Feb 12, 2001
Frequency Space Filtering
First step is to center everything; the image data must be multiplied
by (-1)x+y, while the x and y frequencies, n and
m, must be offset by N/2:
f(x,y) => f(x,y)(-1)x+y,
while for an NxN array
![](images/Image166.gif)
![](_themes/sandston/astonrul.gif)
Image Restoration
Sometimes an image is blurred or degraded by an optical system, motion,
defects, etc. If the transfer function of the degradation is known (this is a big
if) then a process of inverse filtering can restore the original image.
Assuming little or no noise,
G = HF so F = G/H
This works if there is little noise and the transfer function H(n,m)
is known. If there is noise, the process falls apart. Even then, a more
sophisticated method using the so-called Weiner filter can sometimes give
back a fairly well restored image. However, the real limitation of such methods
is the need to know H.
![](_themes/sandston/astonrul.gif)
Non-Linear Spatial Filters
Instead of using the spatial mask in a convolution process, sometimes the
mask is used simply to obtain the neighboring values of a pixel, and various
ordering systems are used to determine the proper substitution to obtain a good
new pixel value. This may include using the median value (as in the median
filter discussed earlier), the maximum or the minimum value, a weighted value
(throw away some of the values from both ends). This is called using rank
or order statistics.
Last modified on February 12, 2001