Elastic Registration for Biomedical Applications - Biomedical Image Analysis - page 341

9.2.1.3 Feature-Based Registration

Feature-based algorithms first reduce the dimensionality of the problem by ex-
tracting a small set of characteristic features from the images. The extraction
mostly involves thresholding.
Landmark-based methods [1, 19-21] use a relatively small and sparse set
of landmarks —important points manually or automatically identified in the
images. Extrinsic markers are artificial features attached to the object,
easily and precisely localizable. Unfortunately, they are often long to install and
uncomfortable for the patient. If they are not available, we have to content our-
selves with features intrinsic to the images. In that case, however, the automatic
landmark identification is far less robust. The manual landmark identification is
often tedious, time-consuming, imprecise, and unreproducible.
If the images cannot be characterized using points, it might be more appro-
priate to use curves such as edges [22], or volume boundaries [23]. Likewise, in
the case of 3D data, surfaces can be used instead of working with the complete
volumes. Popular features are also templates , small subimages of important
regions [24, 25].

9.2.2 Search Space

An important attribute of a registration algorithm is the search space . It is also
called a warp space because it contains warping or correspondence functions,
the candidate solutions of the registration problem. A warping function from
the search space is described by a (finite) set of real parameters (from a set of
permissible values) by means of a warping model . We classify them according
to the number of parameters and the spatial extent of the area influenced by
a single parameter.

9.2.2.1 Local Models

At one end of the scale, we have non-parametric, local methods . The deforma-
tion function sought is basically unconstrained, or belongs to a very large and
unrestrictive functional space, such as the Sobolev space W 2 of twice differ-
entiable functions. We seek the values of this deformation at a very fine grid,
usually coinciding with pixel locations. These methods are formulated either