Biomedical Engineering Reference
In-Depth Information
The EM approach may be motivated by the following
observations. If an improved intensity correction is
available, it is a simple matter to apply it to the intensity
data and obtain an improved classification. Similarly,
if an improved classification is available, it can be used
to derive an improved intensity correction, for example,
by predicting image intensities based on tissue class,
comparing the predicted intensities with the observed
intensities, and smoothing. Eventually, the process con-
verges, typically in less than 20 iterations, and yields
a classification and an intensity correction.
In recent work, the algorithm has been extended in
a number of directions. A spline-based modeling of the
intensity artifacts associated with surface coils have been
described by Gilles
et al.
[34]
. The addition of an ''un-
known'' tissue class and other refinements has been de-
scribed by Guillemaud and Brady
[39]
. Also, Markov
models of tissue homogeneity have been added to the
formalism in order to reduce the thermal noise that is
usually apparent in MR imagery. Held
et al.
[42]
used the
method of iterated conditional modes to solve the
resulting combinatorial optimization problem, while
Kapur
et al.
[59]
used mean field methods to solve a re-
lated continuous optimization problem.
the method of parametric analysis is that it assumes that
all pixel intensity sequence plots have the same general
pattern across the image. In fact, however, many images
have pixels or regions of pixels that do not share the same
characteristics in the time domain and, therefore, will
have dissimilar dynamic intensity plots.
An interesting application of the parametric mapping
technique to the 3D segmentation of multiple sclerosis
lesions on series of MR images was proposed by Gerig
et al.
[33]
. Temporal images were acquired in intervals of
1, 2, or 4 weeks during a period of 1 year. The parameters
chosen for parametric maps were based on lesion char-
acteristics, such as lesion intensity variance, time of ap-
pearance, and time of disappearance. The 3D maps
displayed patterns of lesions that show similar temporal
dynamics.
Another technique for temporal segmentation was
introduced by Rogowska
[91]
. The
correlation mapping
(also called
similarity mapping
) technique identifies re-
gions (or objects) according to their temporal similarity
or dissimilarity with respect to a reference time-intensity
curve obtained from a reference region of interest (ROI).
Assume that we have a sequence of
N
spatially registered
temporal images of stationary structures. The similarity
map NCOR
ij
based on normalized correlation is defined
for each pixel (
i, j
)as
6.4.6.2 Segmentation using multiple
images acquired over time
ðR½n
m
R
Þ
P
n¼
1
A
ij
½n
m
A
P
n¼
1
NCOR
ij
¼
s
;
Multispectral images can also be acquired as a sequence
of images, in which intensities of certain objects change
with time, but the anatomical structures remain sta-
tionary. One example of such sequence is a CT image
series generated after intravenous injection of a contrast
medium that is carried to an organ of interest. Such an
image sequence has constant morphology of the imaged
structure, but regional intensity values may change from
one image to the next, depending upon the local phar-
macokinetics of the contrast agent.
The most popular segmentation technique that em-
ploys both intensity and temporal information contained
in image sequences is the
parametric analysis technique
[44, 45, 79a, 89a]
. In this technique, for each pixel or
region of interest, the intensity is plotted versus time.
Next, the plots are analyzed, with the assumption that
the curves have similar time characteristics. Certain pa-
rameters are chosen, such as maximum or a minimum
intensity, distance between maximum and minimum, or
time of occurrence of maximum or minimum. The ap-
propriate set of parameters depends on the functional
characteristics of the object being studied. Then, an
image is calculated for each of the chosen parameters. In
such images the value of each pixel is made equal to the
value of the parameter at that point. Therefore, the
method is called parametric imaging. The disadvantage of
A
ij
½n
m
A
2
P
n¼
1
ðR½n
m
R
Þ
2
(6.4.8)
where
A
ij
[
n
] is the time sequence of image intensity
values for the consecutive
N
images:
A
ij
[1],
A
ij
[2],.,
A
ij
[
N
], (
i ¼
1,2,.,
I
,
j ¼
l,2,.,
J
,
n ¼
1,2,.,
N
;
I
is the
number of image rows,
J
is the number of image col-
umns),
R
[
n
] is the reference sequence of mean intensity
values from a selected reference ROI, m
A
is the mean
value of the time sequence for pixel (
i,j
), and m
R
is the
mean value of the reference sequence.
Pixels in the resulting similarity map, whose temporal
sequence is similar to the reference, have high correlation
values and are bright, while those with low correlation
values are dark. Therefore, similarity mapping segments
structures in an image sequence based on their temporal
responses rather than spatial properties. In addition,
similarity maps can be displayed in pseudocolor or color-
coded and superimposed on one image.
Figure 6.4-10
shows an application of correlation mapping technique to
the temporal sequence of images acquired from a patient
with a brain tumor after a bolus injection of contrast
agent (Gd-DTPA) on a 1T MR scanner. The first image in
a sequence of 60 MR images with the reference region of
