Biomedical Engineering Reference
In-Depth Information
some of the drawbacks of the area-based techniques, Shen and Davatzikos [67]
proposed a new deformable registration for brain images, known as “HAMMER.”
This method utilizes an attribute vector, which reflects the geometric characteris-
tics of the underlying anatomical structures, as a signature for each point instead
of using only the image intensity. Part of each attribute vector is a number of
geometric moment invariants (GMIs) calculated locally around each point. We do
not intend to give a comprehensive survey on image registration, but the interested
reader may refer to [68] for such a survey.
Recently, we proposed a new nonrigid registration technique that combines
ideas from the feature-based and the intensity-based registration approaches [69].
Given two images (2D or 3D),
I
s
(
x
) and
I
t
(
x
), of the same anatomical organs,
taken from different patients or from the same patient over a period of time, our
method performs matching between these two images in two main steps and out-
puts a spatial transformation
n
(
n
= 2or3), such that the similarity
between the intensities
I
s
(
x
) and
I
t
(
T
(
x
)) is optimized. The first step of the
introduced approach consists in globally aligning the two images. This corre-
sponds to finding the optimal global transformation
T
global
:
x
→
x
, which maps
any point in one image into its corresponding point in the other image. In 3D
space, the global motion can be modeled, for example, by a 12-parameter affine
transformation that can be written as
n
T
:
R
→
R
a
11
a
12
a
13
x
y
z
a
14
a
24
a
34
·
+
.
T
global
(
x, y, z
)=
a
21
a
22
a
23
(1)
a
31
a
32
a
31
The parameters
a
ij
,
i, j
=1
,
,n
,of
T
global
represent rotation, scaling, shear-
ing, and translation. In this work, these parameters are determined through a
minimization of the mean squared positional error between matched features. The
scale space theory plays a major role here in extracting and matching these fea-
tures. A novel approach to build robust and efficient 3D local invariant feature
descriptors is introduced.
The second step of the proposed approach is to find the optimal transformation,
T
local
, to model the local deformations of the imaged anatomy. The basic idea is
to deform an object by evolving equispaced contours/surfaces in the target image
I
t
(
·
) to match those in the source image
I
s
(
·
). These iso-surfaces are generated
using fast marching level sets, where the built local invariant feature descriptors are
used as voxel signatures. Finally, we combine the local and global transformations
to produce our registration transformation
T
(
x
)=
T
global
(
x
)+
T
local
(
x
). The
following sections present a description of the main components of our nonrigid
registration technique.
···
