Color coding
A D V E R T I S E M E N T
Colors and light are essential to visualization. Most visualization
techniques contain a step in which data values are mapped to colors to make the
range of the data visible (see the next sections). The interpretation of results
produced by these visualization techniques depends crucially on the mapping of
data to colors because the human eye is more sensitive to some parts of the
visible spectrum of light than to
other parts and the brain may interpret different color patterns differently.
Since the mapping of data values to colors involves color coding, we will
describe this in some detail. There exist quite a few color coding systems. We
discuss here the RGB, CMY, and HSV systems.
The RGB code system is mainly used in television sets and computer screens.
Color is determined by the three independent components Red (R), Green (G), and
Blue (B). These components correspond with the red, green, and blue cathode ray
tubes. Each component has values in the interval [0,1]. A value of 0 corresponds
to black and a value of 1 corresponds with full color. For example {R=0, G=0,
B=0}is black, {R=1, G=0, B=0}is full red, {R=0, G=1, B=1}is full cyan, and {R=1,
G=1, B=1}is white. Every color can be constructed by taking the right
combination of the three components. However, the number of values that can be
represented by cathode ray tubes for each component in the interval [0, 1] is
finite. Most graphical display systems currently use 256 different values, which
means that 256**3 = 16,777,216 different colors are supported: more than enough
for most applications.
Another color coding system is the CMY system. Color is determined by the
three independent components Cyan (C=1-R), Magenta (M=1-G), and Yellow (Y=1-B).
It is widely used in the publishing world. The CMY system is related to the RGB
system as follows: C=1-R, M=1-B, and Y=1-G. It is clear that these systems are
complementary to each other.
The color coding which is used most frequently in visual environments is the
HSV system. The three components Hue (H), Saturation (S), and Value (V) have
values between 0 and 1. Whereas one can view the volume spanned up by the three
independent components of the RGB and CMY color systems as a unit cube, the HSV
volume is an inverted cone. The Hue is the angular coordinate in a plane
perpendicular to the symmetry axis, where H=0 corresponds to red and an angle of
0 degrees, H=0.33 corresponds to green and an angle of 120 degrees, H=0.66
corresponds to blue and an angle of 240 degrees, and H=1.0 corresponds again to
red. The Saturation determines the saturation of the color. Saturation is the
radial coordinate in the plane perpendicular to the symmetry axis, so that S=1
corresponds to full saturation and S=0 corresponds to no color (i.e. white), S=0
is situated on the symmetry axis and S=1 corresponds to the maximum radius in
the plane, i.e. the boundary of the cone. The Value determines the intensity of
the color. Value is the coordinate along the symmetry axis of the cone, where
V=0 corresponds to no intensity (i.e. black), and V=1 corresponds to maximum
intensity. V=0 is at the top of the cone and V=1 is at the base of the cone. We
will not discuss the relation between the RGB and HSV system as it is a
complicated one. Interested people are referred to refs. [2] and [3]. HSV is
frequently used in visual environments, because the effects of manipulating the
components are much more predictable than in RGB and CMY. HSV corresponds to a
more natural experience of colors than the other systems provide.
In most visualization techniques, colors from red to blue are used to reveal
transitions in some quantity. If one wants to use the complete set of available
colors one needs to map the range of values to this complete set. Storing this
mapping consumes too much memory.
Therefore, one normally chooses N colors of the available set (typically
N=256) and maps the range of values to these N colors. This mapping of the
values to colors will be denoted as the colormap in the rest of this report.
It is important to notice that using colors to reveal transitions in
quantities can be misleading if there are no transitions at all, e.g. for a
monotonically increasing quantity. For the kind of phenomena in which the
quantity changes smoothly it is better to use continuously changing schemes like
gray scales, saturation scales, and intensity scales. This immediately shows
another advantage of the HSV code
system: saturation and intensity are natural variables in the HSV system.
Surface rendering techniques
This section briefly describes a general set of 3D scalar and vector surface
rendering techniques. The first four descriptions deal with scalar field
techniques and the other two with vector field techniques.
Scalar glyphs
Scalar glyphs is a technique which puts a sphere or a diamond on every data
point. The scale of the sphere or diamond is determined by the data value. The
scalar glyphs may be colored according to the same scalar field or according to
another scalar field. In this way correlations can be found. As no
interpolations are needed for this technique it consumes few CPU seconds.
Isosurfaces
This technique produces surfaces in the domain of the scalar quantity on which
the scalar quantity has the same value, the so-called isosurface value.
The surfaces can be colored according to the isosurface value or they can be
colored according to another scalar field using the texture technique. The
latter case allows for the search for correlation between different scalar
quantities.
There are different methods to generate the surfaces from a discrete set of data
points. All methods use interpolation to construct a continuous function. The
correctness of the generated surfaces depends on how well the constructed
continuous function matches the underlying continuous function representing the
discrete data set. The method which is implemented in the software packages
described in chapter 3, is the Marching Cube Algorithm.
Cutting planes
This technique makes it possible to view scalar data on a cross-section of the
data volume with a cutting plane. One defines a regular, Cartesian grid on the
plane and the data values on this grid are found by interpolation of the
original data. A convenient colormap is used to make the data visible.
Orthogonal slicers
It often occurs that one wants to focus on the influence of only two independent
variables (i.e. coordinates). Thus, the other independent variables are kept
constant. This is what the orthogonal slicer method does. For example, if the
data is defined in spherical coordinates and one wants to focus on the angular
dependences for a specific radius, the orthogonal slicer method constructs the
corresponding sphere. No interpolation is used since the original grid with the
corresponding data is inherited. A convenient colormap is used to make the data
visible.
Vector glyphs
This technique uses needle or arrow glyphs to represent vectors at each data
point. The direction of the glyph corresponds to the direction of the vector and
its magnitude corresponds to the magnitude of the vector. The glyphs can be
colored according to a scalar field.
Streamlines, streaklines, and particle advection
This is a set of methods for outlining the topology, i.e. the field lines, of a
vector field. Generally, one takes a set of starting points, finds the vectors
at these points by interpolation, if necessary, and integrates the points along
the direction of the vector. At the new positions the vector values are found by
interpolation and one integrates again. This process stops if a predetermined
number of integration steps has been reached or if the points end up outside the
data volume. The calculated points are connected by lines.
The difference between streamlines and streaklines is that the streamlines
technique considers the vector field to be static whereas the streaklines
technique considers the vector field to be time dependent. Hence, the streakline
technique interpolates not only in the spatial direction, but also in the time
direction. The particle advection method places little spheres at the starting
points representing massless particles. The particles are also integrated along
the field lines. After every integration step each particle is drawn together
with a line or ribbon tail indicating the direction in which the particle is
moving.
Textures
This is a technique to color arbitrary surfaces, e.g. those generated by the
isosurface techniques, according to a 3D scalar field. An interpolation scheme
is used to determine the values of the scalar field on the surface. A colormap
is used to assign the color.
Volume Visualization
Volume rendering is used to view 3d
data without the usual intermediate step of deriving a geometric representation
which is then rendered. The volume representation uses voxels, or volume
elements to determine visual properties, such as opacity, color, shading at each
point in the computational domain. Several images are created by slicing the
volume perpendicular to the viewing axis at a regular interval and compositing
together the contributing images from back to front, thus summing voxel
opacities and colors at each pixel. By rapidly changing the color and opacity
transfer functions, various structures are interactively revealed in the spatial
domain.
Volumetric rendering
Volumetric rendering allows the entire data set to be viewed at once, and
lets the user "see inside" the data. For each pixel in an image created using
volumetric rendering, a ray is cast through the semi-transparent volume. The
resulting color at the pixel is a composite of all the voxels the ray has
intersected. As a consquence, such images tend to be blurry. Another
characteristic volumetric rendering is that it is typically slower than surface
rendering techniques. Therefore, volumetric rendering of adata set is often not
well suited for realtime visualization. However, it does provide features that
are obscured by surface rendering techniques.
Volume rendering techniques
Volume rendering techniques have been developed to overcome problems of the
accurate representation of surfaces in the isosurface techniques. In short,
these problems are related to making a decision for every volume element whether
or not the surface passes through it and this can produce false positives
(spurious surfaces) or false negatives (erroneous holes in surfaces),
particularly in the presence of small or poorly defined features. Volume
rendering does not use intermediate geometrical representations, in contrast to
surface rendering techniques. It offers the possibility for displaying weak or
fuzzy surfaces. This frees one from the requirement to make a decision whether a
surface is present or not.
Volume rendering involves the following steps: the forming of an RGBA volume
from the data, reconstruction of a continuous function from this discrete data
set, and projecting it onto the 2D viewing plane (the output image) from the
desired point of view. An RGBA volume is a 3D four-vector data set, where the
first three components are the familiar R, G, and B color components and the
last component, A, represents opacity. An opacity value of 0 means
totally transparent and a value of 1 means totally opaque. Behind the RGBA
volume an opaque background is placed. The mapping of the data to opacity values
acts as a classification of the data one is interested in. Isosurfaces can be
shown by mapping the corresponding data values to almost opaque values and the
rest to transparent values. The appearance of surfaces can be improved by using
shading techniques to form the RGB mapping. However, opacity can be used to see
the interior of the data volume too. These interiors appear as clouds with
varying density and color. A big advantage of volume rendering is that this
interior information is not thrown away, so that it enables one to look at the
3D data set as a whole. Disadvantages are the difficult interpretation of the
cloudy interiors and the long time, compared to surface rendering, needed to
perform volume rendering.
We will describe two implementations of volume rendering: ray casting and
splatting. These implementations are used in the four visualization packages we
have compared (see chapter 3). The two methods differ in the way the RGBA volume
is projected onto the 2D viewing plane.
Ray casting
Several implementations exist for ray casting. We describe the implementation
used in Visualization Data Explorer. For every pixel in the output image a ray
is shot into the data volume. At a predetermined number of evenly spaced
locations along the ray the color and opacity values are obtained by
interpolation. The interpolated colors and opacities are merged with each other
and with the background by compositing in back-to-front order to yield
the color of the pixel. These compositing calculations are simply linear
transformations. Specifically, the color of the ray Cout as it leaves
each sample location, is related to the color Cin of the ray, as it
enters, and to the color c(xi) and the opacity a(x) at that sample
location by the transparency formula :
Performing this formula in a back-to-front order, i.e. starting at the
background and moving towards the image plane, will produce the pixel color. It
is clear from the above formula that the opacity acts as a data selector. For
example, sample points with opacity values close to 1 hide almost all the
information along the ray between the background and the sample point and
opacity values close to zero transfer the information almost unaltered. This way
of compositing is equal to the dense-emitter model, where the color indicates
the instantaneous emission rate and the opacity indicates the instantaneous
absorption rate.
Splatting
This technique was developed to improve the speed of calculation of volume
rendering techniques like ray casting, at the price of less accurate rendering.
We will not go into detail here as this technique is rather complicated. It
differs from ray casting in the projection method. Splatting projects voxels,
i.e. volume elements, on the 2D viewing plane. It approximates this projection
by a so-called Gaussian splat, which depends on the opacity and on the
color of the voxel (other splat types, like linear splats can be used also). A
projection is made for every voxel and the resulting splats are composited on
top of each other in back-to-front order to produce the final image.
Data Types
- Hierarchical Data Formats (HDF)
- Network Common Data Format (netCDF)
- Databases- The currently accepted storage method for most scientific
data is the Relational Database Management System. This is the format used
by many commercial databases, such as Oracle. Data can be extracted using
the Standard Query Language (SQL) commands.
Animation techniques
These techniques simulate continuous motion by rapidly displaying images. The
viewer is given the impression that he is watching a continuous motion. To
achieve this impression the graphical hardware needs image display rates of at
least 25 images per second, since otherwise motion will look shaky. As most
graphical hardware can not reach that display rate for moderate sized images
(i.e. 256x256 pixels), one uses video hardware. One either sends every image to
a framebuffer to write one videoframe at a time to videotape or one stores the
images on a fast accessible device, CMY a laserdisk, and, after all images have
been stored, displays them on a television screen from where they can be put on
a videotape. There are two kinds of animation which we will describe below.
Flipbook animation
This is a well known technique. The generated images are displayed one after the
other. Its name is attached to the thumbing or flipping through a series of
images.
Keyframe animation
For this technique one only has to generate so-called keyframes.
Keyframes mark changes in the characteristics of the motion, for example the
sudden change in the direction of motion of an electron due to a collision with
an ion. Interpolation techniques are used to generate a set of images between
two keyframes. The larger the interpolated set of images the smoother the
conversion from one keyframe to the other will appear to the viewer.
|
