Biomedical Engineering Reference
In-Depth Information
1.5.2.2
Optimization Methods
The mutual information metric provides a quantitative measure of spatial align-
ment between two volumes, given a choice of registration parameters. To obtain
the best alignment, it is necessary to maximize the metric. Maximization of the
metric, which is parameterized in terms of the registration parameters, is numer-
ically accomplished with the use of an optimization algorithm. In the original for-
mulation of registration by maximization of mutual information in [31], Powell's
multidimensional optimization method, with Brent line minimizations was used
for maximization of the mutual information metric [32]. Subsequently, [33] com-
pares different classical optimization methods maximizing the mutual informa-
tion metric. One such method included was the use of the classic Nelder and
Mead or simplex algorithm for maximization. This method solely uses the ob-
jective function directly for optimization, and therefore does not require the ex-
pensive computation of derivatives. This method is a geometry-based method,
using the geometric operations of contraction, expansion, and reflection to ma-
nipulate a simplex to a maximum of the objective function. GA was also used as
an optimization criteria in maximizing the mutual information metric as demon-
strated in [34].
1.6
Practical Examples
1.6.1
Composite Approach for Mutlimodal Registration
A composite registration approach can perform a fast, six degrees of freedom
registration and accurately locate the position and orientation of medical vol-
umes (obtained from CT/MRI scans for the same patient) with respect to each
other. The technique uses surface registration technique followed by a volume
registration approach. The advantage of this combination is to have an accurate
alignment and to reduce the time needed for registration. The surface regis-
tration uses the surface signature approach and for the volume registration,
the maximization of mutual information (MI) is used as a matching criterion
and is enhanced by a genetic based optimization technique. Figure 1.12 shows a
block diagram of the composite registration. Figure 1.13 shows some results and
Table 1.2 shows approximate registration time for both single and composition
registration.
