Image Enhancement / Image Sharpening
The problem of image enhancement is usually
considered a problem of quality improvement and image sharpening.
This is a very important branch of image processing. Among
the other processing algorithms, the algorithms that solve
the problems of the image detail extraction against a complicated
background are also part of the image enhancement. These
algorithms may be very useful in different fields, such as
medical and satellite imaging, graphic arts, etc.
The Frequency Correction
and
Image Sharpening
Global and high frequency correction are
powerful spatial domain filters oriented towards the extraction
of image details on the complex, obstructing or noncontrast
background. These filters are the spatial approximations
of the corresponding filters in the frequency domain. High
frequency correction leads to extraction of the smallest
image details and to a sharpening of the image. Global frequency
correction leads to extraction (enhancement) of the details
of various sizes.
Performing this type of operation directly
in the frequency domain is a complicated computing problem.
Current algorithms available on the market for local image
enhancement do not provide the optimum solution for this
problem. These algorithms are based on linear correcting
filters (usually called “unsharp masking”). It is a wellknown
fact that linear filters are not as effective as nonlinear
ones. In particular it means that linear frequency correction
filters often move the global dynamic range of the image
to the “white” or the “black” side. Thus, in extracting some
details others are lost.
We propose strongly nonlinear algorithms
for frequency correction. They are much more powerful and
free of the disadvantages of linear filters. Nonlinear frequency
correction may be accomplished by mediantype filtering,
or by MultiValued nonlinear filtering. This nonlinear approach
is the preferred one, because it provides the most effective
results, even when details being extracted have a very small
amount of contrast. As a result, a global histogram of the
image is by and large preserved; no extra “white” and “black”
pixels appear in the resulting image. These filters also
minimize shifts of the image boundaries.
The second solution is based on mixed spatial/frequency
domain filtering. Image sharpening is achieved by the Median
and Multivalued Frequency Correction algorithms, and then
the resulting image is corrected in frequency domain. This
operation ensures preservation of input image boundaries,
and eliminates possible shifts.
Examples
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Image Sharpening Examples


The original image “Sydney” 
Histogram (Green Channel) 


MVFhigh frequency correction,
3x3 window, Red channel: G=6.5, Green: G=5.5, Blue:
G=8.0 
Histogram of the image to the left (Green Channel).
This histogram does not contain any peaks 


Traditional unsharp masking using high
frequency correction (mean), 3x3 window, Red: G=0.8,
Green: G=1.0, Blue: G=0.5. Many pixels became truly
white or truly black. 
Histogram of the image to the left (Green Channel).
High peaks in “0” and “255” are clearly visible. It
means that many pixels have become truly white or truly
black. As a result, information in the corresponding
pixels is lost 


The original radar satellite image

Histogram 


MVFhigh frequency correction, 3x3 window,
G=6.0 
Histogram of the image to the left. The global histogram
behavior is preserved: no new peaks and a number of
white (255) pixels is even less than on the original
image 


The original Xray medical image (tumor
of lung) 
MVFglobal frequency correction, 35x35 window 


Precise Edge Detection Upward
The structure of the tumor is clearly visible 
Precise Edge Detection Downward
The structure of the tumor is clearly visible 



The original Xray medical image  mammogram. 
MVFhigh frequency correction, 3õ3 window,
G=8.0 
Global frequency correction, 9x9 window, G1=0.5, G2=5.0,
G3=0.5 
