Biomedical Engineering Reference
In-Depth Information
I
I
(7.11)
I
P
c
represents the coordinates of a pixel in millimeters,
x
and
y
stand for the coordinates of the contour referred to the image center
in pixels. The value of
k
is 0.217 mm/pixel, which can be obtained
from the scale marks on the raw image. This notation enables use
these coordinates in the homogeneous coordinate transform for
kinematics.
We assume that the two sensors are aligned at all times, sharing
the same orientation while moving the integrated sensor slowly
inside the silicone model. After obtaining the 6DOF information of
the magnetic tracker, we can calculate the posture of IVUS sensor tip,
which provides position of the center of catheter that, is known from
Hough transform in each image. Figure 7.26 shows the coordinate
systems relation among the Aurora emitter, magnetic tracker and
IVUS. The Aurora system coordinate can be assumed as the global
coordinate. We can calculate the kinematic transformation between
Aurora emitter coordinate system and IVUS coordinate system
according to:
PX Y Z
(,
,
,
1
)
Pkxky
(,
,
0 1
,
)
cPPP
c
O
O
M
TTT
(7.12)
I
M
I
O
O
I
(7.13)
PTP
I
I
C
O
P
[,
T
T
,
T
]
(7.15)
MORG
x
y
z
M
(7.16)
O
T
M
stands for the transformation matrix between the magnetic
tracker coordinate and the Aurora emitter coordinate and
M
T
I
expresses the transformation matrix between the magnetic tracker
coordinate and the IVUS emitter coordinate.
O
P
I
stands for the
coordinate of a pixel measured in millimeters in the global coordinate
system.
O
P
MORG
and
M
P
IORG
are the vectors relating the three frames of
reference.
O
T
M
is given by
2
P
[0,0,
d
]
IORG
¨
2
¸
12
Q
2
Q
2
QQ
2
QQ
2
QQ
2
QQ
T
y
z
x
y
0
z
x
z
0
y
x
©
¹
©
2
2
¹
2
QQ
2
QQ
1
2
Q
2
Q
2
Q Q
2
QQ
T
O
xy
0
z
x
z
yz
0
x
y
T
©
¹
(7.14)
M
©
2
2
¹
2
QQ
2
QQ
2
Q Q
2
QQ
1
2
Q
2
Q
T
xz
0
y
yz
0
x
x
y
z
©
¹
©
0
0
0
1
¹
ª
º
There are seven parameters
T
x
,
T
y
,
T
z
,
Q
0
,
Q
x
,
Q
y
,
Q
z
acquired
from the posture information of magnetic tracker (
T
x
,
T
y
,
T
z
, are
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