Information Technology Reference
In-Depth Information
Fig. 39 Our proposed shape-based segmentation framework
2.6.1 Shape Modeling
The shape is represented using the signed distance function. Let I:
X !
R be an
n
D image usually n ¼
3,
/: X !
R be a function that refers to a
distance function representation for a given shape/contour
2orn ¼
X
R
n
be an
image domain which is bounded. The shape can be represented as follows:
S
where
8
<
0
; ð
x
;
y
Þ2S
/
s
ð
x
;
y
Þ
¼
ED
ðð
x
;
y
Þ; SÞ
[
0
; ð
x
;
y
Þ2R
S
ð
43
Þ
:
þ
ðð
;
Þ; SÞ
\
; ð
;
Þ2XR
S
ED
x
y
0
x
y
½
where
R
S
represents the inside region of the shape
S
. Let
ð
u
;
v
Þ
represents an pixel
location on
S
. For
8ð
x
;
y
Þ2/
, the distance between any
ð
x
;
y
Þ
point and its nearest
surface point can be calculated as follows:
q
ð
2
2
ED
ðð
x
;
y
Þ; SÞ
¼
min
ð
u
;
v
Þ2S
u
x
Þ
þð
v
y
Þ
:
ð
44
Þ
Figure
40
shows an example of a shape representation using the distance
function.
As opposed to conventional PCA, 2D-PCA is based on 2D matrix rather than 1D
vector. This means that, the image does not need to be pre-transformed into a vector
[
42
]. In addition, the image covariance matrix (G) can be directly constructed using
the original image matrices. As a result, 2D-PCA has two important advantages