Biomedical Engineering Reference
In-Depth Information
A general perspective projection can be described by (see Chapter 3):
x
y
z
1
k
u
0
u
0
0
0
k
v
v
0
0
0010
T
rigid
u
v
1
(12.1)
T
T
where the vectors and are the homogeneous coordi-
nates of a 3D point and its 2D projection. The term
(
x
,
y
,
z
, 1
)
(
u
,
v
, 1
)
represents the distance
from the effective pinhole along the optical axis (the
Z
axis in the above for-
provides the perspective effect
of more distant objects being smaller. There are ten camera parameters, four
intrinsic—(
mulation). Division by
to calculate
u
and
v
) is
the perpendicular projection of the origin—and the six extrinsic parameters
of the rigid-body transformation. A general 3
k
,
k
) are the pixel sizes relative to the focal length and (
u
,
v
u
v
0
0
4 matrix can be decomposed
26
into these ten parameters.
The most widely used calibration method is that
27
developed by Tsai,
where an iterative scheme is used to calculate the ten
parameters. Tsai also incorporates a polynomial radial distortion model.
12.4.1.2
Video Registration
The use of calibrated stereo video with patterned light, either a regular grid
from a laser or a speckled pattern to provide high frequency details and high
contrast, can rapidly produce a large number of surface points. These can
then be matched to the same surface from the preoperative scan.
4
A method which can potentially match a single video image to a preoperative
scan surface was originally proposed by Viola and Wells.
28
A rendering of the
3D surface is produced and compared to the video image. The 3D rigid trans-
formation of the preoperative surface is iteratively updated, and the mutual
information (MI) between the normal vectors in the model and the video frame
calculated. Tracking with such a method can be enhanced by the use of texture
mapping
29
30
and has improved efficiency by rendering using OpenGL.
Single view algorithms invariably suffer from inaccuracies along the optical
axis of the camera. While it is possible to resolve to better than 1 mm perpen-
dicular to the optical axis, errors increase to 3-5 mm at best along the line of
sight.
28
31
Using two or more cameras enables must better 3D resolution.
A new method which can be used with two or more video images has been pro-
posed by Clarkson et al.
32
This method requires the surface visible in the video
images, such as a skin or bone surface, to be segmented from the preoperative
image. The algorithm uses a similarity measure termed photoconsistency.
The measure takes each point on the segmented surface and calculates the
image intensity where this point projects in each video image. Assuming a
fixed light source and a Lambertian reflectance, the intensity value in each
video image should be the same at registration. The photoconsistency mea-
sure is based on the variance of the difference between the intensity values in
