Information Technology Reference
In-Depth Information
The basic HK segmentation algorithm works as follows: the input is a raw im-
age
G
and a set of six kernel shape labels
{
}
s
K
, associated to the classes of
Table 1. The first and second order gradients of the input image,
G
x
,
G
y
,
G
z
,
G
xy
,
G
xz
,
G
yz
,
G
xx
,
G
yy
and
G
zz
should be computed first. The expressions of
H
and
K
are
evaluated at each image point, with signs from Table 1. The Gaussian curvature
operator
K
for 3D images can be computed as [6]:
( )
,
,
s
1
6
( )
( )
T
T
T
⊥
⊥
⊥
⊥
⊥
⊥
∇
G
S
∇
G
+
∇
G
S
∇
G
+
∇
G
S
∇
G
1
G
1
1
2
G
2
2
3
G
3
3
K
(
x
,
y
,
z
)
=
(6)
2
∇
G
using (subscripts
x, y, z
indicate partial differentiations)
−
G
⎡
−
G
⎤
⎡
−
G
⎤
⎡
⎤
z
y
z
⊥
⊥
⊥
G
1
=
,
G
2
=
,
G
3
=
(7)
⎢
⎣
⎥
⎦
⎢
⎣
⎥
⎦
⎢
⎣
⎥
⎦
G
G
G
y
x
x
and
⎡
G
G
⎤
⎡
G
G
⎤
⎡
G
G
⎤
xx
yy
z
xy
xx
x
z
y
S
1
=
,
S
2
=
,
S
3
=
.
(8)
⎢
⎣
⎥
⎦
⎢
⎣
⎥
⎦
⎢
⎣
⎥
⎦
G
G
G
G
G
G
G
G
G
yx
yy
yz
zz
zx
zz
Mean curvature
H
of a 3D image can be extended from a 2D expression as [6]:
(
)
(
)
(
)
2
2
2
G
G
+
G
+
G
G
+
G
+
G
G
+
G
x
yy
zz
y
zz
xx
z
xx
yy
H
(
x
,
y
,
z
)
=
−
(
)
3
2
2
2
2
2
G
+
G
+
G
(
x
y
z
)
(9)
2
G
G
G
+
G
G
G
+
G
G
G
x
y
xy
x
z
xz
y
z
yz
−
.
(
)
3
2
2
2
2
2
G
+
G
+
G
x
y
z
After computing the
H
and
K
, the shape image
L
can be computed by assigning a
shape label
l
i
to each voxel, according to the rules in Table 1. The output is the
shape image
L
. In order to be used by subsequent tasks, the output of segmentation
algorithm can be converted into a list of symbolic patch descriptors. In each de-
scriptor, a surface patch is associated with a number of attributes which may in-
clude a unique identifier position of the patch centre, patch area, information on
normals and curvature contour representations, and pointers to neighbour patches.
Closed form surface models (e.g. quadrics) are fitted to the surface patches ex-
tracted by the HK segmentation, and only the model's coefficients and type
(e.g. cylinder, cone) are stored in the symbolic descriptors.
3 3 D Image Segmentation and Classification
The main goal of the segmentation process is to divide an image into subregions
(also called subvolumes) that are homogenous with respect to one or more charac-
teristics or features. There is a wide variety of segmentation techniques and proc-
esses depending on the input data. Computer segmentation is desirable to perform,
