Page 50 -

24 Chapter 2 ■ Edge-Detection Techniques

variation in level from pixel to pixel, and so the smooth lines and ramps of the
ideal edges are never encountered in real images.

Edge position Edge position
Grey Grey
10 Level 10 Level

5 5

0 0

0 5 10 15 20 0 5 10 15 20
Position Position
(a) (b)
Edge position Edge position
Grey Grey
10 Level 10 Level

5 5

0 0

0 5 10 15 20 0 5 10 15 20
Position Position
(c) (d)
Figure 2.3: Step edges. (a) The change in level occurs exactly at pixel 10. (b) The same
level change as before, but over 4 pixels centered at pixel 10. This is a ramp edge.
(c) Same level change but over 10 pixels, centered at 10. (d) A smaller change over 10
pixels. The insert shows the way the image would appear, and the dotted line shows
where the image was sliced to give the illustrated cross-section.

2.2.1 Models of Edges

The step edge of Figure 2.3a is ideal because it is easy to detect: In the absence
of noise, any significant change in grey level would indicate an edge. A step
edge never really occurs in an image because: a) objects rarely have such a
sharp outline; b) a scene is never sampled so that edges occur exactly at the
margin of a pixel; and c) due to noise, as mentioned previously.