Graphics Reference
In-Depth Information
B
B
R
R
G
G
Figure 2.1.
RGB color space as unit cube (left) and its intersection with a plane (right).
of zero luminance (black). Therefore, the simplified color space for the 2-channel
compression is defined by a single three-dimensional vector—the plane normal.
2.2.1 Color Plane Estimation
Fitting a plane to approximate a set of 3D points is a common task and various
algorithms exist. In order to find the best plane for color simplification we have
to take the following preparatory steps.
First, we have to remember that RGB pixel color values in most image file
formats do not represent linear base color contribution. For the purpose of this
algorithm, we want to operate in the linear RGB color space. Most common file
formats provide values in sRGB space [Stokes 96]. While being internally more
complex, this representation can be approximated with gamma 2.2, i.e., after
raising RGB values to power of 2.2 we obtain approximately linear light stimuli
for red, green, and blue. We can approximate this with a gamma value of 2, which
allows a simple use of multiplication and square root for conversion between sRGB
and approximate linear RGB spaces. Strictly speaking, we will then be operating
in a RGB space with a gamma of 1.1. While this slight nonlinearity will have
only a minor impact on the estimation and the encoding, it is important to use
the same simplified gamma value of 2 during the conversion back to the sRGB
space after decoding for the final presentation to avoid change in the luminance
levels.
After (approximately) converting color values to the linear RGB space, the
other thing we have to remember is the fact that the hue perception is a result
of the relation between the RGB components and is not linear. To correctly
match hues as closely as possible, we could ideally use a perceptually linear color
space (e.g., L*a*b*, explained in [Hoffmann 03]). However, this results in a much
more costly decoding stage and thus we will limit ourselves to the linear RGB
color space, accepting potential minor hue errors. Still, to minimize the impact
of not operating in a perceptually correct linear RGB space, we can apply non-
