5.3 Relating HSV to RGB
To better understand the HSV and RGB colorspaces, it helps to
understand their relationship. A very useful exercise is to identify
the parts of the RGB cube that correspond to surfaces of constant hue,
saturation, and value.
We begin by better defining
brightness. This term was
introduced in the previous section, and it is a measure of the visual
perception of how much light an area is emitting. A lamp with a
variable control switch allows the level of brightness to be changed.
Turning the lamp up increases our perception of brightness. Note that
the notion of brightness does not depend on the color of the light.
It makes as much sense to talk about the brightness of a red lamp as
it does a white one.
A color monitor is just a collection of thousands of lamps (that is,
pixels) that emit red, green, and blue light. Because each of the
lamps can be independently controlled, the total brightness of an area
on the monitor is the sum of brightness from each color. Colors of
equal brightness in the RGB cube, then, are those whose three color
components sum to the same value. For a particular level of
brightness, this represents a plane perpendicular to the neutral axis
(that is,
). Figure
5.5
Figure 5.5:
Planes of Constant Brightness in the RGB Cube
 |
shows three examples of planes perpendicular to the neutral axis in
the RGB cube. The cube in Figure
5.5(a) shows the
darkest plane, the cube in Figure
5.5(c) the
lightest, and the cube in Figure
5.5(b) a plane of
intermediate brightness. Note how the colors in each plane seem about
equally bright. The three cubes in the figure show color planes at
25, 50, and 75% brightness. Pure white and pure black have a
brightness of be 0% and 100%, respectively, and consist of single
points in the cube.
There are many concepts closely related to brightness and that have
various useful properties. Brightness is formally defined to be
(R+G+B)/3; it is a physical property of color and does not
correspond well to human color perception. For this reason,
brightness is not actually used in the GIMP. However, the GIMP does
use
-
lightness,
![$L=[\max(R,G,B)+\min(R,G,B)]/2$](img154.gif)
,
-
value,
,
and
-
luminance,
Y=0.30 R + 0.59 G + 0.11
B.
Luminance
is the representation of brightness that corresponds best to human
perception because the weightings 0.30, 0.59, and 0.11 most closely
match the sensitivity of the eye to red, green, and blue.
Figure
5.6
Figure 5.6:
Different Projections Onto the Neutral Axis
 |
shows how the different definitions for brightness project onto the
neutral axis. The figure shows the position in the RGB cube of a
representative color,
220
R 60
G 120
B, and the locations on the
neutral axis corresponding to the value,
V, the lightness,
L, and
the luminance,
Y. As can be seen from
Figure
5.6, value is the brightest. The
luminance and the lightness are variable and either one can be the
darkest depending on the choice of the RGB triple.
Next, we define saturation.
The definition of saturation is related to that of brightness.
Saturation is the relative colorfulness of an area with respect to its
brightness. What is colorfulness? An answer can be given in the
context of the RGB cube and the neutral axis. As already noted, the
neutral axis is the diagonal in the cube going from
0R 0G 0B to
255R 255G 255B, and which consists of black, white, and the
grayscale between them. Thus, in the usual sense, this axis has no
color (that is, hue). The colorfulness of any point in the RGB cube,
then, is proportional to its perpendicular distance to the neutral
axis. Points closer to the axis are less colorful (that is, closer to
gray) and those that are further away are more colorful. The
saturation, then, of a point in the RGB cube is the ratio of its
colorfulness to its brightness.
This means that surfaces of constant saturation in the RGB cube are
cones centered around the neutral axis.
Figure
5.7
Figure 5.7:
Cones of Constant Saturation in the RGB Cube
 |
shows two instances of the RGB cube. The cube in
Figure
5.7(a) shows the cone corresponding to 20%
saturation and that in Figure
5.7(b) to 70%
saturation. Note that the colors on the rightmost cone seem more
vivid because they are more saturated. The colors of the leftmost
cone are much paler because their colors are more relatively neutral.
When a color is more neutral we call it
pastel.
Finally, the definition of hue is related
to what we colloquially think of as color. The hue of a point in the
RGB cube is defined to be its angular position around the neutral
axis. Looking at the corners of the RGB cube shown in
Figure
5.2, you can see that red, yellow,
green, cyan, blue, and magenta are distributed equally in angle around
the neutral axis. Thus, the wedge defined by the neutral axis and any
point on the surface of the cube is a plane of constant hue.
Figure
5.8
Figure 5.8:
Wedges of Constant Hue in the RGB Cube
 |
illustrates three instances of the RGB cube with different wedges of
constant hue. Because hue is a function of angle, its range is from 0
to 360 degrees. The red corner of the cube is defined to be the hue
at 0, which, forcibly, is also the hue at 360. This hue is shown in
Figure
5.8(b). The cube in
Figure
5.8(a) shows a hue of 330, which is purple,
and that in Figure
5.8(c) a hue of 30, which is
orange. Note that although the hue of each wedge is constant, the
brightness and saturation vary over the range of possible values.
Figure
5.9
Figure 5.9:
The HSV Coordinates in the RGB Color Cube
 |
summarizes the relationship between RGB and HSV. Although, the
neutral axis represents brightness and not value, I will often abuse
this notion and refer to it as the value axis. The model shown in
Figure
5.9 will be useful for understanding
the explanations of the color blending modes described later in this
chapter.
With the HSV coordinate system in mind several observations can be
made about regions of color in the RGB cube. The first is that the
cyan, magenta, and yellow vertices of the cube represent brighter
colors than red, green, and blue because these latter project lower
down onto the neutral axis. Similarly, all colors in the pyramid
defined by the C, Y, M, and W vertices correspond to lighter colors,
and the pyramid defined by the origin and the R, G, and B vertices
correspond to darker colors. Colors near the neutral axis in the cube
will have a more pastel or washed out look because they are less
saturated, and colors further away from this axis will appear more
vivid.
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