VORONOI DIAGRAM BASED DIMENSIONAL ANCHOR ASSESSMENT FOR RADIAL VISUALIZATIONS - Information Visualisation: Techniques, Usability and Evaluation - page 256

coordinates, star glyphs, and scatter plot matrices. These authors do not
include the more recently developed general class of NRVs.
By examining the individual properties of each visualization, an
individually tailored metric is developed to assess clutter. We take a
similar approach in that our methods are based, initially, on qualitative
notions of what specifically constitutes an informative NRV. Their work
on reducing clutter via dimension reordering explores an important idea
that we find useful for our future work on dimensional anchor placement
in NRVs. Bertini and Santucci have done extensive work in the area of
visualization quality and clutter reduction [8]. Their work is based
principally on sampling digital images. They use several clutter related
metrics to validate the resizing and reordering of axes in parallel
coordinates [8].
While working exclusively in two dimensions, these authors claim that
their principles work more generally with any visualization such as
RadViz that allows visual elements to overlap each other. Their work [8]
provides many possible avenues for work in visualization quality.
We are motivated to examine Voronoi partitioning to define regions of
the image space and then proceed to do the perceptual non-uniform
sampling. In Section III our work is seen to diverge from that of Bertini
and Santucci in that we do not concern ourselves with the detailed pixel
level aspects of visualizations. For example, a Voronoi partitioning of the
image space at once divides the image space into rigorously defined
regions. These regions have well studied theoretical properties which we
introduce later and which provide direction for future work. We prefer
generating these regions over their method of dividing the image space
into an 8×8 pixel grid. Also, NRVs may be of arbitrary dimension and we
wish to pursue methods which scale beyond two dimensions.
In Section II we introduce the method of dimension selection we will
use for testing the visualization quality metric we describe in Section IV.
Our metric will work with any method of dimension selection. We chose
one method here to focus on the visualization quality metric itself. Section
III contains an introduction and summary of the Voronoi diagram on
which our method is based. Section V contains examples of applying our
Voronoi-based quality metric to several real data sets. Section VI is both a
summary of our current work and an outline of open problems.