Fast directional weighted median filter for removal of random valued impulse noise

An Efficient

Directional WeightedMedian Filter

for Random Valued Impulse Noise

National University of Computer and Emerging Sciences (NUCES)

(FAST)

PresenterWaqas Nawaz (08-0824)

SupervisorDr. Irfan Jaffer

AGENDA

• Motivations• Paper: Directional Weighted Median

Filter• Paper: Fast Median Filters• Proposed Strategy• Simulation Results• Conclusion• References

MOTIVATIONS

• 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.

DIRECTIONAL WEIGHTED MEDIAN FILTER [1]

• 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.

DIRECTIONAL WEIGHTED MEDIAN FILTER [1] CONT…

• 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.

2. After detecting the impulse noise, we incorporate it with the Weighted Median Filter [3] to come up with new Directional Weighted Median Filter.

DIRECTIONAL WEIGHTED MEDIAN FILTER [1] CONT…

• New Impulse Detector1. 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:

DIRECTIONAL WEIGHTED MEDIAN FILTER [1] CONT…

• New Impulse Detector2. Now the summation which is minimum

from all four directions is used to detect whether the pixel is noisy or noise-free.

DIRECTIONAL WEIGHTED MEDIAN FILTER [1] CONT…

• DWM Filter1. 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.

DIRECTIONAL WEIGHTED MEDIAN FILTER [1] CONT…

• DWM Filter2. We assign a weight to these pixels and

restore the noisy pixel as:

3. Output of DWM Filter will be as follows:

FAST MEDIAN FILTER [2]

• 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.

FAST MEDIAN FILTER [2]

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).

FAST MEDIAN FILTER [2]

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.

PROPOSED STRATEGY

DWM Filter

Fast Media

n Filter

An Efficient

DWM Filter

PROPOSED STRATEGYNoisy 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

SIMULATION RESULTS

SIMULATION RESULTS

CONCLUSION

• 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.

REFERENCES[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.

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