Biomedical Engineering Reference
In-Depth Information
corresponding points in each surface. A point
P
on a surface/curve
S
, is called
important
point,
P
I
, if and only if the absolute value of the curvature at this
point is larger than a certain positive value (a threshold).
A
={
P
I
}={
P
∈
S
|
Curv(
P
)
|
>,>
0
}
(1.15)
As the
important
points are landmarks, one may expect that they are stable
for the same object. However, due to scanning artifacts, their number and loca-
tions may vary. By adjusting the curvature threshold, a common subset can be
found. Otherwise, the object has either suffered from non-rigid transformations
or its visible surface has no landmarks.
The signature, computed at each important point, encodes the surface cur-
vature seen from this point, thus giving it discriminating power. As shown in
Fig. 1.10 (a), for each important point
P
∈
A
defined by its 3D coordinates and
the normal
U
P
at the patch where
P
is the center of gravity, each other point
P
i
on the surface can be related to
P
by two parameters: The distance
d
i
=||
P
−
P
i
||
(1.16)
and the angle
α
i
=
cos
−
1
U
P
·
(
P
−
P
i
)
||
P
−
P
i
||
(1.17)
Also you can notice that there is a missing degree of freedom in this represen-
tation which is the cylindrical angular parameter. At each location in the image,
the gray value encodes the angle
β
i
=
cos
−
1
(
U
P
·
U
P
i
)
(1.18)
This represents the change in the normal at the surface point
P
i
relative to
the normal at
P
. Figure 1.10 (b) shows some signature images taken at different
important points on the skin model of a patient's head.
The next step in the registration process is to match corresponding signature
images of two surfaces. The ultimate goal of the matching process is to find at
least a three-points correspondence in order to calculate the transformation pa-
rameters. The benefit of using the signature images to find the correspondence is
that we can now use image processing tools in the matching, hence reducing the
time taken to find accurate transformation. One such tool is
Template Matching
in which a value defines how well a portion of an image matched a template.
