Image Processing Reference
In-Depth Information
transformation to RGB color for display. In essence, one may regard this fusion as
a mapping from H to L where H is the original and L the reduced number of chan-
nels, with the latter being three in this case. These types of reductive mappings are
often encountered in low-dimensional embeddings of high-dimensional data. Such
embeddings are ill-defined once the number of significant principal components in H
is greater than L, which is most often the case. Hence, when applying such techniques
for channel fusion, one must make certain trade-offs which are also determined by the
type of dimension reduction technique used. There are a great many of these, some
linear (PCA, LDA, and others) and some non-linear (MDS, LLE, and others). The
former require some kind of component thresholding for channel reduction, while
the latter suffer from distortion problems. Since in our specific case, both thresh-
olding and distortion will affect the color composition of the display—as opposed
to the spatial layout—the effects are possibly more noticeable. This leaves much
room for further study. For example, it will be interesting to examine to what extent
feature analysis and user-defined or learned constraints can be used to alleviate or
control the adverse effects of dimension reduction in color display. A targeted and
intuitive user interface might be needed to determine the appropriate fusion map-
ping. Finally, since gradients and higher-order derivatives are often employed in the
graphics rendering of the data, it will be beneficial to study how the tensor resulting
from high-dimensional derivative calculus can be interpreted for shading and other
gradient-enhancements in 3D.
Vijay Natarajan on Categorizing Relationships between Fields:
Scientists try to understand physical phenomena by studying the relationship between
multiple quantities measured over a region of interest. A characterization of the
relationship between the measured/computed quantities will greatly enable the
design of effective techniques for multifield visualization. For example, the depen-
dence between fields could be linear or non-linear, the fields could be statisti-
cally correlated, or the relationship can be inferred using information theoretic
measures. A challenging problem in this context is the categorization of different
types of relationships and the design of measures that quantify the relationship in
each case.
Harald Obermaier on Field Prioritization:
Modern simulation andmeasurement techniques can generate large numbers of fields
spanning a wide range of types. While some of these fields may be crucial for the
understanding and analysis of the behavior of the system, others may be used to
enhance or extend the insights gained bymulti-field visualization, while further others
are largely irrelevant from an application or visualization point-of-view. Such a static
prioritization of fields in a multi-field setting limits the potential of in-depth visual
analysis especially in the area of application-driven data analysis, where the focus
of interest can change during exploration. Future research in (interactive) multi-field
visualization has to develop and integrate techniques that allow for a dynamically
changing focus or field prioritization. Especially for inhomogeneous field types the
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