0
0
0
(A – 1)
0
1
0
0
0
0
–1
–1
–1
+1/9
–1
8
–1
–1
–1
–1
–1
–1
–1
=1/9
–1
W
–1
–1
–1
–1
55
Image Filtering, Enhancement, and Restoration
FIGURE 3.17 High-boost mask.
Or simply, in terms of filters
High-boost filter = (A −1) all-pass filter + high-pass filter
(3.6)
As can be seen, setting A = 1 would result in the standard high-pass filter. But in a
typical high-boost filter by setting A > 1, a weighted version of the original image
is added back to the high-pass components. Such choices of A maintain the lowfrequency components lost in the pure high-pass filtering and therefore produce
improved images that not only emphasize the high frequencies (i.e., sharpen the
image) but also show almost all low-frequency components that are often lost in the
standard high-pass filters.
Figure 3.17 shows a high-boost filter. This mask is simply the weighted summation of the all-pass mask and the high-pass mask. The coefficient A determines the
share or weight of the original image on the filtered image. As it can be seen, the
second mask is nothing but a simple high-pass filter mask.
From the diagram of Figure 3.17, it should be apparent that W = 9A − 1 and any
choice of A will create a different high-boost filter with a different influence of the
original image on the final image.
The following example shows how MATLAB can be used to form a high-boost
filter. It also shows the impact of the parameter A on the filter performance.
Example 3.10
In this example, we explore the implementation of a high-boost filter in MATLAB.
In this implementation, we add a weighted version of the identity matrix K to the
matrix H. Figure 3.18 shows the effect of the high-boost filters on the original
image for different values of A.
I=imread(‘test.jpg’);
I=rgb2gray(I);
A=1.2;
H=(1/9)*[1 1 1;1 −8 1; 1 1 1];
K=[0 0 0;0 1 0;0 0 0];
HB=( (A−1).*K) + H;
sharpened = imfilter(I,HB);
imshow(I);
figure,
imshow(sharpened);
The best value of A for a particular image is often found by trial and error, but, in
many images, values around A = 1.15 provide desirable performances.
0
0
(A – 1)
0
1
0
0
0
0
–1
–1
–1
+1/9
–1
8
–1
–1
–1
–1
–1
–1
–1
=1/9
–1
W
–1
–1
–1
–1
55
Image Filtering, Enhancement, and Restoration
FIGURE 3.17 High-boost mask.
Or simply, in terms of filters
High-boost filter = (A −1) all-pass filter + high-pass filter
(3.6)
As can be seen, setting A = 1 would result in the standard high-pass filter. But in a
typical high-boost filter by setting A > 1, a weighted version of the original image
is added back to the high-pass components. Such choices of A maintain the lowfrequency components lost in the pure high-pass filtering and therefore produce
improved images that not only emphasize the high frequencies (i.e., sharpen the
image) but also show almost all low-frequency components that are often lost in the
standard high-pass filters.
Figure 3.17 shows a high-boost filter. This mask is simply the weighted summation of the all-pass mask and the high-pass mask. The coefficient A determines the
share or weight of the original image on the filtered image. As it can be seen, the
second mask is nothing but a simple high-pass filter mask.
From the diagram of Figure 3.17, it should be apparent that W = 9A − 1 and any
choice of A will create a different high-boost filter with a different influence of the
original image on the final image.
The following example shows how MATLAB can be used to form a high-boost
filter. It also shows the impact of the parameter A on the filter performance.
Example 3.10
In this example, we explore the implementation of a high-boost filter in MATLAB.
In this implementation, we add a weighted version of the identity matrix K to the
matrix H. Figure 3.18 shows the effect of the high-boost filters on the original
image for different values of A.
I=imread(‘test.jpg’);
I=rgb2gray(I);
A=1.2;
H=(1/9)*[1 1 1;1 −8 1; 1 1 1];
K=[0 0 0;0 1 0;0 0 0];
HB=( (A−1).*K) + H;
sharpened = imfilter(I,HB);
imshow(I);
figure,
imshow(sharpened);
The best value of A for a particular image is often found by trial and error, but, in
many images, values around A = 1.15 provide desirable performances.