Fusion of Visual Channels - Scientific Visualization: Uncertainty, Multifield, Biomedical, and Scalable Visualization - page 119

it seeks to model the difference between the classes of data. This assumes that
some clustering or classification of the data exists. An inherent constraint of LDA
is that the number of remaining dimensions cannot be below the number of classes
else overlap in the embedded space will occur. Thus, for the multifield data case
one would first perform data clustering, say via k -means setting k to the total
number of available visual channels and then perform LDA.
4. Information-Theoretical Analysis : This approach seeks to identify spatial
regions where different fields may or may not have similar information or a similar
amount of information. Information measures, such as mutual information can be
used to quantify the levels of similarity. Based on such a measurement, different
fields can be fused together, for example, by computing a weighted average of
their values at each point. Haidacher et al. used this approach to design a joint
transfer function in visualizing multiple volume datasets from different imaging
modalities [ 9 ].
5. Expert-guided dimension reduction : PCA,MDS, LDAcan be guided by experts
via suitable visual interfaces. This has come to be known as visual cluster analysis,
where experts use information visualization tools to guide the clustering, the
selection of the principal components, the weighting of the dimensions, and the
selection of influential data points. For multifield data the expert would use a
bi-modal interface consisting of an information display and a suitable scientific
visualization display to interactively and iteratively steer the insight gained.
Lawrence et al. [ 14 ] present a technique that can fuse an arbitrary number of
aligned images into a single color or intensity image. Their method falls into the
second grouping of above, i.e., MDS-based compression. They specifically target
multi-spectral imagery as obtained from remote sensing. They use an iterative stress
majorizationmethod in conjunctionwith clustering to determine the low-dimensional
subspace into which the solution is embedded. A very useful feature of their algo-
rithm is that it allows users to incorporate direct constraints onto themapping process.
This, for example, allows for better preservation of object colors that a user may want
to maintain.
References
1. Bertin, J.: Semiology of Graphics: Diagrams, Networks. ESRI Press, Maps (2008)
2. Botchen, R.P., Bachthaler, S., Schick, F., Chen, M., Mori, G., Weiskopf, D., Ertl, T.: Action-
basedmultifield video visualization. IEEETrans. Vis. Comput. Graphics 14 (4), 885-899 (2008)
3. Cai, W., Sakas, G.: Data intermixing and multivolume rendering. Comput. Graphics Forum
18 (3), 359-368 (1999)
4. Chen, M.: Combining point clouds and volume objects in volume scene graphs. In: Proceedings
of Volume Graphics pp. 127-135 (2005)
5. Chen, M., Silver, D., Winter, A.S., Singh, V., Cornea, N.: Spatial transfer functions—a unified
approach to specifying deformation in volume modeling and animation. In: Proceedings of
Eurographics/ACM Volume Graphics, pp. 35-44 (2003)
6. Chen, M., Tucker, J.V.: Constructive volume geometry. Comput. Graphics Forum 19 (4), 281-
293 (2000). A short version of the paper was presented in VG99 (July 1999)