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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