Biomedical Engineering Reference
In-Depth Information
where
H
refers to the Heaviside function (equal to 1 for negative values and
0 on positive values) and
T
is an optimal transformation to track the targeted
structure of interest between to consecutive time-frames images
I
t
and
I
t
+
1
satisfying the visual consistency constraint:
I
t
(
x
,
y
)
≈
I
t
+
1
(
x
,
y
)
,
∀
(
x
,
y
)
/
H
(
φ
t
(
x
,
y
))
≥
0
(2.36)
with
φ
defined with negative values inside the object to segment (i.e., the ven-
tricle blood cavity in this case).
This work uses a shape-model defined in a level set framework. Several in-
teresting recent efforts have focused on the use of level set framework for shape
modeling and registration toward model-based shape-driven object extraction
as reviewed in [58].
2.3.3
Registering Contours for Multimodalities
Segmentation
In a recent paper Yezzi
et al.
[59] introduced a new variational deformable
model framework that interleaves segmentation and feature-based registration
for combined segmentation of a single organ from multiple screening modalities
(e.g., skin surface from head CT and MRI).
They defined their problem as follows: They want to find closed surfaces
S
and
S
to segment an object in images
I
and
I
so that the curves, segmenting the
same organ, are related through a geometrical mapping:
S
=
g
(
S
). The authors
used rigid registration for the mapping (i.e., combination of rotation and trans-
lation) and defined the following coupled functionals for the surface
S
and the
registration parameters
g
=
[
g
1
,
g
2
,...,
g
n
] :
f
(
x
)
+
f
(
g
(
x
))
N
−
κ
N
∂
S
∂
t
=
f
(
g
(
x
))
∂
g
(
x
)
N
dA
(2.37)
dg
i
dt
=
∂
g
i
,
S
where
κ
and
dA
denote the mean curvature and area element of the surface
S
,
N
,
N
are the unit normals of
S
,
S
. The registration vector is modelized
as:
g
(
x
)
=
Rx
+
T
(2.38)
