Computer Science, Image Processing

2. • Motivations
• Paper: Directional Weighted Median Filter
• Paper: Fast Median Filters
• Proposed Strategy
• Simulation Results
• Conclusion
• References

3. • The known median-based de-noising methods
tend to work well for restoring the images
corrupted by random-valued impulse noise with
low noise level, but poorly for highly corrupted
images [1].
• In Directional Weighted Median approach
[1], standard Median filter is applied, which is
not an efficient and effective method for
calculating median value of a particular window.

4. • In this approach, there are two major steps:
1.
New Impulse Detector, which is based on the
differences between the current pixel and its
neighbors aligned with four main directions.

5. • In this approach, there are two major steps:
New Impulse Detector, which is based on the
differences between the current pixel and its
neighbors aligned with four main directions.
2. After detecting the impulse noise, we incorporate it
with the Weighted Median Filter [3] to come up with
new Directional Weighted Median Filter.
1.

6. • New Impulse Detector
1.
First, calculate the sum of all absolute differences of
gray level values in a particular direction. Repeat it
for all four directions using the following formula:

7. • New Impulse Detector
2. Now the summation which is minimum from all four
directions is used to detect whether the pixel is
noisy or noise-free.

8. • DWM Filter
1.
We calculate the Standard Deviation of gray level
values for all directions because it describes how
tightly all the values are clustered around the mean
in the set of pixels.
where li,j shows that four pixels aligned with this
direction are the closest to each other.

9. • DWM Filter
2. We assign a weight to these pixels and restore the
noisy pixel as:
3.
Output of DWM Filter will be as follows:

10. • Median filter, with its fine detail preservation
and impulsive noise removal characteristics, has
taken its place in many signal and image
processing application.
• But an important shortcoming of the median
filter is that the median algorithm has low speed
so as to restrict its application.

11. Median Computation based on Histogram (MBH)
• Considering that array values used for calculating
median have limited distribution scope,
denote the array for calculating median, where
0≤xi ≤M and xi is an integer. Our basic idea is to apply
cut and try method from zero to M in turn till the
median is found. In this way, the maximum number of
times of experiments for searching median is M, that
is to say the algorithm complexity is O(M).

12. Median Computation based on Histogram and
staged search (MBHSS)
• In
this extended version of the previous
algorithm, the histogram is divided in equal chunks,
• If the summation is smaller than the index of the
middle value then we do not need to traverse that sub
region for median ,
• Otherwise, the median value lies inside that region.

14. Noisy image's pixel values for calculating
median value, e.g. 5x5 window
impulse detection using weighted difference
along four directons in its neighborhood and
threshold value
determine direction on the basis of standard
deviation and add pixel values to the window
apply the fast median filter on the updated
window and return the median value
replace the central value of the considered
window with median value

17. • Standard Median Filter is very effective for impulse
noise removal but it is inefficient because its time
complexity is O(N2) or O(NlogN) and Fast median
filter can be applied in linear time (i.e. O(M)).
Simulation results shows that the time complexity of
Directional Weighted Median Filter has been
improved by incorporating the fast median filter.

18. [1]
Dong. Yiqiu, Xu. Shufang, “A New Directional Weighted Median
Filter for Removal of Random Valued Impulse Noise” IEEE Signal
Processing Letters. VOL. 14, No. 3, March 2007.
[2]
Tang. Quanhua, Zhou. Yan, Lei. Jine, “Fast median filters based
on histogram and multilevel staged search”, IEEE Fourth
International Conference on Image and Graphics, 2007.