Biomedical Engineering Reference
In-Depth Information
calibration volume. The pixel scalings (in mm) of the B-scan are given by
s
u
and
s
v
.
For the calibration we are interested in calculating eight parameters, six for
the rigid-body transformation
T
R
←
P
plus
s
u
and
s
v
. A number of phantoms
have been proposed, which have an associated constrained set of
P
coordi-
nates. The simplest is a crosswire.
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The origin of the calibration volume is set
to be at the crosswire, so
P
T
in homogeneous coordinates. The
position of the crosswire in the B-scan and the tracking of the probe are mea-
sured for a number of scans giving measurements of (
u
,
v
) and
T
T
←
R
. An iter-
ative search can then give the desired parameters. A crosswire is a rather
laborious calibration phantom, since holding the probe still is awkward and
the position in the B-mode scan usually needs to be marked manually. A flat
plane can also be used, however. In this case
P
(
0, 0, 0, 1
)
T
if we define
the plane as perpendicular to the z axis. With an ingeniously manufactured
device known as the Cambridge phantom, Prager manages to create a vir-
tual plane with a surface that remains largely perpendicular to the probe
throughout the range of required movements.
41
This provides a quick and
accurate calibration.
A further method is to use a 3D calibration object with multiple features
of known shape. These could either be measured using 3D scan of the phan-
tom or accurately manufactured. Taking a number of B-scans of the phan-
tom and their associated tracking matrices, it is possible to iterate over the
eight calibration parameters to achieve the best match between the 3D
model and the set of B-scans. Using normalized mutual information (NMI)
43
described in Section 3.4.8 of Chapter 3, as a similarity measure and employ-
ing a hierarchical search strategy, this approach has been shown to provide
accurate calibration.
44
Advantages of this method include the fact that no
segmentation of the B-scans is required and that the phantom can be made
from tissue-equivalent gel rather than using water. Both this method and
the Cambridge phantom have provided calibration accuracy of better than
1 mm on a 10 MHz probe.
(
x
,
y
, 0, 1
)
12.4.3.2 Ultrasound Registration
A-mode ultrasound can provide a number of points on the interface between
two tissue types. These can be matched to the same interface from a preoper-
ative scan using a points-to-surface matching algorithm such as iterative
closest point.
24
The proposed application of a calibrated A-mode probe is
location of points on the skull surface for noninvasive registration to bone for
image-guided neurosurgery.
40
A calibrated B-mode probe can also provide points on the interface
between bone and soft tissue if this surface is segmented from the B-mode
scans. These points can be matched to a preoperatively segmented dataset in
the same way. This has been proposed as a method of registration for pedicle
screw implantation in the spine.
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