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<TITLE>Interactive Illustrations of Color Perception</TITLE>
<IMG SRC="images/screenshot.gif" WIDTH=374 HEIGHT=176 ALIGN=RIGHT>
<H2>Interactive Illustrations of Color Perception</H2>
<P><HR><P>
For the color theory portion of the introductory computer graphics
course at <A HREF="/">Brown University</A> (<A
HREF="/courses/cs123">CS123</A>), Professor <A HREF="/people/jfh">John
Hughes</A> sketched out some ideas for interactive
illustrations. These were programmed in <A
HREF="/research/graphics/information/documentation/flesh_tutorial/0intro.html">Flesh</A>
by <A HREF="/people/jeb">Jeff Beall</A>, and later ported to C++ and
GP (also by Jeff). They have recently been ported to Java by <A
HREF="/people/amd">Adam Doppelt</A>. The illustrations will be used
during the lectures in the course, and they will also be available to
students outside class; the following informal text by Professor
Hughes is meant to help guide the viewer in understanding the
illustrations.
To view the interactive illustrations themselves, you must be running
a <A HREF="http://java.sun.com/">HotJava</A> compatible browser.
<P><HR><P>
Colored light arrives at the eye, and somehow gets to the brain, and
extensive research shows that the brain perceives the color of the
light in a 3-dimensional way -- that is to say, there are three
independent components to the brain's perception of color. This
matches physiological evidence that there are three types of
color-receptor cells in the eye.<P>
The light that arrives at the eye, however, is a much more complex
phenomenon: it consists of photons with varying amounts of energy,
which correspond to varying wavelengths (or frequencies) of light. In
most ordinary light, there is a mix of various frequencies, and at a
macroscopic scale, one can indicate this mix of photons by drawing a
graph of intensity versus frequency. If light is generated very
carefully, it sometimes consists of photons that all have the same
energy, so that the light is of a single frequency. We'll refer to
such light as "monospectral." Laser light is the standard example of
a monospectral light.<P>
How does incoming light affect the three types of cells? Let's look at
one cell-type at a time, such as the "green" cells (ones that are
sensitive to light primarily in the 520 nm wavelength). First of all,
at a very coarse level, the response is linear: if the green cells are
stimulated by one light and produce one response -- some amount of
signal to the brain -- and if in response to a second light and
produce another, then when they are stimulated by both lights at once,
they produce the <I>sum</I> of the two responses.<P>
Second, the green cells will respond to monospectral light of many
different wavelengths. If we take a variable-frequency light of
constant intensity, and measure how much "response" we get from a
typical "green cell" in response to this light, we can plot this
response against frequency, and call it "the frequency response" of
the green cells.<P>
If we've done this, and we then send the eye a mix of light rather
than a pure monospectral light, we can compute the total response by
summing up the product of the "incoming light intensity" and the
"frequency response" at each frequency. In equations, this is
<CENTER>
<P><IMG SRC="images/image1.gif" WIDTH=72 HEIGHT=45><P>
</CENTER>
or, assuming that we've actually determined the frequency response at
every single frequency, we can write this as an integral:
<CENTER>
<P><IMG SRC="images/image2.gif" WIDTH=91 HEIGHT=48><P>
</CENTER>
To compute this integral, we can first compute the product of the two
functions, and then compute the area under this product function. <A
name="1"></A><A HREF="spectrum1.html">Illustration 1</A> shows this:
the user can draw a distribution of input intensity as a function of
wavelength; the frequency response of the "green cells" is indicated
in the middle, and the product of the two is shown at the bottom. The
user draws in this illustration, and all the others, by holding down
the left mouse button within one of the red boxes and moving the mouse
-- try it and the interaction should rapidly become obvious. The mouse
may go outside the box during a single click-and-drag sequence, but it
must start inside or nothing will happen. The area under this product
curve is shown on the bar indicator at the right. In this
illustration, the "frequency response" is not the real frequency
response of the green cells, but rather a graph whose shape is
somewhat similar, but the method of computing the total response does
not depend on the particular shape of the response curve.<P>
One thing to try here is drawing "input" that's more or less
monospectral -- draw a "bar" of light all near one frequency, and note
how the total response depends on where you draw the bar -- the total
response is largest when the bar is near the "hump" of the response
curve.<P>
<A name="2"></A>
<H3>Multiple types of color cells</H3>
There are cells other than the green cells in the eye -- there are two
other kinds, one more responsive to lower frequencies, and one more
responsive to higher frequencies. Naturally, this leads to three
different "total responses" to any given input frequency
distribution. The <A HREF="spectrum2.html">second
illustration</A> shows this: the reader can draw any input
distribution, the three response curves for the three cell types are
shown in the middle, the products of these with the input are shown at
the bottom, and the upper right shows the three "total responses."
Once again, try to see what the total response to "nearly
monospectral" lumps of light looks like as you vary the central
frequency of the nearly monospectral light.<P>
<A name="3"></A>
<H3>Different lights that look the same</H3>
The way we perceive light depends on the three "total responses"
produced by the light that enters the eye. It's a surprising fact that
different incoming light distributions can generate the same three
total responses. The </A><A HREF="spectrum3.html">third
illustration</A> lets you examine this. In particular, you can draw a
nearly uniform frequency distribution on the left side, generating a
mix of equal parts of red, green, and blue "total responses." But you
can also draw, on the right, a more sawtooth pattern which produces
the same total responses. Such pairs of light distributions are called
"metamers," or "metameric lights." Try to play with the illustration
to see how different two incoming lights can be and still produce the
same response in the eye.
<H3>What about reflection?</H3>
Suppose that we shine a light onto a surface. The surface may well be
good at reflecting certain frequencies and good at absorbing
others. (Indeed, this reflectivity may vary with the angle at which
light arrives and departs from the surface, but for a first
approximation we'll assume that a single "reflectivity number" at each
frequency suffices to characterize the surface). We'll plot this
reflectance against frequency, and we can then say when a given
distribution of light is shined <I>on</I> the surface that the light that
comes <I>off</I> the surface will be the product of the reflectance
function and the incoming light distribution. The <A name="4"></A><A
HREF="spectrum4.html">fourth illustration</A> shows this, and allows
the reader to play with examples that are hard to get ahold of in the
real world -- materials that reflect more or less a single frequency
of light, illuminated by various sorts of light. Try seeing what
happens when high-frequency light arrives at a surface that reflects
only low-frequency light -- a "very blue light" shining on a "very
pure red" surface.<P>
<P>
<A HREF="page2.html">Next Page</A>
<P><HR><P>
<A HREF="/research/graphics"><IMG SRC="/icons/bcgg.gif/"></A><P>
Questions or feedback on these illustrations should be sent to <i><A
HREF="mailto:jfh@cs.brown.edu">John F. Hughes</A></i>.<BR>
Questions on the Java source should be sent to <i><A
HREF="mailto:amd@cs.brown.edu">Adam Doppelt</A></i>.
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