Adaptive Multi-Shell Mdian Filter for Improving Image Quality
Multi-shell median filter
This method is proposed to solve the blur of image. Considering the median of set of number for one-dimensional as in equation (1)
Median [a1, a2, a3,] =
median [min a1, a3], a2, max [a1, a3]] (1)
a
2 will be considered and {a
1, a
3} are the neighbors around a2. The two-dimensional of 3 x 3 window can be carried out, at the center of the window, the central sample will be considered as in equation (2).
S1m,n =
{am-1,n-1, am-1,n, am-1,n+1, am,n-1
am,n+1 am+1, n-1, am+1,n,
am+1,n am+1,n+1} (2)
Given Y
m,n is output of multi-shell median filter at point m, n and
a
m,n is the data at the center of the considered window.
S
1m,n is the set of the called the first shell or the set of data around the center of window at point am,n as show in Fig. 1.
Fig. 1 First shell for 3 x 3 window.
The output of the multi-shell median filter is defined by;
Ym,n = median [min[S1m,n], am,n, max [S1m,n]] (3)
The equation (3) shows the considered sample and it is isolated impulse or the large difference from the neighbor around the considered point. It is separated from the group and substituted by the minimum of maximum of the first shell. The output equation depends on the considered central sample. It means that the center of the window keeps the status of median filtering output.
It is obviously that the multi-shell median filter can filter the salt or pepper noise for 1 pixel. For the impulse has more than 1 pixel, it is difficult to filter. It can maintain the salt and pepper noise and this picture is not so good.
The results are shown in Fig. 3(e) which has the higher sharp when compared with the 3x3 constant window.
Automatically adjustable window size.
Fig. 2 shows the ability to eliminate noise by using median filtering for the various length (L) of the windows.
Fig. 2 Various length of the window to compare the ability filtering the noise.
From Fig. 2 the length of the window con be made to decide for the suitable window by examining the number of point of the noise. The process is to examine for the horizontal and vertical window size. The first procedure is to examine the window length for horizontal window size
(L
h) and find out the window length for vertical window size
(L
v). Having finished both processed, it is necessary to arrange the data. Suppose that the set of P and Q are the difference of gray level of picture for various point of the window. After that to find the threshold level for testing P and Q, the threshold level is between 16 to 48 for each picture. The procedure for pepper noise and salt noise are he same, except the sign for P and Q is opposite.
