view of the figures shows dramatic changes on true scale levels 
(figure 3.2) and significant generalization on the coarser levels 
(figure 3.4). 
  
  
  
  
  
  
  
  
0.0 : 150.0 
  
Figure 3.2 Roughness of the signal in scale space (o varies 
from 0 to 7, AO= 1) 
  
1 1 
0.0 50.0 100.0 150.0 200.0 
pixel 
Figure 3.3 Roughness for the scale levels o= 8-15, ao= 1 
In w 
20- 
0.0 - 
      
! ! ' 
0.0 50.0 100.0 150.0 200.0 
pixel 
Figure 3.4 Roughness for the scale levels o- 16-23, A0= 1 
Further in figure 3.4 two nodes (at x = 70 and x = 90) are easy 
to recognize. A local maxima in w (at x= 160) could also be 
noticed. It is verged on local minima and which are far away 
from the edge. 
A closer look to the data shows some of the scale space pheno- 
mena mentioned in section 1.1. For this purpose the range 0 < 
x s 35 is zoomed in figures 3.5 - 3.9. The ac intervals in the 
multiscale image are chosen smaller with step sizes A02= 0.5. 
The area marked by a rectangle in figure 3.2 (cf. also figure 
3.5) shows that an edge is splitted into two edges increases as 
the scale parameters. 
fine 
In w 
  
8.0 
  
  
6.0 - US 
  
4.0 - 
coarse 
2.0= 
0.0- 
-2.04 ' ' 1 1 ' i 1 
0.0 5.0 10.0 15.0 200° : 290. — 300 — 350 
pixel 
Figure 3.5 Roughness of the scale space images for high 
resolution levels (0= 0-2, ao2= 0.5) 
The area marked by a circle in figure 3.2 indicates a local mini- 
ma which switches to a local maxima. That means the edge is 
detected up to a certain level and then it is lost. This effect in 
figure 3.6 (at x= 11 and x= 27) can be visually tracked very 
well. 
In w 
5.5 - 
4.5 - 
3.5 - 
2.5 - 
$5- 
  
0.54 
0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 
Figure 3.6 Roughness for the scale range (o= 3.1-3.5, A02= 
0.5) 
The node to the right (x= 13) seems to have a certain meaning 
for this process. For a lot of other nodes which are stable in 
their position over a certain o range similar processes are to be 
recognized: local maxima which are weaker and lie in the 
neighborhood of such a node will be absorbed, i.e. the edge is 
lost at this point. The comparison of figures 3.6 and 3.7 gives 
further hints to the stability of nodes. 
In w 
5.0- 
4.0 
30- 
2.0 - 
10 - 
0.0 - 
-1.0- 
1 1 ' ' 1 ' 1 | 
0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 
pixel 
Figure 3.7 Roughness for the scale range (o= 3.6-4.0, A02= 0.5) 
298 
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