Due Mar 12, 2001
1. When too few levels of gray are used to represent an image, the result
is that relatively smooth areas where the gray levels change only a few
steps may be represented as a single level and appear as flat areas or
bands. In fact, discrete contours are seen throughout the image at pixel
boundaries of these bands. These artificially introduced boundaries are
commonly referred to as false contours. Assume that a flat area with
its center at (xo, yo) is illuminated by a light
source with intensity distribution
i(x, y) = K exp{-[(x - xo)2 + (y - yo)2]}.
Assume that the reflectance of the area is 1, and let K = 255. If the
resulting image is digitized with m bits of resolution, and the eye
can detect an abrupt change of 8 shades of intensity between adjacent pixels, what is the maximum value of m
that will still cause false contouring?
2. Use the shifting property of the Fourier transform to prove the
convolution theorem, i.e., show
f(x)*g(x) <=> F(u)G(u).
3. Improve the picture below left as best you can, and indicate your
procedure. Do you think that contrast stretching or histogram equalization
is the more helpful? 
4. (a) Enlarge the central picture above by a factor of two, make a copy of
it and add gaussian noise to the image. Now choose the left vertical
third of the image and apply a mean filter to clear up the noise. Does
sharpening the edges of the picture help? Choose the middle third and apply
a median filter. Compare your results with those from the median filter and comment. (b)
Start over and repeat the process with salt-and- pepper noise instead of
gaussian noise. (c) Put both types of noise in the picture. (d)
Keep the two types of noise separate, but determine what happens if there is
a lot of each type in the image.
5. Clean up the Betsy sunken ship picture (above right) as was
done in class. Try various methods to improve your final image. Try both
spatial domain procedures and frequency domain procedures.
Last modified on February 26, 2001
