Biomedical Engineering Reference
In-Depth Information
Many registration methods follow a feature matching procedure. Feature
points (often referred to as “control points,” or CP) are first identified in both
the reference image and the input image. An optimal spatial transformation
(rigid or nonrigid) is then computed that can connect and correlate the two
sets of control points with minimal error. Registration has always been con-
sidered as very costly in terms of computational load. Besides, when the input
image is highly deviated from the reference image, the optimization process
can be easily trapped into local minima before reaching the correct transfor-
mation mapping. Both issues can be alleviated by embedding the registration
into a “coarse to fine” procedure. In this framework, the initial registration
is carried out on a relatively low resolution image data, and sequentially re-
fined to higher resolution. Registration at higher resolution is initialized with
the result from the lower resolution and only needs to refine the mapping be-
tween the two images with local deformations for updating the transformation
parameters.
The powerful representation provided by the multiresolution analysis frame-
work with wavelet functions has lead many researchers to use a wavelet expan-
sion for such “coarse to fine” procedures [104-106]. As already discussed previ-
ously, the information representation in the wavelet transform domain offers a
better characterization of key spatial features and signal variations. In addition
to a natural framework for “coarse to fine” procedure, many research works
also reported the advantages of using wavelet subbands for feature character-
ization. For example, in [107] Zheng
et al.
constructed a set of feature points
from a Gabor wavelet model that represented local curvature discontinuities.
They further required that a feature point should have maximum energy among a
neighborhood and above a certain threshold. In [108], Moigne
et al.
used wavelet
coefficients with magnitude above 13-15% of the maximum value to form their
feature space. In [109], Dinov
et al.
applied a frequency adaptive thresholding
(shrinkage) to the wavelet coefficients to keep only significant coefficients in
the wavelet transform domain for registration.
6.6 Summary
This chapter provided an introduction to the fundamentals of multiscale
transform theory using wavelet functions. The versatility of these multiscale
