Information Technology Reference
In-Depth Information
another target image according to some dissimilarity measure, needs to be esti-
mated. The dissimilarity measure can be de
ned according to either the curve or to
the entire region enclosed by the curve. The source and target images and trans-
formation can be de
ned as follows:
Source (I
s
): Image which is kept unchanged and is used as a reference. This
image can be written as a function I
s
:
R
2
!
R for
8
x
2 X
s
.
Target (I
t
): Image which is geometrically transformed to the source image. This
image can be written as a function I
t
:
R
2
!
8
2 X
t
.
R for
y
Transformation (T): The function is used to warp the target image to take the
geometry of the reference image. The transformation can be written as a
function T
:
R
2
which is applied to a point x in I
s
to produce a transformed
point which is calculated as X
R
2
!
¼
T
ð
x
Þ
. The registration error is calculated as
T
ð
x
Þ
y for each transformed pixel.
Steps in the registration can be categorized in 5 different ways such as:
(i) Preprocessing: Image smoothing, deblurring, edge sharpening, edge
detection, and etc.
(ii) Feature selection: Points, lines, regions and etc. from an the source and
target image.
(iii) Feature correspondence: The correspondence between two images.
(iv) The transformation functions: Af
ne, rigid, projective, curved and etc.
(v) Resampling: Transformed image should be resampled in the new image
domain.
In general, there are three categories of the registration methods: rigid, af
ne,
and elastic transformation. In literature the rigid and af
ne transformations are
classi
ed as global transformations and elastic transformations are as local trans-
formation. A transformation is global if it is applied to the entire image. A trans-
formation is local if it is a composition of two or more transformations determined
on different domains (sub-images) of the image.
A rigid body transformation is the most fundamental transformation and is
useful especially when correcting misalignment in the scanner. This transfor-
mation allows only translation and rotations, and preserves all lengths and
angles in an image.
An af
ne transformation allows translation, rotation, and scaling. Some authors
de
ne
transformations involving shearing (projection) are called projective transfor-
mation. An af
ned the af
ne transformation as the rigid transformation plus scaling. Af
ne transformations will map lines and planes into lines and planes
but does not preserve length and angles.
An elastic transformation allows local translation, rotation, and scaling, and it
has more number of parameters than af
ne transformations. It can map straight
lines into curves. An elastic registration is also called as a non-linear or curved
transformation. This transformation allows different regions to be transformed
independently.
