IEEE Xplore At-A-Glance
  • Abstract

Depth-Dependent Halos: Illustrative Rendering of Dense Line Data

We present a technique for the illustrative rendering of 3D line data at interactive frame rates. We create depth-dependent halos around lines to emphasize tight line bundles while less structured lines are de-emphasized. Moreover, the depth-dependent halos combined with depth cueing via line width attenuation increase depth perception, extending techniques from sparse line rendering to the illustrative visualization of dense line data. We demonstrate how the technique can be used, in particular, for illustrating DTI fiber tracts but also show examples from gas and fluid flow simulations and mathematics as well as describe how the technique extends to point data. We report on an informal evaluation of the illustrative DTI fiber tract visualizations with domain experts in neurosurgery and tractography who commented positively about the results and suggested a number of directions for future work.

SECTION 1

Introduction

Illustrative depictions have been playing an essential role in the communication of knowledge for centuries. Traditionally, illustrators used graphic tools such as pen-and-ink to draw—with the goal to depict, e. g., the shapes of objects. The choice of tool was typically dictated by the means of reproduction, usually the printing in books. Therefore, illustrators often chose techniques that result in black-and-white imagery, for example pen-and-ink, woodcuts, or copper plates. Despite being limited to two "colors," these techniques still allowed illustrators to convey shape, material, and illumination through techniques such as stippling, hatching, or cross-hatching. More importantly, illustrators also made use of the fundamental illustration principles of abstraction and emphasis to effectively communicate their intentions.

With the advance of computer support, illustrators started to use general purpose graphics programs (e. g., Adobe's Illustrator" or Photoshop") for creating illustrations. One reason for this tool change is that general purpose programs, in many aspects, provide more freedom than traditional tools. In a separate development, the visualization community has created numerous successful techniques to solve specialized visualization problems, e. g., in the medical domain. In both cases, the availability of color processing and reproduction has invited the use of shading techniques, i. e., representing surfaces through shades of color, in contrast to the traditional black-and-white methods.

While illustrators in their use of general purpose tools can still apply the illustration principles of abstraction and emphasis, this is more difficult for automatic techniques as it is challenging to "teach" importance to an algorithm. In the areas of non-photorealistic rendering (NPR) and illustrative visualization, however, abstraction and emphasis techniques have been investigated. Examples include the use of halos for simple line rendering [2], [11] or shading [22], [37] and volume rendering [5], the use of additional depth cueing by influencing line or shading parameters (e. g., [11]), interactive emphasis techniques (e. g., [27], [35], [41]), or focus+context techniques (e. g., [13], [39]).

In this paper we build on these previous approaches but focus on a specific subset of data—line datasets (see the example result in Fig. 1). This type of data is generated in a number of application domains such as medical imaging (e. g., DTI fiber tract extraction), meteorology (e. g., particle traces in storm data or simulations), physics (e. g., particle tracts from 3D gas or fluid flow simulations), or astronomy (e. g., particle traces from mass distribution simulations for galaxy formation). In all these application areas, line data with a comparably high density of elements is generated and needs to be analyzed. This data lends itself more to the traditional black-and-white depiction techniques rather than shading-based methods because lines occupy much less space than shaded elements such as cylindrical shapes. In addition, detail in the visualizations is often important so that reducing the number of depicted lines may not be a suitable approach.

To address this problem of depicting dense line datasets in their full detail our paper makes the following contributions: We show how to illustratively visualize dense line datasets at interactive frame-rates using modern graphics hardware. We introduce a conceptually simple technique that allows us to only render the front layer of the data, i. e., the lines or points that lie close to each other and closest to the viewer. These front elements are rendered such that they do not overlap each other but at the same time they occlude elements much further away from the viewer. This depth-dependent halo technique emphasizes bundles of co-linear line segments (which are likely to be important, see Fig. 1) and abstracts from less structured segments. Moreover, we de-emphasize elements that are farther away to enhance depth perception, and filter the dataset for further emphasis of important structures. We further show how the discrete and black-and-white nature of the depicted elements lends itself to anaglyphic stereo rendering.

The remainder of the paper is organized as follows. In Section 2 we place our work in the context of related approaches. Next, we present the technical details of the approach in Section 3. Then in Section 4, we show examples of visualizations created with our technique for several application domains. In Section 5 we give details on an informal evaluation of our technique with domain experts in neurosurgery and tractography and, finally, conclude the paper in Section 6, where we also mention some avenues for future work.

SECTION 2

Related Work

To place our work on illustrative line rendering into context, we discuss techniques for both line visualization and illustrative rendering.

2.1 Line Data Visualization Techniques

Numerous techniques exist to depict paths of particles or other linear structures, in particular for flow visualization. For example, people have employed (shaded) lines, tubes, or strips (ribbons) whose color and shape can be changed depending on data properties such as velocity, flux, or direction [30] (e. g Fig. 2(a)). Particularly related to our work are scalable, self-orienting surface techniques [23], [24], [33], [34] which create shaded, view-aligned strips to visualize 3D vector fields. In contrast, our goal is to create high-resolution black-and-white visualizations for dense datasets using illustration principles. As an alternative to explicitly representing streamlines, texture-based methods [21] such as line integral convolution [7] provide both a global and local impression of flow data. This technique was extended to 3D [14], [16] where, related to our work, halos are used to increase depth perception. For a similar purpose, halos are used in streamline-based volume visualization [40]. Both streamlines and texture-based techniques are employed in many other domains which rely on the visualization of line data resulting from real or simulated linear structures or particle traces. Examples include physics (e. g., electric or magnetic field lines), chemistry (e. g., protein structures), and meteorology (e. g., storm data).

Figure 1
Fig. 1. Illustrative visualization of a subset of DTI fiber tracts with depth-dependent halos.

In particular in the medical domain, line data such as tracts of muscle or brain fibers is important. Here, fiber tracts are estimated from diffusion weighted magnetic resonance imaging (DW-MRI) [25]. The fiber tracts represent, for example, bundles of neural axons connecting different parts of the brain. Such fiber tracts are typically rendered as lines or tubes with coloring or shading applied to them to enhance understanding of spatial relationships [28], [43], [44].

Rendering all possible fiber tracts or particle traces in a dataset is often not feasible with visualization techniques due to performance and occlusion issues. Thus, a selection is typically made, showing only fiber tracts that pass through a certain region of interest. Various methods are available for making this selection (e. g., [3]).

2.2 Illustrative Visualization and Rendering Techniques

In a number of line-based scientific visualization techniques, people make use of illustration principles. For instance, Joshi et al. [18] employ techniques that enhance the boundary or silhouette to accentuate internal features in visualizations of hurricanes. Similar contour enhancing techniques have also been investigated for flow data [36] or medical volume data [6], [10]. Related to illustrative visualization is non-photorealistic rendering (NPR), where lines have been used as a means to illustrate surfaces (e. g., [15], [42]) but are usually placed onto surfaces during rendering rather than being the original carrier of the depicted data or shape. Such techniques have been applied, for example, to medical volume visualization [9], [26], [38] as well as rendering of fiber and vessel structures [20], [31]. In the latter examples, line rendering techniques are used to enhance and supplement traditional techniques that are based on larger cylindric structures.

Techniques that enhance depth perception are important specifically in line rendering and have been introduced to NPR in its early days. Such techniques include the use of visibility information [1], [19] as well as the use of halos [2], [11], the illustration method we also use in our own work. Halos, however, can not only be used in line rendering but have been applied in more traditional visualization techniques based, e. g., on line integral convolution [16] or volume rendering [5] to enhance depth perception. Related to these approaches as well as to our own are techniques that make use of depth buffer manipulations to enhance the depth perception in the created images. Noteworthy in this respect are, in particular, depth buffer unsharp masking [22], depth cueing in molecular visualization [37], and pen-and-ink tree rendering using depth discontinuities [8]. In contrast to these techniques, our approach extends similar illustrative rendering principles to the domain of dense line or point data which are rendered without shading and which, thus, rely even more on cues to indicate depth relations.

SECTION 3

Illustrative 3D Line Rendering

Based on the previously discussed techniques to visualize line data, we combine these with principles of halo-based non-photorealistic rendering of lines. We focus on datasets where dense sets of lines are important, for example, DTI fiber tracts or particle traces in physical simulations. In this section we first give a general motivation and overview of the technique and then discuss its realization in detail. Next, we show how the technique is extended to point clouds, present a number of visual enhancements, and address data filtering.

Figure 2
Fig. 2. Comparison of rendering techniques for line datasets

3.1 General Motivation and Technique Overview

The rendering of line data requires, in particular, that the depth relation of the lines is clearly depicted. As discussed in the previous section, shaded cylindrical representations were traditionally employed for this purpose. This approach has a number of limitations. Due to the use of shading, each line needs to have a certain minimum width in order for viewers to be able to discriminate each individual line's orientation and location in space (Fig. 2(a)). This limits the number of lines that can simultaneously be depicted and also hinders the visualization of natural line bundles if each line is to be visible individually. An alternative approach would be to use simple black lines on a white background (Fig. 2(b)). On the one hand, a higher number of data elements can potentially be depicted because lines can easily be packed more tightly. Moreover, it also becomes more feasible to use such illustrations in print, because these do not require shading and thus do not rely on halftoning. On the other hand, this introduces a lot of visual clutter into the image and results in large regions of black being shown. Thus, it is no longer possible to distinguish foreground from background lines, which also means that the depth relation is lost.

To address these issues and to be able to use the advantages from both techniques, we employ line halos as previously used in line rendering [2], [11]. Since we are dealing with dense datasets of lines, simply assigning a halo to each line is not sufficient (Fig. 2(c)). Instead, we present a technique that assigns halos to all lines, but these halos are only rendered if the lines are sufficiently separated in depth (Fig. 2(d)). This causes the halos of lines that lie in front of others to occlude lines further away. If lines have the same distance to the viewer, however, they do not occlude one another. This depth-dependent halo reduces visual clutter, emphasizes line bundles by visually clustering them, and depicts depth relations as in previous halo techniques [2], [5], [11], resulting in an effective illustration of the data.

The general approach is to use view-aligned triangle strips. Each strip represents one of the lines and always faces the viewer (similar to billboards). Strips are textured so that the center is black, representing the line, and the perimeter is white to create the halo. In addition, each strip is bent away from the viewer as shown in Fig. 3(a). This way the part of the strip that is not black prohibits parts of other lines to be drawn that are close in image space but further away from the viewer in depth. This approach is related to the -z-buffering used in point-based rendering [4], [12] that uses fragment-dependent depth corrections to determine the visibility of splats in a two-pass process.

Our approach, however, makes use of fragment depth manipulations in a single rendering pass to directly render lines that are close together without overlapping halos.

In practice, our approach for rendering 3D lines is a two-stage process. In the first stage we transform the lines into view-oriented triangle strips, while in the second stage we manipulate the shape of the strip and texture it. These two stages are mapped to the two stages in modern GPU processing: vertex shading and fragment shading.

Figure 3
Fig. 3. Schematic depiction of the rendering of the creation of depth-dependent halos for large depth discontinuities: (a) projected view of the depth displacement, (b) view of a line (black) being crossed by a perpendicular line (red) creating a halo. The fat parts are the actually rendered line pixels, the thin lines illustrate the z-buffer manipulation.

3.2 View-Oriented Triangle Strips

Our goal is to display the line data as view-aligned strips that represent both the line itself as well as the halo around it. Therefore, before sending data to the GPU, we organize our input lines in the CPU as sequences of 3D vertices. To be able to later render the lines as triangle strips on the GPU, we create zero-width line strips on the CPU by duplicating each vertex but retaining the vertex locations. On the GPU, this strip needs to be widened by extending it perpendicular both to the viewing direction and the line direction so that it is always oriented to face the viewer. We derive the direction of the line locally at each of the vertices by taking the normalized average direction of both line segments adjacent to the vertex (or one segment for start and end of each line). This step occurs before the vertices are duplicated, and the direction is copied to the new vertex when the duplication is carried out. As a final pre-processing step, each of the vertices is assigned texture coordinates (u v). For this purpose, the u-coordinate is interpolated along the length of the line, while the v-coordinate is set to 1 for the "left" side of the strip and to 0 for its "right" side. As a result, each vertex now has a position, texture coordinates, and a direction. This information in the form of zero-width triangle strips is transferred to the GPU as vertex buffer objects.

During the GPU rendering stage (once for each rendering pass), the strip is widened and view-aligned. For this purpose we extend the zero-width strip into a direction that is perpendicular to both the direction of the line D and the view direction V. Thus, we compute the cross-product between V and D, normalize the resulting vector, and move a vertex along this direction if v = 1 and in opposite direction if v = 0. Hence, the new vertex position pout is calculated as: Formula TeX Source $$p_{{\rm{out}}} = p_{{\rm{in}}} + ||{\bf{V}} \times {\bf{D}}||(v - 0.5)w_{{\rm{strip}}},$$ where pin is the input vertex position and wstrip is the strip width. The result is that the strip always faces the viewer, and the centerline of the strip is located along the original line.

3.3 Fragment Texturing and Depth Displacement

The next step in the process is to assign either black or white to the individual pixels of the line strip so that both line and halo are created, but without the halo obstructing nearby lines. This occurs in the fragment shader after the previously created line strip has been rasterized. We first determine the distance (s) to the center of the strip for each fragment, again using the texture coordinates: Formula TeX Source $$s = w_{{\rm{strip}}} |v - 0.5|\,.$$ If this distance s is smaller than half the line width (wline), the fragment's output color is set to black and its depth value is left untouched. Otherwise, the fragment's output color is set to white and its depth is adjusted depending on the distance from the strip's center (Fig. 3(a)): Formula TeX Source $$d_{{\rm{new}}} = d_{{\rm{old}}} + d_{\max } f_{{\rm{displacement}}} (2{\rm{|}}v - 0.5|).$$

Figure 4
Fig. 4. Illustration of how the line halos change depending on the distance of the lines with respect to each other.
Figure 5
Fig. 5. Comparing rendering (a) without and (b) with tapering.

Here dnew is the fragment's new depth dold is the its old depth dmax is the maximum displacement, and fdisplacement is a function that maps a scalar value x ∊ [0, 1] to [0, 1], representing the specific shape of depth displacement. A simple linear function has proven to be suitable, and we use fdisplacement(x) = x for all our examples (except Fig. 17).

The effect of this depth displacement of fragments is illustrated in Fig. 3(b) which shows one line (black) being rendered on top of another one (red). Because depth testing is enabled in the rendering, parts of the red crossing line are obscured by white fragments of the triangle strip belonging to the black foreground line. The visual effect is a halo around the black foreground line.

If the red line in Fig. 3(b) were to move further back, the width of the halo would increase until the difference in depth between both lines is larger than dmax, after which the halo width remains constant (see Appendix A). Moving the background line toward the foreground line, in contrast, would decrease the halo width until the halo completely disappears. This happens if the background line is closer to the foreground line than fdisplacement(0 .5 wline). This effect is illustrated in Fig. 4 in which a series of vertical lines of decreasing distance to the viewer are rendered with respect to a horizontal line. Notice how the changing halo widths enhance the depth perception in this case.

3.4 Visual Enhancements

So far the technique correctly represents haloed lines that do not occlude each other if they lie close together. For an individual line that lies clearly in front of a bundle of other lines this has the effect of showing the rectangular strip—visible, in particular, at the line ends (Fig. 5(a))—which can be distracting. We improve the visual appearance of the lines by tapering (gradually narrowing line ends Fig. 5(b)). We place a stencil texture over the strip to be checked in the fragment shader which only lets fragments pass that are inside the mask. To make the amount of tapering independent from the line length, the u texture coordinate is, in fact, interpolated non-linearly along each triangle strip. For the first ntapered vertices the u-coordinate is linearly interpolated between 0 and ttapered, assuming they are approximately equidistant. Similarly, the last ntapered vertices are mapped to u-values between 1 − ttapered and 1. We use ntapered = 2 and ttapered = 0 .2.

Figure 6
Fig. 6. Rendering (a) without and (b) with additional depth cueing.

One important aspect of visualization of 3D data is to correctly display spatial relationships. While the depth-dependent halo rendering already supports depth perception (Fig. 6(a)), we further enhance this effect by employing depth cueing via adjusting the line width [11]. The perspective projection that we use already introduces some fore-shortening of the line strips with growing distance from the viewer. We further emphasize this effect by manipulating the portion of the strip that is rendered as line, reducing it the further away a line section lies from the viewer (Fig. 6(b)). This is realized in the fragment shader by modifying wline with respect to the current fragment's z-value. The degree of depth cueing can be adjusted w.r.t. the desired effect.

Finally, the visual quality of a line rendering depends to a large degree on the way the resulting image is represented. While using vector graphics could be advisable for the line renderings we are producing [17], we can also achieve similar results by rendering high-resolution 1-bit black-and-white images as used throughout the paper. For on-screen rendering we either use a gradual transition from black to white in the fragment shader or employ full-scene anti-aliasing (FSAA). For example, Coverage Sampling Anti-Aliasing (CSAA) can be enabled to produce higher-quality images with less sampling artifacts.

3.5 Extension to Point Cloud Data

In addition to rendering line data, the technique can also be extended to visualize point clouds. This approach relates to point-based graphics [12] such as point splatting (e. g., [4]) or surfels [29], the latter having previously been used in NPR [32]. To add explicit halos around points we render view-aligned geometry, i. e., quads, similar as before with lines. Thus, we quadruple each vertex during pre-processing but do not need to extract a direction. Instead, each zero-sized quad is oriented to the viewer in the vertex shader by extending it in the positive and negative x- and y-direction in screen-space. The actual size of the quad is determined in model-space, however, to guarantee a consistent behavior when zooming in and out.

For this purpose we back-project an up-vector (positive y-direction) and side-vector (positive x-direction) in screen-space to model-space, which are then used as basis-vectors for enlarging the quads. Again, with the texture coordinates of the zero-sized quad we determine the precise transformation for each vertex. In the fragment shader, the depth-displacement occurs similar to the case of lines, resulting in a cone shape being rendered to the z-buffer. The distance from the center is computed using the Euclidean distance, the same is also used for masking the halo to a circular shape. The overall processing is slightly more computationally and memory intensive than with lines, due to the quadrupling of points and the use of the Euclidean distance.

3.6 Filtering

As another means of illustrative abstraction (and in addition to selecting a subset of lines through a ROI) we implemented filtering of the data to remove selected parts, e. g., low velocity streamlines or fiber tracts in areas with low fractional anisotropy (FA). For this purpose we assign an extra scalar attribute to each vertex of the data based on which the filtering will occur. This filtering attribute is passed onto the GPU and replicated for each fragment in the rasterization stage. The fragment shader then compares each fragment's filtering attribute with a pre-determined threshold and discards fragments that do not pass this test. The threshold can now be changed at run-time and permits an interactive selection of the amount of filtering that is to occur.

Figure 7
Fig. 7. Three example stages of filtering, using the fractional anisotropy (FA) value of a DTI fiber tract dataset. With the growing filtering threshold for FA, more of the internal structure of the dataset is revealed.
Figure 8
Fig. 8. Anaglyphic stereo visualizations for two example datasets: (a) simulated air flow in an office and (b) DTI fiber tracts. For use with redcyan or red-green glasses (red on the left eye).

Unfortunately, this process re-introduces the problem of the rectangular shape of line ends discussed in Section 3.4. To address it, we change the process of halo masking when filtering is enabled. Instead of using the actual interpolated u texture coordinate we derive a new u-value from the interpolated filtering attribute and the currently active threshold such that the ends of the filtered lines are tapered. Limitations are that this assumes the filter attribute changes gradually and that it does not result in the same visual quality as before.

The scalar attribute used for filtering needs to be meaningful with respect to the specific dataset. For example, for DTI fiber tract data we use fractional anisotropy, which is a measure for the amount of directionality in the data (Fig. 7). Since this value is defined based on a volume representation, it is interpolated for each vertex in the pre-processing stage based on the vertex' location in the volume.

3.7 Anaglyphic 3D Rendering

The three-dimensionality of the data is one important aspect that needs to be visualized, even beyond the support of halos. In regular rendering for visualization this is achieved through regular shading, potentially combined with special techniques such as depth buffer unsharp masking [22] or ambient occlusion [37]. Alternatively, stereo rendering and projection can be used, i. e., computing separate images for each of the viewer's eyes. The black-and-white character of our visualization technique does not permit using shading-based techniques, but lends itself to stereo rendering without requiring complicated projection setups: anaglyphic rendering. For this purpose we render the scene from two different viewpoints, color these red and cyan, and overlay them on top of each other for use with red-cyan glasses (Fig. 8).

Figure 9
Fig. 9. Illustration principles at work. Detail regions from Fig. 1.

The illustrative line rendering technique lends itself, in particular, to this stereo vision technique because it is monochrome and the discrete elements (lines and points) allow the human visual system to make an easy association between related elements. The halos around lines and line bundles enhance this effect because it makes the separation of individual elements that belong to each other easier. In addition to anaglyphic rendering, we also applied the technique to passive stereo rendering using polarized light, resulting in a comparable experience but without the small color artifacts caused by the red-cyan glasses.

SECTION 4

Discussion

After having described the illustrative line rendering technique and its implementation in detail, we now discuss some application aspects. In particular, we address how depth-attenuated halos incorporate the illustration principles of abstraction and emphasis, how specific visual results can be achieved, and how the technique can be applied to a number of application scenarios and input data types.

4.1 Illustration Principles in Depth-Attenuated Halos

Our illustrative rendering technique for lines has the effect that no or only small halos are created between lines that form concentrated bundles (Fig. 9(a)). This effect emphasizes line bundles visually, through larger dark regions or tightly packed co-linear lines and through separation from the background. This emphasis may make the individual lines less distinguishable, but supports and highlights the importance and the coherency of such dense line bundles. Lines that do not form concentrated bundles (which are less aligned), in contrast, are visually de-emphasized and abstracted (Fig. 9(b)): For crossing lines that are not at the same distance from the viewer many halos are generated, splitting these lines up into smaller segments. These emphasis and abstraction effects are enhanced further through the usage of additional depth cueing via line width attenuation, emphasizing front parts and de-emphasizing distant parts of the scene. These methods allow us to refrain from using any lighting while still illustrating spatial relations.

The illustrative line rendering technique using depth-attenuated halos has the additional effect that lines behind tight bundles are visually separated due to the halo that is rendered around the bundle. Thus, the technique renders the line data as implicit layers that are visually separated from each other through their halos. Occlusion situations are clearly visible through the halos surrounding the front line bundles, leading to a visual depth clustering similar to the halos in [37]. Moreover, this effect also means that for bundles or other co-linear lines only the front-most layer of lines are displayed in the resulting images—visible, in particular, in videos, during interactive manipulation, or when viewing anaglyphic stereo images (Fig. 8). Therefore, despite the fact that no surfaces exist explicitly in the data, the rendering has the interesting effect that surfaces that implicitly exist in the data by means of densely packed bundles are visually noticeable.

Figure 10
Fig. 10. Fiber tracts from diffusion tensor imaging (DTI). Notice the visual bundling and depth clustering in (b).
Figure 11
Fig. 11. Simulated air flow in an office, same dataset as in Fig. 8(a).

4.2 Case Studies of Application Scenarios

To illustrate the applicability of our technique we now discuss a number of case studies, using line datasets from a variety of domains.

4.2.1 DTI Fiber Tracts

Nerve fiber tracts extracted from diffusion tensor imaging (DTI) give an indication of how actual bundles of axons connect different parts of the brain. Depending on the resolution of the underlying MRI scan, a large number of fibers can be extracted. In our example in Fig. 10, 150 352 tracts with 1 625 472 vertices in total were extracted using the program Diffusion Toolkit, the small average vertex number per tract resulting from many short tracts. Because of such large dataset sizes, fibers are difficult to visualize with traditional techniques due to performance, rendering technique (shaded cylinders need a certain amount of space), and overview/occlusion issues. Hence, usually subsets of the fiber tracts are selected and visualized. Our illustrative line rendering technique can easily render whole datasets at interactive rates but also suffers from overview/occlusion issues (Fig. 10(a)). Thus, we also select subsets (e. g Fig. 1 and 8(b), where the ROI is a sagittal slice) and/or use filtering to cope with this type of data (e. g Fig. 7 and 10(b)). Nevertheless, our technique is able to display all fibers in a subset so that no automated data reduction technique is necessary that would cluster several lines into single ones. With our technique it is possible to visually distinguish single fibers from smaller or larger fiber bundles rather than requiring algorithmic support for this task.

4.2.2 Simulated Flows of Fluids or Gases

Another domain where line data is generated is the simulation of fluids or gases. For example, we used VTK's "office" example dataset and extracted 786 streamlines from it using VTK (Fig. 8(a) and 11). The visualization in Fig. 11 shows where the simulated air flow is focused and where it branches off, highlighting concentrated bundles of air movement Fig. 12 shows two views of a similar simulation of water flow using 1 400 streamlines and 2 603 605 vertices in total. Here, the twisted flow of the water in a number of vortices is illustrated, while focused flow is still emphasized. The combination of these illustrative effects gives the illustrations a vividly three-dimensional appearance Fig. 13 shows two additional illustrative renderings of the same data (without and with filtering) but using a much higher number of streamlines (7 910 911 vertices and 4 475 streamlines), thus demonstrating how filtering on velocity can reveal inner structures.

Figure 12
Fig. 12. Two views of a selection of simulated water flow streamlines.
Figure 13
Fig. 13. Illustrative line rendering of a denser set of streamlines of the data used in Fig. 12, without and with filtering on velocity magnitude to reveal inner structures, showing the detail our technique can reveal.
Figure 14
Fig. 14. Visualization of point-based elevation data ( 4 .4 · 106 points; data obtained from http://www.OpenTopography.org/).

4.2.3 Point Data: Elevation and 3D Scanning

The extension to point cloud data lets us explore rendering datasets such as elevation scans from radar measurements or 3D object scans Fig. 14 shows an example of the former. The figure shows how points that are close together do not generate halos (planar areas), while for regions where points are further apart along the view direction more halos and, consequently, brighter shades are generated (e. g., note the trees in the foreground). Rows of trees are emphasized with a completely empty halo around them Fig. 15 shows how the technique can be applied to rendering "normal" 3D shapes that are represented by points on their surface. Notice here as well the effect of visually separating contiguous regions of points at depth discontinuities.

4.2.4 Mathematical Shapes

As a last example Fig. 16 shows a selection of much simpler and less dense datasets from knot theory. This illustrates that our method can also handle simple shapes with similar results as in previous work [11].

4.3 Parametrization

A good set of parameters for a dataset depends to a certain degree on the specific dataset. For the illustrations shown in this paper we chose wline and wstrip such that wline is between 4 and 8 times as large as wstrip, for point data the factor was between 8 and 27. The size of wline also depends on the specific data and needs to be smaller for datasets with more elements. The maximum displacement dmax, is set to 0 .01 for all illustrations in this paper. Setting dmax to zero has the effect of giving all lines a halo, potentially blocking other lines, see Fig. 2(c). In general, once a good setup for these parameters is found for a given dataset, they do not need to be changed for interactive exploration and filtering or when visualizing lines resulting from a different ROI.

Figure 15
Fig. 15. Point datasets representing the surface of 3D shapes.
Figure 16
Fig. 16. Visualizations of simple mathematical shapes from knot theory.
Figure 17
Fig. 17. The effect of using nonlinear displacement functions.

Unless otherwise indicated, we always use the same linear displacement function fdisplacement(x) = x. Changing this function can easily be accomplished by adapting the function in the shader or by using a non-linear gray-ramp texture. The resulting visual effect differs to some degree from previously shown images as shown in Fig. 17 and can be used to achieve the impression of more or less densely packed bundles. For example, using fdisplacement(x) = x2 results in less emphasis for the bundles but more individual lines being visible (Fig. 17(a)), while fdisplacement(x) = Formula has the opposite effect (Fig. 17(b)).

4.4 Performance and Limitations of the Technique

In Table 1 we give average frame rates for a selection of datasets. The measurements were taken on a 3GHz Intel Core2 Extreme with 4GB RAM, running Windows Vista, and using an NVIDIA GeForce 8800 GTX graphics card. The rendering performance for both lines and points is determined mainly by the number of lines, the number of vertices, the size of the dataset on the screen, and the size of the strips or quads. For the measurements, we maximized each visualization on the 812 × 600 pixel rendering window and then measured the average speed for animating a rotation, with vertical sync disabled and without anti-aliasing or filtering. The offline pre-processing to extract streamlines from 3D vector data took in the order of several seconds to several minutes and was done with VTK.

Table 1
TABLE 1 Performance measurements, sorted by dataset size.

Besides the obvious limit in the number of lines and vertices that the technique can handle as just indicated by the performance data, there are two aspects that are of further importance. One is that, while the technique works well when the data elements (lines or points) inherently form a surface or closely bundled structures, it performs not as well for datasets with less structured but still dense elements. For example, if a volume were to be filled with a dense set of random lines, the technique would not create meaningful visualizations. The second limitation is that the technique performs best for visualizing the outer layer of closely bundled elements. While filtering does allow to look at subsets of the data, it still does not allow to look beyond the surface of the visible structures. Transparency based on a given parameter cannot easily be added because this would require sorting based on individual line segments which would greatly diminish the technique's performance and, thus, its suitability to large and dense line datasets.

SECTION 5

Informal Evaluation

To evaluate our illustrations we conducted a small informal study of DTI-based fiber tract visualizations with four medical domain experts, three of them neurosurgeons and one a researcher in tractography. We showed them still images and the interactive tool, both in the regular and the anaglyphic versions. We were interested in their initial response but also asked questions about the quality of the illustrations, the ability to show detail and depth relations, and the usefulness for specific applications. We also asked about shortcomings, possible improvements, and potential applications scenarios for our technique.

The result from this evaluation was that all experts were impressed by the visualizations, commenting that they were "beautiful," "impressively good," that they "almost look like an anatomical specimen," and that they visualize "what the fibers would look like if a brain was dissected by an anatomist." All said that, compared to the tract visualizations they are used to (i. e., lines or tubes colored based on direction), our illustrative visualizations "show better depth relation and structure" and that they emphasize bundles well. One commented on the visible detail saying "one can really see how structures are fanning out." Looking at anaglyphic images, all liked that the fibers "really come out and show structure" and that the images are "extremely clear." All confirmed our design decisions and said that our technique would be particularly useful for illustration purposes, for example for using the created images in educational contexts such as brain atlases.

All domain experts used the term "very suggestive" in their descriptions, meaning that the illustrative character of the technique is very powerful and shows the bundling and path as well as depth relations very well. However, they also noted that our technique suggests the path of the visualized fibers would actually be like the real neural fibers in the brain, something that the underlying DTI data may not be able to provide. Thus, to avoid the illustrations showing something that does not actually exist they suggested using a fiber tracking method that does a better job at detecting fiber crossings (e. g., Q-Ball). Additional suggestions were to provide context by combining the technique with other data visualization methods such as volume rendering or by adding relevant structures such as tumors to the visualization. Moreover, while they all liked the interactive application, they all requested even more interactivity such as being able to select subsets of smaller fiber bundles that, e. g., connect two regions of the brain. We plan to integrate these suggestions in a future version of the tool.

SECTION 6

Conclusion

We have presented a technique for illustrative visualization of dense line datasets. We create depth-attenuated halos around lines that do not overlap each other if the lines are close in depth, but do occlude lines located further away in depth. This has the effect of emphasizing tightly bundled line structures and abstracting from less organized regions in the data. An additional important illustrative effect is the resulting visual depth clustering of visually connected regions. The visually connected regions portray surfaces implicitly existing in the dataset due to its inherent structure. These illustrative rendering techniques are augmented by traditional interaction and line rendering techniques such as filtering and depth cueing. While supporting the rendering at interactive to real-time frame rates depending on the size of the dataset, the technique is also capable of producing high-quality black-and-white renderings so that the results can easily be used in printed materials. In addition, it easily extends to point cloud datasets.

An informal evaluation with domain experts revealed that our visualizations are successful in illustrating brain fiber structures, in particular showing detail, emphasizing fiber bundles, and depicting spatial relationships. While these results are encouraging, we need to continue our evaluation and explore both a richer collection of data sources (i. e., other than DTI) and evaluate the technique in the other domains for which we have created visualizations. Moreover, combining the visualization technique with other methods can provide both context and additional detail that is necessary in some domains.

Additional future work includes, for example, adapting the process of turning lines into view-oriented triangle strips which consists of a data duplication part that unnecessarily uses too much memory. This can be avoided by using modern graphics cards extensions such as geometry shaders or the instanced arrays extension. In the case of point data, the point sprite extension could be used. The visual appearance could also be improved by exploring alpha-blending, for instance guided by the filtering process. By employing line style rendering techniques such as used in [42] it may even be possible to maintain the black-and-white character necessary for high-quality print output.

Acknowledgments

We thank Cris Lanting and Pim van Dijk from the BCN NeuroImaging Center in Groningen, NL, for the brain datasets used in this paper. The turbulent flow simulation dataset is courtesy of Martin Rumpf, Univ. Bonn, Germany. The armadillo and dragon datasets are from the Stanford Computer Graphics Laboratory. We also thank Alessandro Crippa, Moritz Gerl, Wladimir van der Laan, and Alex Telea for interesting discussions. This research is funded by the Dutch National Science Foundation (NWO), "VIEW" project, project no. 643.100.501.

A Width of the Depth-Attenuated Halos

Assuming a depth displacement that is proportional to the distance from the center line and, more specifically, that fdisplacement(x) = x, the width of the generated halo between two lines whalo can be derived as follows. Let Δ z be the relative distance in the z-direction of the two considered lines, then three possible cases need to be considered: Formula TeX Source $$w_{halo} \left\{ {\matrix{0 \hfill {{\rm{for 0}} \le \Delta z \le {\textstyle{{w_{line} d_{\max } } \over {w_{strip} }}}} \hfill \cr {{\textstyle{1 \over 2}}\left({w_{line} - {\textstyle{{w_{strip} \Delta z} \over {d_{\max } }}}} \right)} \hfill {{\rm{for }}{\textstyle{{w_{line} d_{\max } } \over {w_{strip} }}} < \Delta z < d_{\max } } \hfill \cr {{\textstyle{1 \over 2}}\left({w_{line} - w_{strip} } \right)} \hfill {{\rm{for }}\Delta z \ge d_{\max } } \hfill \cr} } \right.$$ Fig. 18 illustrates cases 1 & 2 using a blue and a red crossing line, resp.

Figure 18
Fig. 18. Figure based on Fig. 3(b), the black line in front (when looking in the viewing direction) is crossed by two other lines (blue and red line) further away from the viewer. The width of the halo Whalo depends on the relative distance Δ z of either of these lines to the line in front (indicated by the differently colored Δ z distances). In the figure, there is no halo between the black and the blue line, but there is a halo between the black and the red line. The halo does not grow further (maximum halo) when Δ z grows to be larger than dmax.

Footnotes

All authors are with the University of Groningen, the Netherlands; e-mail: m.h.everts|h.bekker|j.b.t.m.roerdink@rug.nl, isenberg@cs.rug.nl.

Manuscript received 31 March 2009; accepted 27 July 2009; posted online 11 October 2009; mailed on 5 October 2009.

For information on obtaining reprints of this article, please send email to: tvcg@computer.org.

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Maarten H. Everts

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Henk Bekker

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Jos B.T.M. Roerdink

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Tobias Isenberg

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