Visual Exploration of Multivariate Volume Data Based on Clustering - Scientific Visualization: Uncertainty, Multifield, Biomedical, and Scalable Visualization - page 168

16.3 User-Guided Clustering of Attribute Space
Instead of using completely automatic clustering approaches, it may be favorable to
keep the user in the loop. A simple way of doing this is to start with a coarse clustering
result and iteratively refine it in an adaptive manner. Ivanovska and Linsen [ 17 ]
presented an approach, where simple and efficient clusteringmethods such as median
cut [ 14 ], k -means [ 30 ], and c -means [ 7 ] are used to cluster multivariate volume
data, the results are visualized using a 2D slice viewer, and clusters are selected to
adaptively refine them by further splitting (i.e., clustering) operations. Because of
the simple clustering methods used, the process is highly interactive. The approach
was only applied to RGB color data, where the clusters can be represented by their
average color, which makes it easy to identify clusters for adaptive refinement.
A different approach for user-guided clustering is to interact in object space. The
user brushes in the volume visualization to select some samples and assigns to them
a cluster ID. Based on this sparse information about the desired clustering result, a
clustering of the full data set is obtained using machine learning techniques. Tzeng
et al. [ 38 ] presented an approach, where the user brushes on 2D slices using different
colors, where the colors function as cluster identifiers. The selected voxels of the
data set are used as training set for a neural network. With the trained network, the
entire data set in classified. The neural network is implemented on the GPU to assure
that computations can be done in an interactive setting. Thus, the selection can be
modified anytime by further brushing operations. The updated training set is then fed
to the neural network classifier, again. Tzeng et al. applied their approach to scalar
fields and RGB color data. El-Moasry et al. [ 11 ] presented an approach that builds
on this idea, but uses a rough set classifier instead of a neural network. The rough set
classifier reports back probabilities that a certain voxel belongs to a certain cluster.
The probability information can be used for uncertainty visualization. Figure 16.2
shows a result of the approach.
Dobrev et al. [ 10 ] present an approach that, in principle, embeds an automatic
clustering approach. However, it is shown that the clustering can also be generated
completely interactively by brushing on a parallel coordinates plot representing the
attribute space and seeing the selection in a linked volume rendering of the object
space. Although it is possible to create some meaningful clusters, the approach would
be very cumbersome for extracting higher-dimensional clusters with non-axis aligned
shapes.
16.4 Visual Encoding of Clustering Result
16.4.1 Object-Space Representation
The simplest way of displaying the result of clustering a multi-dimensional attribute
space is to use volume visualizations of the object-space representation of each
cluster and show the visualizations all next to each other. Tzeng and Ma [ 39 ]