Table 1. A Taxonomy of Colormaps based on Data Type, Representation Task, and
Principles of Perception.
Figure 1. Sensitivity to Spatial Variations of Hue and Luminance.Lawrence D. Bergman
bergman@watson.ibm.com
Bernice E. Rogowitz
rogowtz@watson.ibm.com
Lloyd A. Treinish
lloydt@watson.ibm.com
IBM Thomas J. Watson Research Center
Yorktown Heights, NYIntroduction
Visualization is a process of mapping
data onto visual dimensions to create a visual representation. A successful
visualization provides a representation which allows the user to gain insight
into the structure of the data, or to communicate aspects of this structure
effectively (Bertin [1967]; Tufte [1983]; Cleveland [1991]). Even with modern
visualization systems, which give the user considerable interactive control over
the mapping process, it can be difficult to produce an effective visualization.
One strategy for improving this situation is to guide the user in the selection
of visualization parameters. In our previous work, we have described an
interactive rule-based architecture for incorporating such guidance, and have
described certain perceptual and cognitive rules which may be relevant (Rogowitz
and Treinish [1993a]; Rogowitz and Treinish [1993b]; Rogowitz and Rabenhorst
[1994]).
In this paper, we focus on improving the user's selection
of colormaps. To do so, we have built a library of colormaps, and a set of
perceptual rules for selecting appropriate maps based on the structure of the
data and the goal of the visualization. We have encapsulated this rule-based
colormap selection process as a tool, PRAVDAColor, in the IBM Visualization Data
Explorer software package, and demonstrate how this module can be incorporated
into visualization applications involving the mapping of color onto two- and
three-dimensional surfaces. This implementation demonstrates the viability of
the technique, and provides a testbed for evaluating the rules.
Interactive Rule-Based Architecture
We have
previously presented a rule-based architecture called PRAVDA (Perceptual
Rule-Based Architecture for Visualizing Data Accurately) for assisting a user in
making choices of visualization parameters (Rogowitz and Treinish [1993a];
[1993b]). This architecture provides sets of appropriate choices for
visualization based on a set of underlying rules which are used to constrain
operations (e.g., selecting a colormap, selecting iso-contour line color). Rules
incorporate information about the data, which we call metadata, such as minimum,
maximum, or spatial frequency, and also information supplied by the user.
The architecture also provides for linkages between rules
that control different visualization operations, with a choice of parameters for
one operation constraining choices that are available for others. For example,
if the user selects a colormap, that information is fed back to the operation
for selecting contour lines, where rules constrain the parameters of the contour
lines depending on which colormap has been selected. Hence, if the contour lines
are superimposed over a dark region, as defined by the colormap, legibility
rules would constrain the set of color choices to those offering sufficient
luminance contrast to be detectable (Carswell and Wickens [1990]). This network
of linked, intelligent operations help guide the user through the complex design
space of visualization operations.
In our previous work, we have described the general
principles for implementing such an assemblage of rule-based visualization
operations. In this paper, we describe a full implementation of one of these
operations, colormap selection. In PRAVDAColor, perceptual rules constrain the
set of colormaps offered to the user based on system-provided metadata (data
type, data range), metadata computed by algorithm (spatial frequency) and
metadata provided by the user (the visualization task). This is in contrast to
previous rule-based systems for visualization which do not explicitly support
user tasks nor color perception in the guidance they offer (e.g., Senay and
Ignatius [1994]).
Rule-Based Colormap Selection - Limitations of Current Technology
Perhaps the most common operation in visualization mapping the
values of a variable onto a color scale. Despite the importance of this
operation, the creation and selection of colormaps is often not adequately
supported in modern visualization systems, which typically offer the user a
default color map and a tool for creating custom colormaps. More importantly,
however, these systems do not guide the user in selecting which colormaps will
help the user understand the structure of the data, segment the data
meaningfully, or highlight important characteristics of the data.
The most common default colormap, the rainbow colormap, is
a hue-based scale from blue, through a rainbow of colors, to red. When this
scale is mapped onto scalar data, the user is conceptually mapping a linear
scale in hue onto a scalar variable. Perceptually, however, this scale does not
appear linear. Equal steps in the scale do not correspond to equal steps in
color, but look instead like fuzzy bands of color varying in hue, brightness and
saturation. When mapped onto scalar data, this colormap readily gives the user
the erroneous impression that the data are organized into discrete regions, each
represented by one of the rainbow colors. This can lead the user to infer
structure which is not present in the data and to miss details that lie
completely within a single color region (Rogowitz, Ling, and Kellogg [1992];
Rogowitz and Treinish [1993a]).
Some visualization systems provide the user with tools for
creating alternatives to the default colormap. These custom colormap facilities
allow the user to construct almost any conceivable colormap, but tend to be
difficult to use for creating complex colormaps. This inadequacy has led us to
develop our own colormap generation tool, described below. Even when an adequate
tool is provided, moreover, deciding what colormap to create is essentially an
unbounded problem. Some systems, such as Interactive Data Language, address this
problem by providing a library of colormap lookup tables (RSI, 1993). They do
not, however, provide guidance about their application or alert the user to
constructs that may introduce visual artifacts. In this paper, we improve on
this approach by offering the user colormaps guided by principles of human
perception. In this way, PRAVDAColor can offer the user a richer set of choices
than a single default colormap, while ensuring that each choice is appropriate
to the user's visualization task and the data being represented.
A Taxonomy for Colormap Selection
Table 1 shows our
working taxonomy for the generation of colormaps. This table both incorporates
recommendations currently in the literature, and provides new contributions,
especially in the incorporation of spatial frequency.
Following other researchers (Della Ventura and Schettini
[1993]; Carswell and Wickens [1990]; Ware [1988]; Robertson [1988]; Robertson
[1994]; Lefkowitz and Herman [1992]), we find the data types described in
measurement theory to be very powerful in characterizing data representation
strategies. The data type is shown in the left-most column. Currently, we
support interval and ratio data, but plan to extend this approach to include
ordinal and nominal data types. For each data type, we distinguish between low
and high spatial frequency data, depicted in the second column.
The next three columns contain recommendations on creating
colormaps for these eight data types which are appropriate for three different
representation tasks. Following our earlier work (Rogowitz, Ling, and Kellogg
[1992]; Rogowitz and Treinish [1993a]), an isomorphic task is one where the goal
of the representation is to faithfully reflect the structure in the data. In a
segmentation task, the goal is to divide the data into perceptually distinct
categories. In a highlighting task, the goal is to call attention to particular
features in the data.
The notes within each cell show our understanding so far
of which types of colormap fulfill the requirements for each type of data for
each task, broken down by spatial frequency. The following section describes the
psychophysical rationale underlying these selections.
Isomorphic Representation of Interval and Ratio Data
In order to accurately represent continuous data, the visual
dimension chosen must appear continuous to the user. In an MRI image, for
example, the degree of magnetic resonance, a continuous variable, is represented
as a gray-level because continuous variations in gray-scale appear continuous to
the user. That is, if the resonance increases monotonically over a spatial
region, the brightness of the image will appear to increase monotonically over
that spatial region. An inappropriate colormap, however, could create a visual
representation which does not look monotonically increasing, for example, the
default colormap described above.
Candidate colormaps which preserve the monotonic
relationship between data values and perceived magnitude can be drawn from
experiments done by Stevens [1966]. He identified a set of sensory dimensions
(visual, auditory, and tactile) for which a monotonic increase in stimulus
intensity produced a monotonic increase in perceived magnitude. In particular,
Stevens found the shape of this relationship to be a power law, with each
sensory dimension characterized by the exponent of this power law. Perceived
brightness obeys a power relationship with physical intensity (gray-scale) over
a very large range of gray scales, making it a very good candidate for
representing ratio or interval data. Another good candidate includes the color
attribute saturation.
The Importance of Spatial-Frequency for Ratio and Interval Data
Ensuring that continuous variables are mapped onto perceptually
continuous dimensions, however, will only give a faithful representation of the
structure of the data if the spatial characteristics of the representation are
taken into account. Human sensitivity to spatial variation is sketched in Figure
1. The two curves show that our ability to resolve spatial variations differs
for the hue and luminance mechanism in human vision. The luminance mechanism is
tuned to higher spatial frequencies (that is, high resolution, finely detailed,
or small-grained features). Colormaps which include a luminance component,
therefore, are can adequately represent high-spatial-frequency information. The
hue mechanism is tuned to lower spatial frequencies.
Colormaps for Segmentation Tasks
The rules for
providing isomorphic colormaps for ratio and interval data are also effective in
creating maps for segmented data. The luminance component conveys monotonicity
in the data for high spatial frequency data, while the saturation component can
be used to convey monotonicity in low-spatial-frequency data. Since the steps
are explicitly defined, however, luminance steps can also be effectively used
for low spatial-frequency data. In creating a segmented colormap, it is
important that the segments are each discriminably different from one another,
which limits the number of steps which can be represented. We have found that
more steps can be effectively discriminated for low-spatial-frequency data than
for high. For ratio data, where the zero is a semantically-important attribute,
PRAVDAColor only offers segmented maps with an even number of steps (a
transition occurs at the zero level).
Colormaps for Highlighting Tasks
Rules for selecting
colormaps which highlight particular features in the data can be drawn from the
literature on attention (e.g., Treisman and Gelade [1980]). Based on these
rules, PRAVDAColor offers colormaps which allow the user to identify ranges of
data to highlight perceptually. We currently provide colormaps which identify
the mid-range data value, or set a threshold and highlight data values which
exceed it.
In highlighting data, it is important that the dimension
selected does not interfere with one previously chosen. For ex-ample, in our
schema, nominal data are distinguished by hue. Increasing the luminance of the
item to be highlighted draws attention to it without changing its hue, and
therefore, without losing perceptual information about its semantic class.
The PRAVDAColor Interface
The PRAVDAColor user is
presented with a set of colormaps appropriate to the data set and specified
representation task. These colormaps are presented in a panel which pops up on
the display when PRAVDAColor is executed. An example of this pop-up panel can be
seen in the lower left corner of Figure
2. Each colormap is displayed as a colorbar and has an associated button,
used for selecting that colormap. PRAVDAColor automatically selects one of the
colormap set as an initial output, which is used to color the data. The user is
then free to select a sequence of colormaps by pressing buttons, and can
immediately see each selection applied to the data.
Figure 2. Data Explorer Visual Program Incorporating PRAVDAColor.
Implementation
The PRAVDAColor Module
PRAVDAColor has been
implemented as a module for the IBM Visualization Data Explorer (Data Explorer)
software package. Data Explorer is a general-purpose visualization system that
supports visual programming through the construction of data-flow networks
(Abram and Treinish [1995]). Data Explorer facilitated the development of
PRAVDAColor's capabilities by providing a unified, extensible data model and
polymorphic modules. Thus, rules were readily incorporated without the
complication of accounting for multiple data types, and metadata (either
calculated or provided by a user) can readily be added to data objects.
Figure 2 shows a sample Data Explorer data-flow network
and the visualization that it produces. The PRAVDAColor module accepts as input
the data set to be visualized (read by the Import module in this example) and a
user representation task index (created by the interactive Selector module).
The PRAVDAColor tool consists of two main portions. The
first is a macro that selects the set of colormaps to be presented to the user
based on characteristics of the data and a user-specified representation task.
This macro, called ColorMapLookup, examines two characteristics of the data --
spatial frequency, and presence or absence of a zero-crossing.
The spatial frequency analysis is performed in a simple
fashion using existing Data Explorer modules. The resolution of the data is
reduced (using a reduction factor derived from user input) and then interpolated
back to the original resolution. This has the effect of low-pass filtering the
data. The original data values are subtracted from the filtered values and then
the standard deviation of the difference values computed and divided by the
range of the original data values. This normalized standard deviation is used to
determine whether the data contain predominately low-frequency or high frequency
information. When the normalized standard deviation is less than or equal to
0.1, we consider the data to be low frequency, based on empirical results.
Using the computed values and a representation task,
ColorMapLookup computes an index into a lookup table structured as shown in
Table 1, which is used to determine a set of colormaps to be read into memory.
If the data contain a zero-crossing (i.e., the minimum and maximum values have
different signs), the data are treated as ratio data. Otherwise, data are
treated as interval data. The current implementation does not handle nominal or
ordinal data.
The second major component of PRAVDAColor is the
interactive colormap displayer/selector. This component is implemented as an
outboard module in Data Explorer called ColorMapPicker, written in C using
Motif/Xlib. Outboard modules are separately compiled and linked executables
which are invoked by Data Explorer and communicate with the Data Explorer
executive (main control component) via socket. As described above,
ColorMapPicker allows the user to interactively select sequences of colormaps,
as well as dynamically alter the assignment of colormap values to data values.
Colormap construction
To construct colormaps, we
developed a tool similar to the interactive tool described by Rheingans [1990].
Figure
3 shows this three-dimensional colormap tool, an image that has been created
using its output, and a view of its output in the Data Explorer Colormap Editor.
Figure 3. Construction of a Data Explorer Colormap with a Three-Dimensional
Colormap Tool.
Figure 4. Specification of a Colormap in HLS Space.
Results -- Applications of PRAVDAColor
PRAVDAColor
has been utilized internally as part of an informal testing effort prior to
making these tools available to users of Data Explorer. PRAVDAColor has been
integrated into various operational visualization activities.
Preserving the spatial structure of data
Consider Figure
5, which is a screen dump of a typical Data Explorer program applied to
two-dimensional data, where the default hue-based colormap from AutoColor is
utilized to create an image of fluid density from a simulation of the noise
produced by a jet aircraft engine.
Figure 5. Data Explorer Visual Program Using the Default Colormap Tool
(AutoColor).
The representation is dominated by the
segmentation inherent in the default rainbow type of colormap. In order to study
the spatial structure of these data as a continuum, AutoColor was replaced by
PRAVDAColor to help in the selection of an isomorphic colormap. The results are
shown in Figure 2. It shows more of the fine spatial structure and turbulence
inherent in these continuous data.
Different colormaps for different tasks
Figures 6 and
7 illustrate the importance of task specification for colormap selection. They
show the result of a photochemical grid model of transport and deposition of
airborne pollutants over the midwestern portion of the United States on June 26,
1987 at 18:00 local time. Ozone pollution concentration is shown in parts per
billion by volume (ppbv). An isomorphic colormap was employed in Figure
6. It effectively captures the inherent dynamics of the model by showing a
snapshot of atmospheric motion (e.g., roughly circular filaments in yellow
corresponding to higher ozone concentrations). On the other hand, the ability to
indicate regions of moderate to high pollution is a different task. PRAVDAColor
was used to select a segmented colormap in Figure 7
for color-filled contours. In this case, higher pollution levels (e.g., above
160 ppbv) are clearly visible as yellow and red over Lake Michigan, to the east
of Chicago. It should also be noted that this colormap allows the user to see
some artifacts of the limited grid resolution of the model.
Figure 8. Global Temperature and Precipitation with Complementary
Colormaps.Figure 6. Photochemical Pollution Model with an Isomorphic
Colormap.
Figure 7. Photochemical Pollution Model with a Segmented
Colormap.
Color interaction
The analysis of concurrent color
use by multiple objects is an additional criterion in colormap selection in
order to avoid undesirable artifacts of color mixing. While the current
implementation does not support dynamic interaction between visualization
operations, PRAVDAColor does allow the user to address some of these issues
explicitly. Several efforts to show multiple parameters using different
colormaps were attempted. In these cases, the choices offered by PRAVDAColor
were manually inspected for potential conflicts. The user can then choose
colormaps that have minimal overlap in use of specific colors.
Figure
8, for example, is a display of global temperature and precipitation
observed from weather stations. An isomorphic colormap is chosen for
precipitation as a continuous pseudo-colored field, while contours of
temperature every five degrees C. are colored using a segmented colormap
composed of entirely different colors. This representation illustrates
correlation between lack of precipitation with very high temperatures and high
precipitation with moderately-high temperatures.
Figure 9. Ocean/Atmospheric Conditions Shown with Two Isomorphic
Colormaps.
Three-dimensional Data
The application of PRAVDAColor
is not confined to two-dimensional data. Figure
10 shows one time step of a regional, three-dimensional weather model shown
as an isosurface of wind speed at 20 m/sec. The surface is colored by the
temperature values in the computed volume interpolated on the isosurface.
PRAVDAColor is used to create an isomorphic colormap corresponding to the full
temperature volume.
Figure 10. Data Explorer Visual Program Using PRAVDAColor with
Three-Dimensional Data.
Integrating PRAVDA into real applications
PRAVDAColor
can easily be incorporated into actual applications built with Data Explorer. Figure
11 is a screen dump of a generalized application that provides cartographic
representations from a selection of available parameters stored in a
user-defined file. The package was extended by replacing the standard Colormap
Editor with PRAVDAColor. This enhanced application allows a user to select a
colormapping task, for which PRAVDAColor then offers a set of choices. The image
shows a segmented colormap applied to filled contours of total column ozone
displayed as orthographic maps for the northern and southern hemispheres. The
seasonal ozone depletion is visible as a black region over the south pole for
these data taken on October 1, 1991. The available choices are illustrated in
the ColorMapPicker panel.
Figure 11. Data Explorer Application Incorporating PRAVDAColor.
Discussion
PRAVDAColor has been used effectively
within IBM. For complex colormap selection activities, this tool has reduced the
length of time required to develop satisfactory results. This has been
sufficiently encouraging to warrant further enhancements, and to make the tools
available to current Data Explorer users.
Importance of Spatial Frequency in Colormap Selection
Previous guidance for colormap selection has established the
importance of various classes of colormaps appropriate for specific
visualization tasks (e.g., Lefkowitz and Herman [1992]; Ware [1988]). However,
there can be considerable variation in the collection of colormaps that
effectively satisfy a given task from one data set to the next. The analysis of
the spatial frequency coupled with a large library of colormaps offers a unique
method for characterizing the appropriate representation of the data. The user
is shielded from the intricacies of psychophysical research and color theory,
and is automatically offered colormaps with significant luminance variations for
representing fine spatial structure. Similarly, the user is offered colormaps
with significant variation in saturation for representing coarse spatial
structure.
Because of its obvious simplicity, the current algorithm
for estimating spatial frequency might be criticized as being naive. However, it
does have a number of virtues. The typical approach to such a problem would
involve applying a (fast) Fourier Transform (FFT) to the data of interest. An
estimate of the spatial frequency for use herein could be specified in the
following manner for two-dimensional data:
F(u,v) = |G(u,v) Mi(u,v)|
where: G(u,v) is the Fourier transform of the data
represented by G(x,y).
Mi(u,v) is the frequency mask or filter for the ith class
of spatial variation.
In practice, several Mi(u,v) functions would need to be
defined, one for each class of spatial frequency for which a separate collection
of colormaps would be made available. Generic versions of filters may be
non-trivial to construct. Clearly, this approach could be extended to
three-dimensional data. However, the development of three-dimensional filters
would be even more difficult. Of course, a more complex representation of the
spatial frequency than this might be required to be effective (e.g.,
introduction of weighting functions in the frequency domain). As with the
approach of filtering in the spatial domain, metrics for evaluating the results
to assign spatial frequency classes would need to be developed.
Unfortunately, an FFT-based method of frequency-domain
filtering is generally limited to regularly gridded data (e.g., an image).
Hence, this approach would not directly apply to curvilinear, partially regular
or irregular data. In addition, it is not sensitive to disparate scaling that
might apply to each dimension of a grid. Therefore, an alternative was required
to support rule-based colormapping of more general classes of data. The
spatial-domain filtering approach described earlier has the advantage of
operating on any topologically regular gridded or structured data set and is
affected by dimensional scaling. Finally, the approach would appear to be
computationally quicker than using FFTs, especially for three-dimensional data,
which has enabled the application of PRAVDAColor to be interactive.
Integration of Intelligence into Existing Systems
In
our earlier work, we established the importance of interactive rule-based tools
to extend the utility of modern visualization software systems. The approach
capitalizes on the breadth of their capabilities while minimizing the number of
iterations required to create more appropriate and better visualizations. As a
first step in this effort, the implementation of PRAVDAColor has demonstrated
that this is feasible and practical. We expect other visualization systems to be
extensible to incorporate PRAVDAColor-like tools through the addition of custom
code as well as existing visual programming modules (e.g., Rasure and Wallace
[1991]; SGI [1991]; Upson et al [1989]).
Extensions
In this paper, we have presented a Data
Explorer module for guiding the user in selecting colormaps. The next step would
be to add additional rule-based operations and provide feedback between the
operations.
The PRAVDA architecture can be readily extended to allow
the user to interactively modify the metadata and the rules. For example, the
user could choose to modify the algorithm for computing spatial frequency, or
decide to see what mapping choices were available if the goal of the
visualization were changed. Likewise, the rules could be changed to reflect new
insights or information. For example, if the user realized that the structure
being sought was confined to a certain range of values in the data set, the rule
could be modified so that data in this range would be highlighted by mapping it
to an appropriate visual dimension. Our first focus has been on implementing
rules based on perceptual principles, but could be easily extended to include
other types of rules, for example, rules about mappings or conventions
particular to certain domains (Rogowitz and Treinish [1994]).
Conclusions
A framework for rule-based guidance can
improve the effectiveness of systems by assisting the user in making two types
of appropriate representation choices. One concerns domain-independent factors,
such as ensuring that data content is reflected in images and that perceptual
artifacts are not erroneously interpreted as data features. A second type
concerns task-dependent factors. For example, different advice on representation
is required depending on whether the goal of visualization is exploration or
presentation.
The PRAVDA architecture explicitly incorporates guidance
based on principles of human perception, cognition and color theory (Rogowitz
and Treinish [1993b]). These principles are incorporated in rules which the user
can select during the visualization process. Depending on the higher-level
characteristics of the data, the rule constrains the way in which the data are
mapped onto visual dimensions. This architecture has been utilized to build a
tool which eases the burden of creating colormaps for many visualization
applications.
The PRAVDAColor module has been implemented as an initial
proof-of-concept of the PRAVDA rule-based architecture for advising a
visualization developer. We have developed a set of rules that simplify the task
of colormap selection. The user is presented a set of choices that are
appropriate, based on characteristics of the data being visualized and the
desired form of the representation.
Using this rule-based colormap advisor, we have
constructed a set of visualizations that demonstrate the advantages of colormaps
that conform to perceptual principles over an uninformed choice. We anticipate
users finding the current implementation helpful in constructing visualizations,
and the utility increasing as we add additional rules and visualization
operations to the system.
Acknowledgments
We thank the Data Explorer
development team for their cooperation in this effort and valuable discussion
that led to the successful implementation of PRAVDAColor.
Jet engine noise data are available courtesy of Combustion
Research and Flow Technology.
Surface station temperature and precipitation data,
oceanographic temperature, pressure and wind data, magnetic field data and total
column ozone data are available courtesy of NASA/Goddard Space Flight Center.
Three-dimensional weather model data are available
courtesy of Glenn Wightwick, IBM Australia.
Photochemical model data are available courtesy of the US
Environmental Protection Agency, RTP .
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