Image Processing Basics - Digital Signal Processing: Fundamentals and Applications - page 717

After processing using the Sobel horizontal edge detector, we have
2
4

3
5

330 440 440 330
0 0 0 0
30 40 40 30
0 0 0 0
300 400 400 300

Adjusting the scale level leads to

2
4

3
5

222 255 255 222
121 121 121 121
112 109 109 112
121 121 121 121
30 0 0 30

Disregarding the first row and column and the last row and column, since they are at image boundaries, we identify
a horizontal line of 109 in the third row .

Figure 14.28 shows the results from edge detection.
Figure 14.29 shows the edge detection for the grayscale image of the cruise ship in Figure 14.3 .
Sobel edge detection can tackle only the horizontal edge or the vertical edge, as shown in Figure 14.29 ,
where the edges of the image have both horizontal and vertical features. We can simply combine the
two horizontal and vertical edge-detected images and then rescale the resultant image in the full range.
Figure 14.29 ( c) shows that the edge detection result is equivalent to that of the Laplacian edge detector.
Next, we apply a more sophisticated Laplacian of Gaussian filter for edge detection, which is
a combined Gaussian lowpass filter and Laplacian derivative operator (highpass filter). The filter
smoothes the image to suppress noise using the lowpass Gaussian filter, then uses the Laplacian
derivative operation for edge detection, since the noisy image is very sensitive to the Laplacian
derivative operation. As we discussed for the Gaussian lowpass filter, the standard deviation in the
Gaussian distribution function controls the degree of noise filtering before the Laplacian derivative
operation. A larger value of the standard deviation may blur the image; hence, some edge boundaries
could be lost. Its selection should be based on the particular noisy image. The filter kernel with
a standard deviation of s ¼ 0 : 8 is given by
2 3

43634
13

4 5

9 25 9 13

16 25 124 25 16 (14.15)

13 9 25 9 13

43634

The processed edge detection using the Laplacian of Gaussian filter in Equation (14.15) is shown in
Figure 14.30 . We can further use a threshold value to convert the processed image to a black and white
image, where the contours of objects can be clearly displayed.