# Structure-Aware Trail Bundling for Large DTI Datasets
## 3 Method
### Structure-Emphasizing Rendering
#### 3.3.2. Shading and Blending  
As outlined at the beginning of Section 3.3.1, we render \(T\) by drawing a viewplane-parallel circular luminance splat texture \(t\) centered at the location of every sample point \(\mathbf{x}_{i}\in T\). Tuning the splat radius effectively'merges' close trails even further than what bundling can do, creating visually compact shapes. Choosing different profiles for the texture \(t\) allows obtaining rendering effects that range from flat-shaded-like to smooth-shaded surfaces and finally to specularly shaded tubes showing local fiber details. We discuss next four such profiles. To illustrate them, we made a selection of trails that emerge from the _corona radiata_ and merge with those in the _corpus callosum_. These selected trails are shown in Figure 7, overlaid atop of a sagittal slice encoding fractional anisotropy (FA), for context Figure 7- show the four luminance textures corresponding to these profiles (topmost inset) and also as a 3D height plot of the luminance values (inset below) and how these profiles affect the rendering of the selected trails. The profiles are detailed further below. **Flat (\(t_{F}\)):** This profile contains a constant (bright) luminance and is useful when one wants to show additional information by e.g., color coding. When combined with outl  
Figure 7: **(a)** Selected trail set consisting of a tube-like bundle from the _corona radiata_ (blue) merging into the _corpus callosum_ (red). (**b–e**) Same bundle as in (a) shaded with four different profiles. (**f–i**) The four shading profiles applied to a full 100 K-trails bundled dataset. See Section 3.3.2. Section 3.3.4), it shows a minimalistic, illustrative rendering style that allows easily separating trail bundles at a coarse scale. For instance, in Figure 7b, we easily see that the trail set consists of one large vertical bundle and one curved bundle--compare this image with Figure 7 where the same two bundles have been manually separated by color coding. **Gaussian (\(t_{\text{C}}\)):** This profile sets the luminance texture to a Gaussian map--see the height-plot inset in Figure 7c. The actual luminance texture (also shown in the inset of Figure 7d) resembles a diffusely shaded sphere. The obtained effect is to create a subtle shading close to the borders of a bundle. **Spherical (\(t_{\text{S}}\)):** This profile sets the luminance of a pixel \(\mathbf{x}\in t\) to its distance to the circular splat's boundary. As visible in the insets in Figure 7d, the profile resembles a specularly shaded sphere; if we depict \(t\) by a height plot, the profile shows as a conical shape. The obtained effect, also visible in Figure 7d, is to create slightly sharper highlights and shadows than the Gaussian profile. **Conical (\(t_{\text{C}}\)):** This profile corresponds to a cone lit by a light source of direction \(\mathbf{a}\), seen from above--see the insets in Figure 7e. We tested two options for setting the light direction \(\mathbf{a}\), as follows (see also Figure 8). First, we use a global, fixed, direction \(\mathbf{a}\). This is equivalent to the well-known directional lighting in OpenGL. Although easy to understand, and creating a granular rendering where individual trails can be discerned, fixed lighting does sometimes not create strong-enough shading cues to differentiate overlapping bundles (Figure 8a). Alternatively, we set \(\mathbf{a}\) to a vector locally orthogonal to the view-space tangent \(\tau\) to each trail, the latter being estimated by projecting the 3D line segment \((\mathbf{x}_{j},\mathbf{x}_{j+1})\) to the view plane--see inset in Figure 8b. The effect is that lighting always'sticks' to the same side of a trail, and follows the trail's curvature. As visible in Figure 8b, this creates stronger shading contrasts allowing one to separate easier overlapping bundles. Figure 7f-i show the application of the above four shading profiles to a fill 100 K-trails bundled dataset. Here, we use color (hue) to encode the trails' directions, similar to earlier images in this paper (e.g., Figure 2).