Biomedical Engineering Reference
In-Depth Information
3D view
Kernel/Uniform
Kernel/Gaussian
Kernel/Manual
Figure 8. Comparison of the segmentations obtained with the kernel prior (white) and with
alternative approaches (black).
mentations are in general not perfect. Figure 7 provides qualitative comparisons
to the manual segmentation, as well as to the segmentations obtained with uniform
and Gaussian approximations of the shape distribution.
5.2.2. Quantitative analysis of segmentation accuracy
To further quantify the segmentation accuracy, we consider three different cri-
teria: the Dice coefficient, the average surface distance, and the centroid distance.
The Dice coefficient is defined as
2 |
S manual
S auto |
DSC =
,
(9)
|
S manual | + |
S auto |
where
|
S manual |
and
|
S auto |
are the volumes of the manual and automatic segmen-
tations, and
is the volume of their intersection. This coefficient
can be expressed directly with the level set representations:
|
S manual
S auto |
2
H ( φ manual ) H ( φ auto ) dx
H ( φ manual ) dx
DSC =
H ( φ auto ) dx .
(10)
In general, a value of DSC superior to 0.7 is considered a good agreement. The
other two criteria can also be expressed in similar manner. The average surface
distance is given by
|∇
|∇
.
H ( φ manual ) ||
φ auto |
dx
H ( φ auto ) ||
φ manual |
dx
D surf ace = 1
2
|∇
|∇
+
H ( φ manual ) |
dx
H ( φ auto ) |
dx
(11)
Essentially, this quantity amounts to averaging the distance of each contour point
on one contour to the nearest contour point on the other contour (and vice versa).
The centroid distance is the distance between the centers of mass:
xH ( φ manual / auto ) dx
c manual / auto =
.
H ( φ manual / auto ) dx
 
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