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Processing Articles
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| What
is Image Averaging?
Basic DETAILS... |
| Consider
a noisy image g(x,
y) formed by the addition
of noise µ(x, y) to
an original image
f(x, y); that is, |
|
 |
|
| where
the assumption is
that at every pair
of coordinates (x,
y) the noise is un-correlated. |
| Uncorrelated
Noise Means: the Variance
of a random variable
x with mean m is defined
as E[(x - m)2], where
E{.} is the expected
value of the argument.
The covariance of
two random variables
xi and yj is defined
as e[(xi, - mi)(xj
— mj)]. If the variables
are uncorrelated,
their covariance is
0.) |
| Thus
the noise has zero
average value. The
objective of the following
procedure is to reduce
the noise content
by adding a set of
noisy images {gi(x,y)}.
If the noise satisfies
the constraints just
stated, it can be
shown (Problem 3.15)
that if an image £(*,
y) is formed by averaging
K different noisy
images |
 |
then
it follows that
E{g(x, y)}=f(x,y)
Eq. 3
and
∂2g(x, y) =1/k ∂2µ(x,
y) Eq. 4 |
|
where
E{g(x, y)} is the
expected value of
g and ∂2g(x, y) and
∂2µ(x, y) are the
variances of g and
µ, all at coordinates
(x,y). The standard
deviation at any point
in the average image
is
∂g(x, y) =1/k ∂µ(x,
y) Eq. 5 |
|
| As
K increases, Eqs.
(4) and (5) indicate
that the variability
(noise) of the pixel
values at each location
(x,y) decreases. Because
E{g(x, y)} = f(x,y),
this means that g(x,
y) approaches f(x,
y) as the number of
noisy images used
in the averaging process
increases. In practice,
the images g(x, y)
must be registered
(aligned) in order
to avoid the introduction
o| blurring and other
artifacts in the
output image. |
|
| Where
to Use Image Averaging? |
|
| An
important application
of image averaging
is in the field of
astronomy where imaging
with very low light
levels is routine,
causing sensor noise
frequently to render
single images virtually
useless for analysis.
Following is an image
of a galaxy pair called
NGC 3314, taken by
NASA's Hubble Space
Telescope with a wide
field planetary camera.
NGC 3314 lies about
140 million light-years
from Earth, in the
direction of the southern-hemisphere
constellation Hydra.
The bright stars forming
a pinwheel shape near
the center of the
front galaxy have
formed recently from
interstellar gas and
dust. |
|
| the
images obtained so
far are then subjected
to applications to
make the image average
to get maximum information
from these images. |
|
| Basic
Algorithm Of Image
Averaging |
|
| Two
images are combined.
To determine the value
of each pixel in the
resulting image, the
corresponding intensity
values from the two
original images were
multiplied. This result
was divided by the
average intensity
over both images.
This process was repeated
for red, green, and
blue. |
|
| Guidelines
for Use |
| To
understand the working
of the Image Averaging,
take the example of
the following images: |
|
  |
|
| the
Resultant Image Obtained
by the Averaging of
the above images is
as: |
|
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|
| Sample
Project |
|
| Please
Review other articles
based on Logical Operators
to get the better
understanding of the
project. The application
seems to be in this
GUI. |
|
 |
|
| The
project is a part
of the series of the
image processing articles
written just for the
prosperity and help
for the students searching
for Image Processing
free stuff. |
|
Download
Project Files
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