Parallel Coordinates
Yisheng Chen & Tianfang Xu
Background
First introduced by Inserberg and Dimsdale during the 1980's and early 90's, Parallel Coordinate is a two-dimensional technique to visualize multidimensional data sets (Inselberg and Dimsdale, 1990). In the past few years, researchers have been working on improving this technique for better data investigation and user interaction, such as data clustering (Fua et.al., 1999), brushing (Martin and Ward, 2003; Hauser et.al, 2002.) and using curves to resolve the difficulty of differentiate distinct lines sharing same points in the parallel coordinates (Graham and Kennedy, 2003). With all these improvements, Parallel Coordinate becomes very effective in visualizing relationship between designated neighboring dimensions.
Statement of Work
In our project, we will use Parallel Coordinate to help us analyzing the motion features. More specifically, we will focus on the visualization of the seven Hu moments, which is a set of seven translation, rotation and scale invariants .
Initially we had a frame sequence of a ballet dancing (1023 frames), which is generated from motion capture data. Then we extracted the silhouettes from the sequence and generated the Motion History Images (MHI), and finally we calculated the Hu moments (mhi_moment.txt).
Each MHI is represented by the seven Hu moments as a feature vector, and we can use the feature vector to classify existing actions and recognize new actions. Most works on classification and recognition are using distance as the metric to measure the difference between two MHIs. When the number of MHIs is big, it is very difficult to quickly and effectively classify the MHIs into different groups with similar feature values and recognize MHIs fulfilling the specified requirements. This inspires us to seek help from Parallel Coordinates to visualize the Hu moments, and do a better job by using powerful human visual conceptual system.
Though Parallel Coordinate is a well-known technique for information visualization, it still has some disadvantages. For example, due to the limited display space and high load of information representation (a single point in N-dimension will be represented as a polyline in Parallel Coordinates), the density of polylines in the 2-D graph is very large. Thus it is very hard to quickly identify and get focus on the portion we are interested when there is large number of data. Also, it lacks an effective way to weight the importance of different dimensions and get rid of those provide trivial information. We will try to improve this technique in terms of these disadvantages.
Both video clips are using Divx codec.
Data Overview
User Interface
Using Matlab, we implemented several Focus+Context techniques:
1. User can select specific coordinates in the list box and also can exchange the display order by selecting and dragging.
2. User can overview the frames they are interested in by inputting the frame range
If user press play button, the data will be displayed frame by frame, and the corresponding image will be displayed too. demo
User can also input a particular frame number to view the corresponding data and image. Another way is to move the slider bar .
3. User can limit the shown data by specifying the data value range.
4. Matlab has provided Zooming and Panning tools. As the figure shown, user can pick a specific datum by clicking LMB, and then the datum is highlighted by red, and the corresponding image is shown.
5. We support B-Spline.
6. We support hierarchical cluster view. User can classify the data by inputting the number of clusters he wants. Every cluster is shown by a distinct color, and the data range in the cluster is shown by a vertical line along every coordinate. If a specific cluster is selected, the closest frame to the mean of the cluster is shown.
7. To view how a single dimension value reflects the image, we place a Sort button to sort all data with respect to a specified dimension, and open a new window to play the sorted images.
Explore the properties of the data
first let look at the majority of the dataset.
Explore the data column by column
M1
We selected some frames according to their m1 values, from large to small. From those images, our guess is m1 is a parameter representing the spread of a image.
Unfortunately, after we used Sort function and watched how the images change along with m1, we rejected our initial guess. Video
Max(m7) vs Min(m7)
Symmetric vs Asymmetric
Correlation
M1 vs M2
M4 vs M5 vs M6
References
Y.-H. Fua, M.O. Ward and E.A. Rundensteiner, "Hierarchical Parallel Coordinates for Exploration of Large Datasets," Proc. IEEE Visualization '99, IEEE Computer Society Press, San Francisco, California, USA, October 24-29, 1999, pp. 43-50.
Martin Graham, Jessie B. Kennedy, "Using Curves to Enhance Parallel Coordinate Visualizations",. Proc. IEEE InfoVis 2003: 10-16.
H. Hauser, F. Ledermann and H. Doleisch, "Angular Brushing of Extended Parallel Coordinates," Proc. IEEE InfoVis 2002, IEEE Computer Society Press, Boston, Massachusetts, USA, October 28-29, 2002.
A. Inselberg and B. Dimsdale, "Parallel Coordinates: A Tool for Visualizing Multidimensional Geometry," Proc. IEEE Visualization 1990, IEEE Computer Society Press, San Francisco, California, USA, October 23-25, 1990, pp. 361-378.
A.Martin and M.O.Ward. “High dimensional brushing for interactive exploration of multivariate data,” Proc. IEEE Visualization 1995, pp. 271-278.
H. Siirtola, "Direct Manipulation of Parallel Coordinates," Proc. Information Visualization IV'00, IEEE Computer Society Press, London, UK, July 19-21, 2000, pp. 373-378.