Image Processing Reference
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literature existed on topological analysis of scalar or vector data, the same is not
true for multi-field topology. For example, Morse-Smale complexes are based on
gradient lines, but in multifield data, the gradient is replaced by the Jacobian, a ten-
sor quantity, and it is far from clear what the equivalent of a gradient line might
be. Even were there to be an equivalent, the mapping to features in the underly-
ing phenomena is not clear—where the Morse-Smale complex can be understood
in terms of drainage patterns, such metaphors are not immediately obvious for s.
As a result, the challenges related to multifield topology are manifold, including
developing the underlying mathematics, insight and metaphors, as well as the usual
topological feature descriptions, algorithms, data structures, visualization methods,
and interfaces.
Min Chen on Standard Protocols:
One of the most fundamental challenges in multi-field visualization is to establish a
set of intuitive and effective protocols for using visual channels. Given a multi-field
data set, a “brute-force” visual design would be to juxtapose the visualizations of
individual fields. However, such a visual design cannot support many comparative
or combinational tasks effectively because of the difficulties in visual search for
spatially corresponding positions across many images. An alternative approach is
to depict information in the multi-fields in a comparative or combinational manner.
However, as existing visual representations have largely been developed for single
field visualization, combining such visual representations into a single visualization
will inevitable cause conflicts in using visual channels. For instance, if the color
channels are being used for one field, the other fields may have to make use of less
desirable channels. Furthermore, there is no commonly agreeable means to depict
the effect of constructive operations on different fields. For example, if one has
used the texture channel to depict the similarity and difference between two scalar
fields, perhaps one should not use such a channel for depicting the addition or union
of these two fields in the same application. Hence, we may challenge ourselves
with the following questions. Should there be some standard (or de facto standard)
visual designs or visual metaphors for depicting different constructive operators (e.g.,
addition, subtraction, mean, OR, AND, etc.)? Should there be some standard (or de
facto standard) protocols for visualizing some common configurations ofmulti-fields,
such as two or a few scalar fields, on scalar field and one vector field, and so on? Can
we evolve such protocols from some ad hoc visual effects, to commonly adopted
visual metaphors, and eventually to standardized visual languages?
Helwig Hauser on Multi-dimensional, Scientific Visualization:
One common notion of scientific data is to consider it as a mapping of independent
variables—usually space and/or time in scientific visualization—to a set of depen-
dent values, very often resembling some measurements or computational simula-
tion results that represent different aspects of a natural or man made phenomenon.
Traditionally, neither the spatio-temporal domain nor the dependent variables are
of higher dimensionality. A larger number of dependent values, however, leading
to multi-variate data (as a special case of multi-field data), however, has recently
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