the actual brushing location but also on the shape of the brushed area. Firstly, the user brushes the region where trajectories of interest are visible. Secondly, the shape of the brushed area is used to select similar items. Thirdly, the user can adjust the degree of similarity to filter out the requested trajectories. This technique encompasses two types of comparison metrics, the piece-wise Pearson correlation and the similarity measurement based on information geometry. We apply it to concrete scenarios with datasets from air traffic control, eye-tracking data and GPS trajectories.
 Aircraft trajectories can be visually represented as connected line segments that form a path on a map. Given the flight level (altitude) of the aircraft, the trajectories can be presented in 3D and visualized by varying their appearances [7] or changing their representation to basic geometry types [11] . Since the visualization considers a large number of trajectories that compete for the visual space, these visualizations often present occlusion and visual clutter issues, rendering exploration difficult. Edge bundling techniques [34] have been used to reduce clutter and occlusion but they come at the cost of distorting the trajectory shapes which might not always be desirable. Analysts need to explore this kind of datasets in order to perform diverse tasks. Some of these tasks compare expected aircraft trajectories with the actual trajectories. Other tasks detect unexpected patterns and perform out traffic analysis in complex areas with dense traffic [7, 30] . To this end, various trajectory properties such as aircraft direction, flight level and shape are examined. However, most systems only support selection techniques that rely on starting and end points, or predefined regions. We argue that the interactive shape brush technique would be helpful for these kinds of tasks, as they require the visual inspection of the data, the detection of the specific patterns and then their selection for further examination. As these specific patterns might differ from the rest of the data precisely because of their shape, a technique that enables their selection through this characteristic will make their manipulation easier, as detailed in the example scenario. We consider a dataset that includes 4320 aircraft trajectories of variable lengths from one day of flight traffic over the French airspace. The proposed brushing technique leverages existing methods with the novel usage of the shape of the brush as an additional filtering parameter. The interaction pipeline shows different data processing steps where the comparison algorithm between the brushed items and the shape of the brush plays a central role. While the presented pipeline contains two specific and complementary comparison metric computations, another one can be used as long as it fulfills the continuity and metric se- Figure 10 . Three different trajectories containing three different event sequences from [60] . mantic requirements (DR2). There are indeed many standard approaches (ED, DTW, Discrete FrÃl'chet distance) that are largely used by the community and could be used to extend our technique when faced with different datasets. Furthermore, the contribution of this paper is a novel shape-based brushing technique and not simply a shape similarity measure. In our work, we found two reasonable similarity measures that fulfill our shape-based brushing method: The FPCA distance comparison provides an accurate curve similarity measurement while the Pearson metric provides a complementary criteria with the direction of the trajectory. In terms of visualization, the binning process provides a valuable overview of the order of the trajectory shapes. This important step eases the filtering and adjustment of the selected items. It is important to mention that this filtering operates in a continuous manner as such trajectories are added or removed one by one when adjusting this filtering parameter. This practice helps to fine tune the selected items with accurate filtering parameters. The presented scenario shows how small multiple interaction can provide flexibility. This is especially the case when the user brushes specific trajectories to be then removed when setting the compatibility metrics to uncorrelated. This operation performs a brush removal. The proposed filtering method can also consider other types of binning and allows different possible representations (i.e. various visual mapping solutions). This paper illustrates the shape based brushing technique with three application domains (air traffic, eye tracking, gps data), but it can be extended to any moving object dataset. However, our evaluation is limited by the number of studied application domains. Furthermore, even if various users and practitioners participated in the design of the technique, and assessed the simplicity and intuitiveness of the method, we did not conduct a more formal evaluation. The shape based brush is aimed at complementing the traditional brush, and in no way do we argue that it is more efficient or effective than the original technique for all cases. The scenarios are examples of how this technique enables the selection of trails that would be otherwise difficult to manipulate, and how the usage of the brush area and its shape to perform comparison opens novel brushing perspectives. We believe they provide strong evidence of the potential of such a technique. The technique also presents limitations in its selection flexibility, as it is not yet possible to combine selections. Many extensions can be applied to the last step of the pipeline to support this. This step mainly addresses the DR4 where the selection can be refined thanks to user inputs. As such, multiple selections can be envisaged and finally be composed. Boolean operations can be considered with the standard And, Or, Not. While this composition is easy to model, it remains difficult for an end user to master the operations when there are more than 2 subset operations [57] [31] . As a solution, Hurter et al. proposed an implicit item composition with a simple drag and drop technique [31] . The pipeline can be extended with the same paradigm where a place holder can store filtered items and then be composed to produce the final result. The user can then refine the selection by adding, removing or merging multiple selections. In this paper, a novel sketch-based brushing technique for trail selection was proposed and investigated. This approach facilitates user selection in occluded and cluttered data visualization where the selection is performed on a standard brush basis while taking into account the shape of the brush area as a filtering tool. This brushing tool works as follows. Firstly, the user brushes the trajectory of interest trying to follow its shape as closely as possible. Then the system pre-selects every trajectory which touches the brush area. Next, the algorithm computes a distance between every brushed shape and the shape of the brushed area. Comparison scores are then sorted and the system displays visual bins presenting trajectories from the lowest scores (unrelated -or dissimilar trajectories) to the highest values/scores (highly correlated or similar trajectories). The user can then adjust a filtering parameter to refine the actual selected trajectories that touch the brushed area and which have a suitable correlation with the shape of the brushed area. The cornerstone of this shape-based technique relies on the shape comparison method. Therefore, we choose two algorithms which provide enough flexibility to adjust the set of selected trajectories. One algorithm relies on functional decomposition analysis which insures a shape curvature comparison, while the other method insures an accurate geometric based comparison (Pearson algorithm). To validate the efficiency of this method, we show three examples of usage with various types of trail datasets. This work can be extended in many directions. We can first extend it with additional application domains and other types of dataset such as car or animal movements or any type of time varying data. We can also consider other types of input to extend the mouse pointer usage. Virtual Reality data exploration with the so called immersive analytic domain gives a relevant work extension which will be investigated in the near future. Finally, we can also consider adding machine learning to help users brush relevant trajectories. For instance, in a very dense area, where the relevant trajectories or even a part of the trajectories are not visible due to the occlusion, additional visual processing may be useful to guide the user during the brushing process.
Interactive technique to improve brushing in dense trajectory datasets by taking into account the shape of the brush.
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