Image Processing Reference
In-Depth Information
1
0.8
0.6
0.4
0.2
0
0
5
2
4
6
8
10
10
τ
12
D
⊥
14
15
16
20
FIGURE 4.7: Quality of approximation for the '
factory
' image shown in
Fig. 4.6. The plot of IEF = f(τ,d
⊥
) versus the error tolerance τ and the
isothetic distance d
⊥
corresponding to criterion C
max
has been shown, and
that corresponding to criterion C
is quite similar. Note that here τ = 0
corresponds to the number of vertices without any polygonal approximation
(i.e., with ADSS only).
P
the count of DSS in covering the same segment. This fact is used to expedite
the subsequent algorithm for polygonal approximation. Further, the ADSS-
recognition algorithm is much faster than a DSS extraction algorithm because
of the recursive nature of the latter.
Fig. 4.6 demonstrates the polygonal approximation with the criterion C
max
for the '
factory
' image
5
for a few values of τ. In Fig. 4.7, the plot on IEF
using criterion C
max
only has been shown, since the plot with criterion C
P
is quite similar. It may be observed from this plot that, for higher values of
τ, the amount of maximum isothetic deviation (d
⊥(max)
) falls quite short of
the permissible limit, i.e., τ; in particular, for a given value of τ, the number
of points (N
d
⊥
) with deviation d
⊥
decreases almost monotonically with d
⊥
.
In Fig. 4.8, approximate polygons for another image with few values of τ,
corresponding to the approximation criterion C
max
, have been shown.
Fig. 4.9 shows the result of using the algorithm directly on a gray-scale
image, as explained in Sec. 4.4. To compute the Prewitt responses, T is taken
as 100. The chain code properties R1 and R2 are used with α = 2 (Eq. 4.18)
to detect the straight edges. To reduce the number of edges by merging the
almostcollinear edges (Sec. 4.4.4), τ is taken as 2. Both the Sobel and the
Prewitt operators can be used to find the straight edges in a gray-scale im-
5
Source:
The
Berkeley
Segmentation
Dataset
and
Benchmark,
http://www.eecs.berkeley.edu/Research/Projects/CS/vision/bsds/
.
