Image Processing Basics - Digital Signal Processing: Fundamentals and Applications - page 710

EXAMPLE 14.7
Perform digital filtering on the noisy image using a 2 2 convolutional average kernel, and compare the enhanced
image with the original one given the following 8-bit grayscale original and corrupted (noisy) images:

2
4

3
5

100 100 100 100
100 100 100 100
100 100 100 100
100 100 100 100

4 4 original image :

2
4

3
5

99 107 113 96

92 116 84 107

4 4 corrupted image :

103 93 86 108

87 109 106 107

" 11
11

#

2 2 average kernel : 1
4

Solution:
In the following diagram, we pad edges with zeros in the last row and column before processing at the point where
the first kernel and the last kernel are shown in the dotted-line boxes, respectively:

99 107 113 96 0

0
0

92 116 84 107

103 93 86 108

1 07

87 109 106

0

000 00

99 107
92 116

To process the first element, we know that the first kernel covers the image elements as . Summing

each product of the kernel element and the corresponding image pixel value, multiplying by a scale factor of ¼,
and rounding the result, it follows that
1
4 ð99 1 þ 107 1 þ 92 1 þ 116 1Þ¼103:5
roundð103:5Þ¼104

107 113
116

In the processing of the second element, the kernel covers . Similarly, we have

84

1
4 ð107 1 þ 113 1 þ 116 1 þ 84 1Þ ¼ 105
roundð105Þ¼105
The process continues for the rest of image pixels. To process the last element of the first row, 96, since the kernel

96 0
107 0

covers only , we assume that the last two elements are zeros. Then

1
4 ð96 1 þ 107 1 þ 0 1 þ 0 1Þ¼50:75
roundð50:75Þ¼51