Biomedical Engineering Reference
In-Depth Information
samples to process. Following computation of the joint histogram, normalization
and computation of the marginal histograms must be performed. This involves
one pass over the joint histogram, therefore processing 256 by 256
=
65,536
elements from the joint histogram. This processing consists of normalization,
and summation to compute the marginal histograms. Following this operation,
the mutual information metric itself may be computed. This processing involves
computation of the sum given in Eq. (1.19), and involves one pass over the joint
histogram, therefore processing 256 by 256
=
65,536 elements that compose the
sum given in Eq. (1.19). Therefore, computation of the joint histogram is by far
the most computationally costly component in computation of the mutual infor-
mation metric. Therefore, performance may be best increased by decreasing the
execution time of the computation of the joint histogram. Computation of the
joint histogram is an amenable problem for parallel execution, as computation
of a part of the joint histogram does not depend on the computational results of
any other part of the joint histogram, allowing individual bins, or entire regions
of the joint histogram to be computed independently, and then merged to form
the total joint histogram. Figure 1.11 illustrates such parallel architecture.
1
256
1
256
2
256
Σ
256
2
256
256
n
256
256
n
volume
joint histogram
sub-volumes
sub-joint histograms
task 1
Figure 1.11: Illustration of the parallel computation of the joint histogram nec-
essary for computation of the mutual information metric.
task 2
