Image Processing Reference
In-Depth Information
1.0
MSD
MI-TRI
MI-PV
0.8
0.6
0.4
0.2
0.0
2
1
0
1
2
FIGURE 7.5 Registration with MSD, MI-TRI, and MI-PV approaches on simulated data.
The pixel resolution was 1.2 mm with a 5-mm slice thickness. Random 3-D roto-
translation was imposed on the data set and the efficiency of the registration
procedure was evaluated for the MSD metric with trilinear interpolation (MSD-
TRI), MI metric with trilinear interpolation (MI-TRI), and MI metric with trilinear
PV distribution interpolation (MI-PV) approaches. MI-PV performs the registra-
tion of data set best, followed by MSD and MI-TRI.
As an example, in Figure 7.5 the normalized values of MSD, MI-TRI, and MI-
PV are shown vs. the translation along the z axis (i.e., the heart's longitudinal axis).
The two data volumes to be registered were shifted by 1 mm along the z axis. The
three approaches lead to comparable results, but MI-TRI and MSD present local
maxima that can trap the optimization algorithm, leading to incorrect results.
7.5
OPTIMIZATION TECHNIQUES IN IMAGE
REGISTRATION
Determination of the parameters set that maximizes a multivariable function is
called the optimization problem . In the rigid registration problem, the optimization
algorithm should find the rotation and translation parameters that will maximize
the similarity function. If the registration is elastic, the number of parameters is
virtually infinite and should be reduced by introducing appropriate hypotheses. A
commonly used approach is to perform a rigid registration extended to the whole
image, followed by a local elastic registration. The elastic registration is constrained
to some mathematical model to limit the needed number of parameters.
To reduce the required processing time, a multiscale approach is often
used [19,20] in which the registration is an iterative process. In the first step,
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