Biomedical Engineering Reference
In-Depth Information
is selected. In the present case, we found the values of
α
=
1
.
5
∼
2
.
5tobethe
most suitable.
9.3.4
Summary of Landmark Interpolation
We have presented the landmark registration technique with focus on the second
step, the problem of landmark interpolation. This problem can be formulated
very concisely in the variational setting. We choose the variational criterion to
impose useful properties on the interpolation process, such as rotational, trans-
lational, and scale invariance. Most notably, when the criterion is quadratic, the
solution is expressed as a linear combination of translated generating (Green)
functions. The coefficients of this linear combination are determined from a lin-
ear system of equations.
The a priori non-local generating functions can be localized [88] for more
efficient and more stable calculation. In some cases this localization leads to
B-splines which gives an additional justification for using splines to solve this
kind of problems.
9.4
Fast Parametric Elastic Image
Registration
This section presents a practical example of a fully automatic algorithm for
fast elastic multidimensional intensity-based image registration with a para-
metric
B-spline model
of the deformation. Its main features are high-order
B-
spline models
of the deformation and of the image, pixel-based similarity crite-
rion, double
multiresolution
strategy (for both image and the model) and so-
phisticated iterative multidimensional optimizer. While the algorithm presented
here is based on our own work [88, 93-96], it is closely related to a number
of similar, independently developed approaches, of which we can only present
a very incomplete list. The use of B-spline deformation models was pioneered by
Szeliski [40,41] and the different pixel criteria were studied by Studholme [48,97]
and Nikou [49]. The hierarchical structure was exploited by Musse [71], Heitz [68]
and Th evenaz [36], who also employed the Marquardt-Levenberg optimizer.
