Biomedical Engineering Reference
In-Depth Information
Table 1.1:
Most important nomenclature used throughout the chapter
x
Vector function denoting a point on the model surface
y
Vector function denoting a point on the experimental surface
S
General surface
T
Transformation matrix
R
Rotation matrix
t
Translation vector
d
(
y
i
,
S
)
The distance of point
y
i
to shape
S
F
()
Registration objective function
C
()
The closet point operator
GCP
()
Grid Closest Point transform
3D space subset
G
r
Displacement vector in the GCP grid
R
C
H
Coordinates of the GCP grid
{
,
,
}
Grid resolution
δ
C
ijk
Grid cell
c
0
ijk
Centroid of the cell
C
ijk
α
,
β
, and
γ
3D-angles of rotations
θ
Simplex mesh angle
P
3D point on a free-form surface
H
Mean curvature of the surface
U
P
Normal vector at point
P
A
Set of landmarks
λ
Curvature threshold
E
n
Matching value
O
Overlap ratio
s
Scale factor
F
A medical volume
h
()
Entropy function
Rf
A reference medical volume.
Another example of the use of medical image registration is in neurosurgery
where it is useful to identify tumors with magnetic resonance images (MRI), yet
the established stereotaxy technology uses computed tomography (CT) images.
Being able to register these two modalities allows one to transfer the coordinates
of tumors from the MR images into the CT stereotaxy. It is similarly useful to
transfer functional information from SPECT or positron-emission tomography
(PET) into MR or CT for anatomical reference, and for stereotactic exploitation.
The currently used imaging modalities can be generally divided into two
main categories, one related to the anatomy being imaged and the other to
the functionality represented in the image. The first one includes X-ray, CT
