Biomedical Engineering Reference
In-Depth Information
5.3.2.4 Scientific Data Visualization
Data visualization involves the exploitation of statistical, computer graphics, and geomet-
ric modeling techniques to transform numeric or symbolic datasets into graphical plots
and displays that help reduce the difficulty of interpreting the behavior of complex phys-
ical systems. These techniques are used to correlate huge volumes of data, reduce the
quantity and dimensionality of the original data to a manageable size, and graphically
encode as much information as possible into the visual display. Key information embed-
ded within the data is represented in the display space using color difference, shape
parameters, relative proximity of graphical icons, and movement of the icons over time.
Problems in visualization arise from the various ways in which different levels of numeric
and symbolic data can be presented to a human observer, and how the individual's per-
ception of these graphical representations affect the final interpretation of the underlying
information.
Over the past decade two branches of visualization research have evolved:
scientific data
and
information visualization
. Techniques that generate graphical displays from raw or trans-
formed experimental data are usually referred to as scientific data visualization. Raw data
are measured signals acquired directly by the transducer while transformed experimental
data, also known as analytical data, is created using mathematical tools that modify or com-
bine single or multimodal raw data into new entities for enhanced interpretation. In scien-
tific data visualization a variety of mathematical techniques are used to transform
multidimensional multivariate datasets into simple graphical objects called
glyphs
that pro-
vide scientists and engineers with a clearer understanding of the underlying system behav-
ior. Information visualization, in contrast, focuses on the graphical display of document
databases and information spaces. Clearly, the functionality and presentation of informa-
tion by the visualization application tool depends upon the tasks to be performed by the
end user and the type of graphical cues needed to represent the data.
The SOFM (15) has been investigated as a visualization tool because of its ability to
internally order and correlate data without making any assumptions on the underlying
relationships present in the data (57-59). While a majority of the glyph-based methods are
directed towards generating graphical forms for individual data vectors, the SOFM clus-
ters the data based on inherent similarities and presents information on the data by ana-
lyzing relationships between the clusters. Knopf and Sangole (58,60) describe how the
spherical SOFM can be utilized to represent arbitrary numeric data vectors as a closed 3D
form. Local surface distortions and colors are introduced to the spherical lattice to display
the local statistical variance or distance metrics between neighboring units. The shape
transformation mechanism is summarized in Figure 5.11. The nodes of the tessellated
sphere represent cluster units and each is defined by a weight vector
w
ijk
.
The relative similarity, dissimilarity, or variation amongst the vectors assigned to a clus-
ter unit or between units in a common map can be displayed on the spherical SOFM lat-
tice using a metric or measure-of-information. The selection of this metric is application
dependent and defined by the observer such that it quantifies a desired characteristic of
the dataset to be displayed on the 3D glyph (60). Common metrics include the Euclidean
distance between the cluster unit and the center of the entire map, and the magnitude of
each unit's weight vector. The standard deviation of all data vectors assigned to a partic-
ular cluster unit is another measure of information that can be used. In this manner, each
unit on the spherical lattice is assigned a scalar value based on a metric that reflects the
type of information required by the observer. The computed metric is then mapped onto
the various visual dimensions of the graphical primitive to generate a unique, repro-
ducible color-coded closed surface of the original dataset. Deformation is introduced in
the spherical SOFM during vector projection using a technique similar to the extended
Gaussian image mapping method that generates spherical representations of objects in an
