We throw that term around quite a bit without always understanding it.
What exactly is being multiplied?
understand digital image multiplication, we must first understand that
it is only useful when images are represented not as 8-bit 0 to 255
values, but as "floating point" 0.0 to 1.0 fractional values
— akin to percentages, if you prefer.
we have an image that is too pink. That is to say, the image is too
red and too blue, but its green channel is just fine. To reduce the
red and blue channels, we need to multiply them by a percentage which
is less than 100%. For example, to pull 20% from the red and blue channels
of an image, one must multiply it by the color (0.8, 1.0, 0.8). Since
multiplication by a color is analogous to looking through a filter of
that color, we need to look at our overly-magenta image through (as
any photographer will have guessed) a "pale green" filter.
The multiplication has no useful meaning when the color values are expressed
in 0 to 255 space, but in 0 to 1 space it all makes sense. Since anything
times zero is zero, black (0.0) times anything is black. Since anything
times 1 leaves that thing unchanged, white (1.0) times anything has
no effect. A point five gray (0.5) times anything will make that thing
half as bright. Pale red (1.0, 0.9, 0.9) times anything makes that thing
just a bit redder looking. Traditional photographers call this process
the subtractive color model which is unfortunate, because
no subtraction occurs.
subtraction did occur, then the physical world would have "negative
colors" which, of course, it does not. A better, more clearly understandable
term would be "multiplicative color model," or "filtration
color model," but the notion of color "subtraction" is
deeply ingrained and won't die anytime soon.
provides a good way to color line drawings. Here you can really see the
"black times anything is black, white times anything is that thing
unchanged" rule in action. The sepia regions of the line drawing
end up simply tinting the corresponding pixels of the color image with
multiplication is commutative, the order of the layering does not matter.
Muliplication also provides a good way of "shading"
artwork. You can use it to introduce a sense of diffuse lighting into
your paintings or 3D CG objects. Notice in the example below how the
warm and cool grays not only darken the final 3D rendering, but also
influence its color temperature.
Understanding of multiplication can lead to a better understanding of
color mixing in pigments. Like photographers,
artists also believe there exist something called subtractive
color mixing. That's unfortunate. Colors are colors, and light
is light, and mixing light can only lead to the production of lighter
subtractive color mixing is really a process akin to filtering.
When an artists mixes one color with another color, he is really layering
one colored filter over another one. Every filter produces less light
on its output side than it receives on its input side. How much less
light? It's best to think in terms of percentages.
The end result is still a mixing of light reflected by various pigments,
it's just that the pigments restrict the wavelengths of the light which
will ultimately be added together.
We can see when
we express color mixing in terms of simple image arithmetic that when
two pigments are mixed (or when two color filters are sandwiched together)
or when two digital colors are multiplied, the resulting color is that
color which is present in some measure in both source colors. Pure
yellow mixed with pure blue would actually
yield black, not green, because pure blue filters only
allow pure blue to pass, and pure yellow filters only allow pure yellow
light to pass, and so there is no green in the final result because
neither filter allows green to pass through.
A greenish blue filter allows some green to pass through. So does a
greenish yellow filter. That's why Cerulean blue mixed with Hansa yellow
yields a green color. If you'd like to learn more about color mixing
and pigments, I recommend you buy and follow the exercises in the book
and Yellow Don't Make Green by Michael Wilcox.
Remember in the example above that 35 * 255 = 35 only when
the math is done in zero-to-one space — the
number 35 is really 35 out of 255 which is really 0.137,
and 255 is really 255 out of 255 which is really 1.0 — so
35 * 255 = 35 only because 0.137 * 1.0 = 0.137 — When Adobe
expresses colors in 8-bit 0 to 255 space, they foster
a poor understanding of many aspects of image arithmetic.