# Structure-Aware Trail Bundling for Large DTI Datasets
## 1 Introduction  
Trails or trajectories are generated by many applications, such as graph drawing and graph visualization [1], monitoring of vehicle motion along large geographical spaces [2; 3] and scanning techniques [4; 5; 6]. Besides their spatial position, trails can be annotated by additional data attributes, such as weights, directions, and types of the entire trail, or speed and travel duration of the item traveling along the trail. Visualizing datasets consisting of hundreds of thousands of trails is challenging, due to the high levels of occlusion, and the difficulty of simultaneously displaying multiple attributes. In information visualization, _bundling_ has emerged as an important technique to handle such datasets [7]. _Edge bundling_ creates simplified visualizations of large graphs by deforming the (typically straight-line) drawing of spatially close and data-similar edges so these get visually grouped, thereby creating whitespace that reduces clutter and allows one to discern the main structure of the graph drawing. _Trail bundling_ generalizes the process to arbitrary sets of curves, or trails, embedded in 2D space. Numerous bundling algorithms have been proposed in the last two decades, offering a wealth of drawing styles, heuristics for grouping the edges or trails, and acceleration strategies to handle datasets of hundreds of thousands of elements in real time [8]. Although bundling has proven its added value for 2D graph-and-trail simplification, only a handful of works have explored its generalization to 3D datasets. Bundling graphs laid out on 3D surfaces has been met with success [9]. However, for the graph visualization use-case, truly volumetric 3D layouts are far less common [1]. The other data type--trails--is also approached by only a fewmethods. This leaves the question whether 3D trail bundling is an efficient and effective tool for the visual exploration of such data. A salient use-case for 3D bundling is the visual exploration of Diffusion Tensor Imaging (DTI) datasets via tractography [10; 11; 12]. This application generates massive sets of 3D curves, representing the paths followed by major fiber tracts in the brain. Due to the volumetric structure of the brain and its complex connection patterns, obtaining simplified views of such patterns has raised much interest in the visualization community. This has been approaches by two main method types. First, so-called _illustrative_ rendering methods aim to draw the actual, raw, 3D fiber tract data in ways that make important spatial patterns show up more saliently [13; 14; 15]. These methods work well for medium-density trail sets; too-high-density ones create, inevitably, occlusions that do not allow visual exploration of a full volume. Secondly, _3D bundling_ methods take the more aggressive step of actually deforming the trails to create more structure at the expense of preserving spatial information [16]. To our knowledge, these methods cannot handle large 3D datasets consisting of hundreds of thousands of trails. Moreover, the _combination_ of illustrative techniques and 3D bundling techniques has been explored only to very limited extents. This is in stark contrast to the aforementioned results for bundling-and-rendering techniques for 2D trail sets [8]. In this paper, we aim to answer the question of how to combine _bundling_ and _rendering_ techniques efficiently and effectively for the visual simplification of large DTI fiber tracts. For this, we adapt a state-of-the-art method for 2D trail bundling [8] to efficiently handle 3D DTI trail sets, taking into account the typical structures that exist and need to be emphasized in such data. Next, we propose a range of rendering techniques to present the 3D bundling results so that the structures of interest in the data get further emphasized.