Visual Exploration of Multivariate Volume Data Based on Clustering - Scientific Visualization: Uncertainty, Multifield, Biomedical, and Scalable Visualization - page 165

Kindlmann and Durkin [ 21 ]. They proposed using 2D histograms of the value and the
magnitudes of first- or second-order directional derivatives of a scalar field to define
transfer functions. Kniss et al. [ 22 ] extend their work by introducing a set of direct
manipulation widgets for multi-dimensional transfer functions. For vector fields,
Daniels II et al. [ 9 ] presented an approach for interactive vector field exploration by
brushing on a 2D scatterplot of two derived scalar properties of the vector field.
When dealing with multivariate volume data, the number of attributes per sample
is typically (significantly) larger than two or three. Hence, purely interactive methods
are of limited use for selecting regions of interest. Automatic components help to
alleviate the problem. The segmentation of the multi-dimensional attribute space
can be achieved by employing a clustering method. Automatic clustering methods
of multi-dimensional spaces is an intensively researched topic and many different
methods can be applied, see Sect. 16.2 . Also, clustering methods with user guidance
are of interest in this regard, see Sect. 16.3 .
With the obtained clustering result, the volume visualization parameters can be
set to highlight the areas in object (or physical) space that correspond to the clusters
in attribute space. The mapping from the clustering result to the volume visualiza-
tion parameters can be obtained automatically, but due to occlusion one needs to
restrict the volume visualization to a subset of clusters. It is desirable to have an
interactive selection of these subsets. This selection mechanism replaces the interac-
tive operation in a high-dimensional attribute space. However, it still requires some
suitable visual encoding of the clustering result to allow for intuitive interactions,
see Sect. 16.4 . The requirements to this visual encoding are that it scales well in the
number of dimensions and in the number of samples, as we may be dealing with a
larger number of attributes and the underlying multivariate field is typically sampled
at many positions of its volumetric domain.
The visual encodings of the clustering result lead to coordinated views of the
object-space volume visualization and the attribute-space cluster visualization, see
Sect. 16.5 . Multiple visual encodings of the clustering results and its value distrib-
utions in attribute space may be coupled with the volume visualization to allow for
an interactive exploration of the clustering result.
Finally, one may also need to consider that the automatic part of the pipeline, i.e.,
the clustering step, may not produce the optimal results. This may be due to some
limitations of the clustering methods or due to the fact that the user may bring in
some domain expertise that goes beyond what one can extract from the raw data.
Consequently, an interactive modification of the clustering result is also of interest,
see Sect. 16.6 .
In this chapter, we present and discuss different approaches for the individual steps
described above. We conclude the paper with open problems and future directions,
see Sect. 16.7 .