Biomedical Engineering Reference
In-Depth Information
operation allows us to end up with a binary segmentation. At grid level
c
, the
partition is initialized by a single cube of the volume size. We iteratively divide
each cube as long as it intersects the segmentation mask and as long as its
size is superior to 2
3
c
. We finally get an octree partition which is anatomically
relevant.
When we change from grid level, each cube is adaptively divided. The sub-
division criterion depends first on the segmentation mask (we want a maxi-
mum precision on the cortex), but it also depends on the local distribution
of the variables
δ
s
(see Eq. (8.3)). More precisely, a cube is divided if it inter-
sects the segmentation mask or if the mean of
δ
s
on the cube is below a given
threshold. As a matter of fact,
δ
s
indicates the adequation between the data
and the estimated deformation field at voxel
s
. Therefore, this criterion mixes
an indicator of the confidence about the estimation with a relevant anatomical
information.
8.3.2.7
Parametric Model
We now introduce the deformation model that is used. We chose to consider an
affine 12-parameter model on each cube of the partition. That kind of model is
quite usual in the field of computer vision but rarely used in medical imaging.
If a cube contains less than 12 voxels, we only estimate a rigid 6-parameter
model, and for cubes that contain less than 6 voxels, we estimate a translational
displacement field. As we have an adaptive partition, all the cubes of a given grid
level might not have the same size. Therefore, we may have different parametric
models, adapted to the partition.
At a given resolution level
k
and grid level
,
k
,
={
n
,
n
=
1
···
N
k
,
}
is
the partition of the volume into
N
k
,
cubes
n
. On each cube
n
, we estimate
an affine displacement defined by the parametric vector
k
,
n
:
∀
s
=
(
x
,
y
,
z
)
∈
d
w
s
=
P
s
k
,
n
,
with
n
,
⎛
⎞
1
xyz
00000000
00001
xyz
0000
000000001
xyz
⎝
⎠
.
P
s
=
A neighborhood system
V
k
,
on the partition
k
,
derives naturally from
V
(see
section 8.3.2):
