Biomedical Engineering Reference
In-Depth Information
to effectively compare different segmentation methods, we need to quantify the
segmentation accuracy. One possible measure of segmentation quality is the
similarity index
(SI) [87]. For a structure
s
, the SI is computed from the set
V
(
s
)
auto
of voxels in
s
according to the automatic segmentation and the set
V
(
s
)
manual
of voxels in
s
according to the (gold standard) manual segmentation:
2
V
(
s
)
auto
manual
∩
V
(
s
)
V
(
s
)
manual
+
V
(
s
)
auto
SI(
s
)
=
.
(11.8)
For perfect mutual overlap of both segmentations, manual and automatic, the
SI has a value of 1. Lesser overlap results in smaller values of SI. No overlap
between the segmentations results in an SI value of 0. A major advantage of the SI
measure is that it is sensitive to both over-segmentation and under-segmentation,
that is, it recognizes both false positives and false negatives among the voxels
of a given structure.
11.5.2
Bias from Structure Volume
In order to understand the SI values computed later in this chapter and to com-
pare them with other published values, we investigated the dependence of SI val-
ues on object size. We performed a numerical simulation in which discretely sam-
pled spheres of various radii were dilated by one or two voxels and the SI values
between the original and dilated spheres were computed. The resulting SI values
are plotted versus object radius in Fig. 11.12. It is also easy to derive a closed-form
expression for the continuous case. The SI between two concentric spheres, one
with radius
R
and the other dilated by
d
, i.e., with a radius of
R
+
d
,is
2(
R
/
d
)
3
SI
=
(11.9)
+
3(
R
/
d
)
+
1
.
2(
R
/
d
)
3
+
3(
R
/
d
)
2
The SI values for the discrete and continuous cases are almost identical
(Fig. 11.12). The SI value between a sphere and a concentric dilated sphere
approximates the SI value for a segmentation error consisting of a uniform
thickness misclassification on the perimeter of a spherical object. Inspection
of Fig. 11.12 and Eq. (11.9) shows that SI depends strongly on object size and is
smaller for smaller objects. A one voxel thick misclassification on the perimeter
of a spherical object with a radius of 50 voxels has an SI value of 0.97, but for a
radius of 10 voxels the SI value is only 0.86. Thus it is not surprising that Dawant
