A sketch-based interface for classifying and visualizing vector fields
Summary (4 min read)
1 INTRODUCTION
- Flow visualization is relevant to many areas of science and engineering from understanding the evolution of universe, analyzing weather patterns, to designing more efficient engines for cars.
- One area of flow visualization can use more innovations is visualization of 3D vector fields.
- Among different solutions to this problem, automatic clustering plays a vital role towards effective understanding of the flow patterns.
- The first category is based on voxel-wise analysis which classifies similar contiguous vectors so that the whole vector field can be divided into several cluster regions.
- Several methods can be used to represent field lines and measure the similarity between them.
3 OVERVIEW
- Figure 1 illustrates the flowchart of their vector field sketching and clustering process.
- The approach introduces user interaction into the clustering.
- The authors assume that they are given enough field lines that could capture as many features as possible in the vector field.
- The authors point out that their method can work with existing seeding strategies that capture different aspects of flow features.
- The resulting field lines may provide valuable information for purposeful sketching.
3.1 Sketching for Field Line Clustering
- For field line clustering, their approach includes two steps: 2D curve selection [22, 2] and similar 3D field lines clustering [14].
- Based on these projected curves, the authors utilize the string matching approach to find the field line that is most similar to the input.
- The only difference is that one 3D curve should be represented by both curvature and torsion.
- After a few iterations, the entire vector filed would be partitioned into different clusters.
- Alternatively, representative field lines from each group can be used for selective display so that a less cluttered visualization can be realized while distinct flow patterns are exhibited.
3.2 Sketching for Template Query
- For field line template query, a list of clusters is pre-generated using a hierarchical clustering algorithm during preprocessing.
- The algorithm allows the user to change the number of clusters interactively at runtime.
- This similarity comparison helps narrow down a potentially large number of templates to only a few most similar ones for user selection.
- As the user keeps drawing the pattern, the template reordering becomes more accurate.
- The user can simply select one from the filtered template list anytime during her drawing and the corresponding filed line cluster will be highlighted in the display.
4.1 Representation of 2D User Sketching
- A meaningful representation of the input drawing is required for the following 2D curve selection and 3D curve clustering.
- In Figure 2(a), the angular difference at the first four points are positive and those at the last three points are negative since the proceeding direction of the curve changes from counterclockwise to clockwise.
- However there is still one problem remaining.
- According to this feature generation method, different field lines would have different numbers of curvatures in the feature representation.
4.2 Matching 2D Field Line Projections
- In their system, the user can observe the vector field from different points of view.
- At a certain viewing direction, the user may find some pattern she is interested in and she can sketch this curve pattern in the given 2D interface.
- The system will find similar field line projections in the 2D space under the current view.
4.2.1 String Matching
- The authors use the string matching approach to find similar curves based on the user’s input.
- To measure the difference between strings, the authors employ the edit distance.
- For the 2D curve representation, every primitive vector composing one string is only one-dimensional which is the curvature.
- The reference curve will be the user’s sketching and all the other lines will be matched accordingly to identify the most similar one.
- One critical issue with string matching is the definition of the cost function.
4.2.2 Repetition, Scale, and Tolerance in Patterns
- If streamlines are traced very long due to the underlying flow pattern, the total length and angle changes of each field line can be very large.
- According to the angle changes along the curve, only sample points at which the absolute value of total angle change is less than a certain value are considered.
- The change of scales for certain flow patterns is an important aspect and should be taken into consideration in curve matching as well.
- In some cases, flow patterns of small size are just noise, but in others, they are probably important areas in the vector field.
- This also makes it possible to show how different groups of field lines are similar to each other as the tolerance parameter varies.
4.3 Matching 3D Field Lines
- Only matching curves in 2D does not complete their work because similar field lines in 3D are likely to have quite different shapes after projected onto the 2D viewing plane.
- The authors goal is to find all similar field lines, and therefore, the authors need to classify field lines in the 3D space.
- The authors point out that the 2D curve matching method can be extended to 3D.
- In 3D, a curve can be uniquely represented by its curvature and torsion while in 2D, using only the curvature information suffices.
- The curvature and torsion at each sample point can be organized into a two-dimensional vector, which serves as a primitive in string matching.
5 SKETCH-BASED TEMPLATE QUERY
- For automatic clustering, the authors use a typical agglomerative hierarchical clustering method.
- All the initial field lines are stored in the leaf nodes.
- When merging two clusters into a new one, the representative string for the new cluster is the mean string of the merged clusters.
- Then, the selected clusters are displayed using the projections of their representative field lines.
- The authors first sample the 2D projection of the field line, and then accumulate the angles of the two consecutive sample line segments, where a larger angle represents more information shown in the 2D projection and therefore a higher viewpoint quality.
6.1 Results
- The authors experimented with their user-centric approach on several flow data sets.
- The first one is the velocity vector field of the hurricane Isabel data set, provided by the National Science Foundation and the National Center for Atmospheric Research (NCAR).
- The third one is the flow field in a computer room.
- Clearly, all rendered images contain a great deal of clutter.
- In the following, the authors demonstrate how their sketch-based interface helps the users specify line patterns and cluster the flow fields.
6.1.1 Sketch-Based Clustering and Template Query
- Examples of the user sketching and the matching streamlines are displayed in Figure 5 (a) and Figure 6 (a) for the hurricane and computer room data sets, respectively.
- The experiments show that their 2D pattern matching and 3D streamline clustering algorithm work pretty well for different kinds of patterns: straight or curved, long or short.
- The user can draw close to what have been observed and similar streamlines will be displayed interactively.
- This ability is very useful for exploring a complex flow data and isolating one interesting cluster at a time.
- The authors system dynamically identifies the most similar templates as the user sketches the pattern on the fly.
6.1.2 Scale and Similarity Threshold Control
- Streamlines sharing the similar shape may have different scales.
- To allow the user to explore the scale, the authors provide a slider where the user can change the magnitude threshold to brush similar streamlines at different scales.
- Figure 7 shows examples with the three data sets.
- This capability is useful as the user may pay attention to larger scale features first and then focuses on smaller scale features in local regions.
- As the user varies the tolerance value, she can have an intuitive understanding of how streamlines with different degrees of similarity differ from each other and how they are distributed over the space.
6.1.3 Visualization of Multiple Clusters
- In their system, the user can iteratively explore the flow data and brush the streamlines to identify multiple clusters in order.
- Once the user is satisfied with her exploration results, the system can display multiple clusters with different color, opacity, or rendering styles to differentiate them.
- The authors can also selectively display a subset of streamlines from each cluster for a less cluttered view.
- Figure 9 shows these visualizations with the three data sets, respectively.
- Compared with the original rendering with all streamlines displayed, Figure 9 demonstrates that the authors can now generate a clearer and more meaningful picture to reveal the different flow patterns.
6.2 Discussion
- During the preprocessing, the authors trace a large number of field lines from the input vector field.
- The authors then parameterize these field lines using the B-spline.
- The algorithm accepts fuzzy input in the sense that the user can sketch patterns close to field line 2D projections.
- Another aspect that needs improvement is the cost function for string matching.
- For a better similarity matching, the cost function should be adaptive to the characteristics of the flow fields.
7 CONCLUSIONS
- Three-dimensional vector field visualization stays a challenging problem.
- The sketch-based technique the authors have introduced complements existing methods by offering a new way to probe and dissect a flow field.
- It dictates a user centered and domain knowledge directed process, which the authors believe is key to the understanding of large and complex flow fields.
- For further work, the authors will involve scientists in the evaluation of their technique.
- In particular, sketching and brushing may be done creatively and quite naturally through touch and stereoscopic interfaces.
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Citations
90 citations
65 citations
Cites methods from "A sketch-based interface for classi..."
...Arnold-Beltrami-Childress (ABC) incompressible flow which is an exact solution of Euler’s equation [30], the liquid flow between two parallel planes [31], the air flow around a car [1], the air flow in a computer room [32], the heat flow around a cooking crayfish [1], a synthesized flow field consisting of five critical points [33], the compressible downflow solar plume [34], the flow around a confined square cylinder [35], the flow of core-collapse supernovae [36], a procedurally generated tornado [37], and swirls resulting...
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65 citations
Cites methods from "A sketch-based interface for classi..."
...Sketching has also been used to generate vector fields, allowing users to draw streamlines and quickly simulate fluid flows [40, 50]....
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64 citations
Cites background from "A sketch-based interface for classi..."
...Similarities can then be defined by the presence or absence of common feature types, shapes, or properties (see for example [32, 19] for feature based similarity metrics in flow fields)....
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61 citations
References
44 citations
"A sketch-based interface for classi..." refers background in this paper
...[19] constructed tract distances between fiber tracts from dual-rooted graphs where both local and global dissimilarities are taken into account....
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42 citations
"A sketch-based interface for classi..." refers background or methods in this paper
...[4] presented a clustering technique based on the centroidal Voronoi tessellation (CVT) to separate the vector field into a fixed number of groups....
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...[10] extended the work in [4] by employing different error metrics in the variational clustering....
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34 citations
"A sketch-based interface for classi..." refers methods in this paper
...For field line clustering, our approach includes two steps: 2D curve selection [22, 2] and similar 3D field lines clustering [14]....
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27 citations
"A sketch-based interface for classi..." refers background in this paper
...[10] extended the work in [4] by employing different error metrics in the variational clustering....
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22 citations
"A sketch-based interface for classi..." refers methods in this paper
...The mean string is calculated using the approach presented in [15]....
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Frequently Asked Questions (2)
Q2. What have the authors stated for future works in "A sketch-based interface for classifying and visualizing vector fields" ?
For further work, the authors will involve scientists in the evaluation of their technique. To support real-world applications, the technique must be extended to handle time-varying vector fields, that is to extract and track complex flow features over time. The authors will also develop advanced interfaces and interaction techniques for such a user centric approach to flow visualization. In particular, sketching and brushing may be done creatively and quite naturally through touch and stereoscopic interfaces.