Biomedical Engineering Reference
In-Depth Information
Bayesian interpretation of elastic matching are reviewed by Gee [74], also in
the context of human neuroanatomy. The last two survey articles we mention
deal specifically with medical imaging applications of image registration. An
article by Van den Elsen
et al.
[75] contains very comprehensive and detailed
classification of available methods. Finally, Lester and Arridge [76] emphasise
the hierarchical concepts of the algorithms.
9.3
Landmark Registration
Landmark registration [1, 19, 20] is a two-step feature-based registration tech-
nique. In the first step, a set of landmark pairs is identified (see Fig. 9.2 for an
example), either manually, or automatically [20, 77]. We get two sequences of
points,
x
1
,...,
x
N
, and
z
1
,...,
z
N
, such that an object at coordinates
x
i
in the
reference image corresponds to the object at coordinates
z
i
in the test image.
In the second step, the correspondence function is interpolated between the
landmark points [78, 79].
Manual landmark registration
has the usual inconveniences of a man-
ual method—poor accuracy and repeatability. On the other hand, it is robust
and reliable thanks to the underlying human expert knowledge. For this rea-
son, it is very valuable as a bootstrap method for further automatic refine-
ment. It can also serve as a reference standard when evaluating the perfor-
mance of other registration methods on real images and under realistic working
conditions.
Landmark interpolation
merits a study in its own right. Choosing an interpo-
lation method or an interpolation function is difficult because the implications of
this choice are not immediately apparent. On the other hand, in the variational
formulation we shall present, the user is asked instead to choose a criterion
of optimality, which is usually more tangible and often related to the physics
(or other specificities) of the problem. The variational formulation of land-
mark interpolation also allows us to make an interesting link with (fractional)
splines [80].
9.3.1
Desirable Properties
The landmark interpolation method should fulfill some basic properties:
