Biomedical Engineering Reference
In-Depth Information
coincide with a grid point of the reference image and interpolation of the refer-
ence image is needed to obtain the image intensity value at this point.
The NMI registration criterion states that the images are geometrically
aligned by the transformation
T
λ
for which
NMI(A, B)
is maximal. (The regi-
stration parameters are denoted by
λ
and
T
λ
is the transformation based on
the six registration parameters given above.) To decide if the NMI is optimal,
algorithms to measure optimality are applied. If the NMI is not optimal, a new
set of parameters will be chosen and evaluated. The Downhill simplex is used to
determine optimality. This method, as shown by NeIder and Mead [19, 20], only
requires evaluation of the cost function, the derivative computation need not be
redone.
13.2.1.5
Two-Stage Multiresolution Registration
Multiresolution approach [7-10] is widely used in medical image registration
due to the following two features:
1. Methods for detecting optimality cannot guarantee that a global optimal
value will be found. Parameter spaces for image registration are usually not
simple. There are often multiple optima within the parameter space, and
registration can fail if the optimization algorithm converges to the wrong
optimum.
2. Time to evaluate the registration criterion is proportional to the number
of voxels: Medical images consist of a large number of voxels. During
registration the main portion of computational time is consumed by the
resampling voxels of the floating image with respect to the reference image
according to actual geometrical transformation.
The idea of a multiresolution hierarchical approach is to register a coarse
(low resolution) image first and then to use the result as the starting point
for finer (high resolution) image registration, and so on [24]. In practice, the
multiresolution approach proves to be helpful. It can improve the optimization
speed, improve the capture range, and the algorithm is relatively robust.
In the first level of our two-stage multiresolution registration method, one
of the three binning techniques, described above, is applied to the segmented
images before they are down-sampled and the registration is performed on the
