Biomedical Engineering Reference
In-Depth Information
FIGURE 12.3
Ultrasound calibration. A tracked A-mode probe (a) has an associated 3D coordinate system.
The calibration challenge is to relate the position along the A-mode time axis (b) to a point
in 3D. For the B-mode probe (c), we want to relate 2D coordinates (
u
,
v
) in the B-mode scan
(d) to 3D space.
where
u
is the speed of sound in tissue,
P
0
is the position of the transducer,
and is the unit vector along the beam direction. The calibration process
involves finding
P
0
and A method to achieve this using multiple scans of
a steel ball is described by Maurer et al.
40
B-mode calibration relates a 2D image pixel, (
u
,
v
), to a 3D point,
P
, with
respect to a tracker on the probe. Prager
41
describes the transformations as
follows:
ˆ
ˆ
.
P
T
C
←
T
T
T
←
R
T
R
←
P
x
(12.2)
T
,
where
x
T
R
←
P
is the rigid transformation from x to the
probe tracker,
T
T
←
R
is from probe tracker to tracking device coordi-
nates, and
T
C
←
T
transforms tracking coordinates to the reconstruction or
(
s
u
u
,
s
v
v
,0,1
)
