Digital Signal Processing Reference
In-Depth Information
TABLE 11.3
Number of Regions in Test Images Segmented by
the ICM and the Split-Merge SOM Algorithms
Image
Ground Truth
ICM
Split-Merge SOM
107931
5
7
7
122100
4
10
8
134975
5
13
8
47794
3
14
8
72398
4
15
11
98640
3
5
8
Figure 11.14 depicts the original image 98640 and the segmentation maps
produced by the ICM and the split-merge SOM. ICM is found to yield
spatially continuous regions of relatively large size that have well-defined
boundaries. The split-merge SOM yields small, spatially connected regions.
However, more regions describe the same object enabling a more accurate
description of the object shape in the latter algorithm.
To evaluate the performance of both algorithms, a ranking scheme of the
segmented images based on visual examination by a human observer is em-
ployed. Let us define by
the set of objects implied by
the qualitative description of the ground truth. Let
O ={
O
1
,O
2
,
...
,O
K
}
be
the set of regions with a unique label derived by the segmentation algorithm.
Three cases associate the segmentation outcome with the ground truth:
C ={
C
1
,C
2
,
...
,C
N
}
Case 1, Best match:
Best match is obtained when there is one-to-one
correspondence between the segmented regions and the ground
truth objects.
Case 2, Reasonable match:
Reasonable match is declared when there
is a one-to-many correspondence between a ground truth object and
the segmented regions.
Case 3, Mismatch:
Mismatch occurs when there is no correspondence
between the ground truth objects and the segmented regions.
Let
i
denote the case number. For the ground truth object
O
j
,
j
=
1
,
2
,
...
,K
,
the three cases are defined formally as follows:
1
if
i
=
1
card
{
O
j
∩ C}=
l
>
1 f
i
=
2
(11.113)
0
if
i
=
3.
Let
r
ij
be a binary index that indicates the detection of object
O
j
in the
i
th
case. The index
r
ij
is determined for each object by a visual examination of
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