# Structure-Aware Trail Bundling for Large DTI Datasets
## 2 Related Work
### Trail and Edge-Bundling Techniques  
In contrast to the above-mentioned rendering techniques, which modify how a 3D trail set is _depicted_, trail and edge-bundling techniques modify the actual _trail set_ to emphasize structures of interest. Bundling essentially aims to (a) identify trails that are spatially close and similar from the perspective of one or several data attributes; and (b) deform these trails so they get spatially closer, so as to create more visual structure in the ensuing rendering thereof. Applications of edge bundling include graph drawing simplification [8; 38], trajectory exploration [7], eye-tracking analysis [5] and streamline bundling [39].  
Bundling of 2D datasets has been extensively explored. Image-based edge-bundling techniques, including SBEB[40], ADEB[5], KDEEB[38], CUBu[8], and FFTEB[41] show that the problem of bundling of 2D trails, as well as the rendering of resulting bundles using a variety of styles, can be efficiently and effectively addressed using image processing approaches that scale well on graphics hardware. Bundling is however far less explored for 3D volumetric trail datasets such as DTI tracts. [PERSON] et al. [42; 43] have proposed mean-shift bundling of 3D connectivity graphs obtained through functional Magnetic Resonance Imaging (fMRI). Simplification of anatomical connectivity using edge bundling is a relatively new topic, one example thereof being KDEEB [38] applied to fiber tracts [25; 44]. Other examples of fiber tract simplification methods include multi-scale local fiber tract contraction [16] and two-dimensional neural maps [45]. To our knowledge, such 3D methods have two main limitations: They cannot, in the same time (1) recover well plausible anatomical structures, such as the mix of surfaces and tube-like structures present in a DTI dataset; and (2) allow interactive visual exploration of DTI datasets of hundreds of thousands of fibers in real time using different rendering styles. For example, the method in [16], which is technically closest to ours, requires hours to complete on a dataset of 78 K fiber tracts. At a higher level, bundling-and-rendering methods for DTI data have evolved largely separated, with the notable exception of [16]. This, we believe, is an artificial separation of two method classes which ultimately aim to the same goal--presenting a large, complex, dense, volumetric 3D trail dataset in a _simplified_ manner to the user.  
Summarizing the above, our contribution to the creation of simplified visualization of large DTI trail sets is three-fold:  
1. We present a method for bundling 3D DTI tracts that allows the user to preserve relevant underlying anatomical elements (fiber tubular bundles, sheets, and manifolds) in a controlled manner;
2. We propose several rendering styles of the 3D bundled structures that emphasize several aspects of interest in the data;
3. We propose a joint implementation of the above two points that can handle 3D trail datasets of hundreds of thousands of trails in real time on consumer graphics hardware.  
As our method builds atop of the backbone of the CUBu technique [8]. We inherit from CUBu the kernel density-based advection of trails that ultimately creates the bundles, and the full GPU-based bundling computation for computational scalability. As described next, we modify CUBu in several respects: We implement the entire pipeline in 3D (using a volumetric density map, Section 3.2); allow trail endpoints to bundle under specific constraints (Section 3.2.1); use the DTI volume anisotropy rather than the CUBu isotropic bundling (Section 3.2.2); reseed tracts in sparsely populated volume areas rather than bundling a fixed, predefined, trail set (Section 3.2.3); and propose several rendering modes designed to emphasize structure specific to DTI fiber sheets (Section 3.3).