Fusion of Visual Channels - Scientific Visualization: Uncertainty, Multifield, Biomedical, and Scalable Visualization - page 118

color, outline, symbol) would create difficulties for comparison and differentiation.
On the other hand, similar visual channels (e.g., red and green hues) might not deal
with occlusion effectively.
Botchen et al. [ 2 ] conducted a small study on visual channels in the context of
video visualization. They conducted a survey that rated the suitability of six visual
channels (i.e., color, luminance, opacity, thickness, symbols and textures) for three
data types (category, uncertainty and size), and optimized their selection of multiple
channels based on the rating. The proposed visual design, VideoPerpetuoGram, is
scalable to an arbitrary number of time steps.
Woodring et al. considered a more challenging problem of time-varying volume
visualization, and used constructive operations to combine different color channels
corresponding with different time steps [ 24 ] and to create combined effects for visu-
alizing set and numerical relationships between different time steps [ 23 ]. Hsu et al.
used color and outline channels for different time steps, in conjunction with spatial
layouts that separate different time steps [ 10 ].
One approach is to have one time step as a reference, and illustrate the rela-
tive changes of the succeeding (or occasionally preceding) time steps using a dif-
ferent visual channel. The illustration-inspired techniques proposed by Joshi and
Rheingans [ 12 ] exemplifies this approach.
12.5 Compression of Multifields
A main obstacle with multifield data is that they can exceed the number of visual
channels available, at least in a general sense. This is very reminiscent to the problem
of multivariate data when the aim is to reduce the dimensionality of the data for
display. A number of strategies have been devised to achieve this, what is called low-
dimensional embedding through dimension reduction . Note that in the following it is
assumed that the multifield data “live” in a spatial context where this spatial context
does not need to be a regular lattice. While spatial context is not a strict requirement,
the spatial coordinates could also be integrated into the analysis.
1. Principal component analysis (PCA) : Methods based on this technique would
first determine the covariance matrix of the multifield data. An eigenvector analy-
sis would then determine the k most significant axes onto which the multifield
data would be projected and then mapped to the available visual channels.
2. Multi-dimensional scaling (MDS) : These methods perform a linear or non-
linear projection of the data into a lower-dimensional space. Since this is an
optimization problem, many different techniques with different strategies are
available. Typically the quality of an embedding is measured by a stress metric
which is the RMS error of the point-wise distances in data space and the respective
distance in embedded space. For multifield data, one would performMDS on the
data and set k to the number of visual channels.
3. Linear Discriminant Analysis (LDA) : LDA is somewhat related to PCA but
unlike PC is does maximize to identify projections of highest variation, but instead