Enhancements

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Enhancements
Techniques for editing an image such that it is
more suitable for a specific application than the
original image. Spatial domain g(x,y)
Tf(x,y) Frequency domain g(x,y)
FT-1H(u,v) F(u,v h(x,y) ?f(x,y)
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Point processing
Gamma transformation s c r ?
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Histogram
Landsat image river Taag Histogram
With histogram equalization we search for a T(r)
that makes the histogram as smooth as possible.
The T(r) that accomplishes that is sk round(
L ?j0 k (nj / n) )with nk the number of pixels
with gray level k, n the total number of pixels
and L the number of gray levels.
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Examples
Local contrast enhancement g(x,y) ?(x,y) kM
(f(x,y) - ?(x,y))/?(x,y)
Original Contrast stretched Hist. equalization
Local histogram Local contrast
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Smoothing
This is used for the blurring of an image the
removal of small details and the filling in of
small gaps in lines, contours and planes, and
also reduces the noise in an image.
In the frequency domain smoothing becomes G(u,v)
H(u,v)F(u,v) low pass filter In the
spatial domain smoothing is the removal of
drastic changes by averaging the gray levels in a
certain region with a positive weight.
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Smoothing Frequency domain
Butterworth LPF Hn(u,v)1/(1(?(u2v2)/D0)2n
) the Exponential LPF Hn(u,v)exp(-?(u2v2)/D0
)n ) the Gaussian LPF H(u,v)exp( - (u2v2) / 2
D02)
Ideal LPF, the rings of especially the rivers can
clearly be seen.Right image Butterworth LPF
with n5. Here the ringing has decreased.
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Gaussian LPF
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Smoothing spatial domain
A linear filter can be shown as a convolution
mask       1 1 1 1 1    0 1 1 1
0       1 2 3 2 1        1  4  6  4  1     
1 1 1 1 1        1 1 1 1 1       2 4 6 4
2        4 16 24 16  4(1/25) 1 1 1 1 1
 (1/21)1 1 1 1 1 (1/81)3 6 9 6 3 (1/256)6
24 36 24  6      1 1 1 1 1        1 1 1 1
1       2 4 6 4 2        4 16 24 16  4     
1 1 1 1 1        0 1 1 1 0       1 2 3 2
1        1  4  6  4  1 The 2 right filters
are examples of separable filters, they can be
executed as a convolution with (1/9) 1 2 3 2 1
respectively (1/16) 1 4 6 4 1   in the x
direction, followed by a convolution in the y
direction. The right filter is a poor
approximation of the Gaussian function g(x,y) c
exp( (x2y2) / 2 ? 2), better ones are not
separable. With a non-linear "rank" or
"order-statistics" filter, the pixel values in
the neighborhood are sorted according to
increasing value, the value at a fixed position
in the row is chosen to replace the central
pixel. Choosing a value in the middle results in
a so-called median filter.
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Examples mean and median
image     average filter 
median filter   9 9 9 0 0 0    . . . .
. .     . . . . . .   9 9 9 0 0 0    . 8 5 3 0
.     . 9 9 0 0 .   9 0 9 0 0 0    . 8 5 4 1
.    . 9 9 0 0 .   9 9 9 0 9 0    . 8 5 4 1
.    . 9 9 0 0 .  9 9 9 0 0 0    . 9 6 4 1
.    . 9 9 0 0 .   9 9 9 0 0 0    . . . . .
.    . . . . . .
Original 5x5 mean 5x5 median 20 impulse
noise 5x5 mean 5x5 median
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Noise models
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Noise models (2)
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Sharpening
This is used to bring fine details to the front
of the image and to sharpen the edges of objects.
High Pass Filter G(u,v) H(u,v) F(u,v).
ideal HPF H(u,v) 1 if  ?(u2v2) gt D and 0
otherwise, see fig. 4.24 Butterworth HPF H(u,v)
1/(1D/  ?(u2v2) )2n, see fig.
4.25Exponential HPF H(u,v) exp(- D/  ?(u2v2)
)nGaussian HPF H(u,v) 1- exp( - (u2v2) / 2
D02) see fig. 4.26
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Examples combinations
Here an example from High Frequency Emphasis,
where the third order Butterworth HPF is added to
the original image using the proportion 0.71.
Blur masking I-LPF(I) The impact of
fragments from the Shoemaker-Levy comet on
Jupiter on July 19th 1994.
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Sharpening in the spatial domain
Differences in the gray levels between pixels,
often as an approximation of the derivative of
the image function f(x,y)    ?f(x,y) (? f/
?x,  ? f/ ?y )  ?( ( ?f/ ?x)2  ( ?f/ ?y)2 )
results in the gradient image. In the simplest
case, one discretely approximates   ? f/ ? x
fx,y - fx-1,y g( fx,y )  ? f/ ? x
 ? f/ ? y Other manners often used to
determine the derivative are 1  0 0 1  -1
-1 -1 -1 0 1  -1 -2 -1 -1 0 10 -1 -1
0  0  0  0 -1 0 1  0  0  0 -2 0
2               1  1  1 -1 0 1  1  2  1
-1 0 1    Roberts           
Prewitt              Sobel Prewitt and
Sobel take more pixels into account and are thus
less sensitive to noise.
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Sobel
Original Simple derivative Sobel
Gausian
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Laplacian
Other sharpening operators are derived from the
Laplacian     ?2 f(x,y)     ?2f/ ? x2   ?
2f/ ?y2 Discretely, one can use masks       -1
-1 -1          0 -1  0(1/9) -1  8
-1 or (1/5) -1  4 -1      -1 -1 -1         
0 -1  0
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Moon
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Whole body bone scan