MATH 5300 - ASSIGNMENT 3

MATH 5300 - ASSIGNMENT 3
MAY 12, 2008
(1) “Why does color space look like a shark fin?” Look at the Chromaticity diagram
on page 400 of your text (I will post a copy of this on the website also). Make a
table of wavelengths versus x, y, and z = 1 − x − y for each of the wavelengths
on the outside of that diagram. Plot wavelengths vs. x/y, wavelengths vs. y, and
wavelengths vs. z/y for wavelengths between 380 and 700 (ignore that 780 value).
’Plot’ the data (this can be done in a program like Octave or Matlab) or you can
do it by hand. What do these three graphs represent?
(2) (problem 6.2 p. 456) Consider any two valid colors c1 and c2 with coordinates
(x1 , y1 ), (x2 , y2 ), in the chomacity diagram of Figure 6.5 (shown below) Derive the
necessary general expressions for computing the relative percentages of colors c1
and c2 composing a given color that is known to lie on the straight line joining
these two colors.
(3) (problem 6.3 p. 457) Consider any three valid colors now c1 , c2 and c3 with coordinates (x1 , y1 ), (x2 , y2 ) and (x3 , y3 ) in the chromacity diagram of Figure 6.5.
Derive the necessary general expressions for computing the relative percentages of
c1 , c2 and c3 composing a given color that is known to lie within the triangle whose
vertices are at the coordinates of c1 , c2 , c3 .
(4) (problem 6.9 p. 458)
(a) Sketch the CMY componenents of the image in problem 6.6 as they would
appear on a monochrome monitor.
(b) If the CMY components sketched in (a) are fed in to the red, green, and blue
inputs of a color monitor, respectively, describe the resulting image.
Date: due May 19, 2008.
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MAY 12, 2008
(5) What is the transformation on the RGB coordinates of the image which inverts
the colors of the image? That is what is the transformation which sends white to
black, a pixel with a lot of blue to a pixel with little blue, a pixel with a lot of
red to a pixel with little red, etc. What effect does this transformation on the HSI
coordinates of the image?
(6) Consider the transformation on color space which switches the red and blue components.
(a) What does this do to the HSI coordinates of the color point?
(b) Take the image of Figure 6.5 and use GIMP or photoshop or another favorite
drawing program to exchange the red and the blue color channels of the image.