2007
IEEE
International
Symposium
on
Signal
Processing
and
Information
Technology
A
NEW
SHAPEBASED
SEGMENTATION
APPROACH
FOR
THE
DCEMRI
KIDNEYIMAGES
Hossam
Abd
EL
Munim1,
Aly
A.
Farag1,
Mohamed
Abo
ElGhar2,
and
Tarek
ElDiasty2
1CVIP
Laboratory,
University
of
Louisville,Louisville,
KY,
USA
2The
UrologyandNephrology
Center,
Schoolof
Medicine,
Mansoura
University,
Egypt
{faraggcvip.uofl.edu}
ABSTRACT
or
underestimation
of
the
extent
ofinflammation
in
theen
Acute
rejection
is
the
most
common
reason
of
graftfailure
tire
graft
[3].
Therefore,
a
noninvasive
and
repeatable
tech
after
kidney
transplantation,
and
early
detection
is
crucial
to
nique
is
notonly
helpful
but
also
needed
in
the
diagnosis
of
survivethe
transplanted
kidney
function.
Automatic
classi
acuterenal
rejection.
In
DCEMRI,
a
contrast
agent
called
fication
of
normaland
acute
rejectiontransplants
from
Dy
GdDTPA
is
injected
into
the
bloodstream,
and
as
it
perfuses
namic
Contrast
Enhanced
Magnetic
Resonance
Imaging
into
the
organ,
the
kidneys
are
imaged
rapidly
and
repeatedly.
DCEMRI)
is
considered.
The
algorithm
is
based
onsegmen
During
the
perfusion,
GdDTPA
causes
a
change
in
the
relaxtation
to
isolate
the
kidney
from
the
surroundinganatomi
ation
times
of
the
tissue
and
creates
a
contrast
change
in
the
cal
structures
viaa
shapebased
segmentation
approach
us
images.
As
a
result,
the
patterns
of
the
contrast
change
gives
ing
level
sets.
So
the
main
focus
of
this
paper
is
the
shape
functional
information,
while
MRI
provides
good
anatomical
based
segmentation.
Training
shapes
are
collected
from
dif
information
which
helps
in
distinguishing
thediseases
that
ferent
real
data
sets
to
representthe
shape
variations.
Signed
affectdifferent
parts
of
the
kidneys.
However,
even
withan
distancefunctions
are
used
to
representtheseshapes.
The
imaging
technique
like
DCEMRI,
there
are
several
problemsmethodology
incorporate
the
image
information
with
the
shape
such
as,
(i)
thespatialresolution
of
the
dynamic
MR
images
prior
in
a
variational
framework.
The
shape
registration
isis
low
due
to
fast
scanning,
(ii)
the
images
suffer
from
the
mo
considered
the
backbone
of
the
approach
where
more
gen
tion
induced
by
the
patient
breathing
which
necessitatesad
eral
transformations
can
beused
to
handle
the
process.
Thevanced
registration
techniques,
(iii)
the
intensity
of
the
kidney
perfusion
curves
that
show
thetransportation
of
thecontrast
changes
nonuniformly
as
the
contrast
agent
perfuses
into
the
agent
into
the
tissue
are
obtained
fromsegmented
kidneys
and
cortex
which
complicates
the
segmentation
procedures.
To
used
in
the
classification
of
normaland
acute
rejection
trans
thebest
of
our
knowledge,
there
has
been
limited
work
on
plants.
Applications
of
the
proposed
approach
yield
promis
the
dynamic
MRI
to
overcome
the
problems
of
registration
ing
resultsthat
would,
in
the
near
future,
replace
the
useof
and
segmentation.
For
theregistration
problem,
Gerig
et
al.
current
technologies
such
as
nuclear
imagingand
ultrasonog
[4]
proposed,using
Hough
transform,
to
register
the
edges
in
raphy,
which
are
not
specific
enough
to
determine
the
type
of
an
image
to
the
edges
of
a
mask
and
Giele
et
al.
[5]
intro
kidney
dysfunction.
duced
a
phase
difference
movement
detection
method
tocor
rect
for
kidney
displacements.
Both
of
these
studies
required
Ievel
Sets,Enerms
Shape
Repreentbuilding
a
mask
manually
by
drawing
the
kidney
contour
on
a
Level
Sets,
Energy
Minimization.
2DDCEMRI
image,followed
by
the
registration
of
the
time
frames
tothis
mask.
Most
of
these
efforts
used
healthy
trans
I.
INTRODUCTION
plants
in
the
image
analysis,
and
edge
detection
algorithms
were
sufficient.
However;
in
thecase
of
acute
rejection
pa
In
the
United
States,
approximately
12000
renaltransplants
tients,
the
uptakeof
the
contrast
agent
is
decreased,so
edge
are
performed
annually
[1],
and
considering
thelimited
sup
detection
fails
in
giving
connected
contours.
For
this
reason,
ply
ofdonor
organs,
every
effort
is
made
to
salvage
the
trans
we
consider
the
combined
usageof
gray
level
and
prior
shape
planted
kidney
[2].
Currently,
the
diagnosis
of
rejection
is
information
to
give
better
results.
done
via
biopsy
which
has
the
downside
effect
of
subjecting
the
patients
torisks
such
as
bleeding
and
infections.
More
II.
SHAPE
MODELING
BY
LEVEL
SETS
Over,
th1e
relatively
smal
needle
biopsies
may
lead
to
over
Shpersnaini
h
ai
akonlsso
hps
'
~~~~~~~~~~~~~~~The
election
ofsuch
representation
is
very
important
in
sev
THIS
RESEARCH
HAS
BEEN
SUPPORTED
IN
PART
BY
THE
NSF
eral
computer
vision
and
medical
applications
such
as
regis
GRANT
OISE06
10528
AND
THE
UNIVERSITY
OF
LOUISVILLE.
tration
and
segmentation.
There
are
several
ways
described
9781
42441
8350/07/ 25.00
©C2007
IEEE
1
186
in
[6].
Although
some
of
these
ways
are
powerful
enough
a
Gaussian
distribution
with
adaptiveparameters.
Expres
to
capture
local
deformations,they
require
a
large
number
sions
for
the
prior
probability
and
the
Gaussian
parameters
of
parameters
to
deal
with
important
shapedeformations
and
are
found
in
[9].
have
problems
withchanging
topology.
An
emerging
way
to
represent
shapes
can
be
derived
using
level
sets
[7].
This
IV.
ALIGNMENT
OFTHE
TRAININGSHAPES
representation
is
invariant
to
translation
and
rotation.
Given
a
curve
V
that
represent
boundariesof
a
certain
shape,
we
Let
thetraining
set
consist
of
a
set
of
training
shapes
can
definethe
following
level
set
function
0
to
be
the
mini
V1,...,VN,
withsigned
distance
level
set
functions
defined
as
mum
Euclidean
distance
between
the
point
X
and
the
shape
above
,
The
goal
is
to
calculate
the
set
of
pose
pa
boundary.
It
is
positive
inside,
negative
outside,
and
zero
on
rameters
used
to
jointly
align
theseshapes,
and
hence
remove
the
shape
boundary.
Such
representation
canaccount
for
lo
any
variations
in
shape
due
to
pose
differences.
The
objective
cal
deformations
thatare
not
visiblefor
isocontours
that
far
is
to
finda
set
of
transformations
A1,
...,
AN
that
register
an
away
from
the
srcinal
shape
and
geometrical
features
of
the
evolving
mean
shape
represented
by
XOM
to
the
given
train
shapecan
also
be
derived
naturally
from
this
representation.
ing
shapes
respectively.
We
assume
that
each
transformation
has
scaling
components
sx,
sy,
rotation
angle
0
(with
a
rota
tion
matrix
defined
by
R),
and
translations
T
=
[Tx,
Ty]T.
SEGMENTATION
The
scale
matrix
will
be
S
=
diag{sx,
sy}.
Globalalignment
details
will
come
in
the
following
sections.
Within
the
level
set
formalism
[7],
the
evolving
curve
is
a
propagating
front
embedded
as
the
zero
level
of
a
3D
scalar
function
(x,
y,
t).
The
continuous
change
of
X
can
be
de
scribed
by
the
partialdifferential
equation:
Given
two
shapes
a
and
/
represented
by
signed
distance
functions
s,
and
/a,
we
need
to
calculate
a
transformation
&(4X,
t)
+
F
VO(X,
t)
0
:
(1)
(A)
defined
as
above
to
move
the
first
shape
to
its
target.
The
At
signed
distance
function
is
invariant
to
rotation
and
translation
where
F
is
a
scalar
velocity
function
depending
on
the
local
butunfortunately
variant
toscaling.
Now
we
are
going
to
geometric
properties
(local
curvature)
of
the
front
and
theex
formulate
a
dissimilarity
measure
to
overcome
this
problem.
temal
parameters
related
to
the
inputdata
e.g,
image
gradient.
Assume
that
the
vector
distancefunction
can
be
expressed
in
The
function
X
deforms
iteratively
according
to
F,and
the
terms
of
its
projections
in
the
coordinates
directions
as
d
a
=
position
of
the
2D
front
is
given
at
each
iteration
by
solving
[dxdy]T
at
any
point
in
the
domain
of
the
shape
a.
Applying
the
equation
0(X,
t)
=
0.
The
design
of
the
velocity
functionaglobal
transformation
A
on
the
given
function
X
resultsin
F
plays
the
major
role
in
the
evolutionary
process.
We
have
a
changeof
its
distanceprojections
as
d,
SRd,.
This
chosen
the
form
F
V
K,
where
v
1
orI
for
the
vector
is
directly
having
a
magnitude:
Sdc,
which
contracting
or
expanding
front
respectively,
c
is
a
smoothing
implies
that
,
.
max(s,
sy)
,
A
dissimilarity
measure
coefficient
which
is
always
small
with
respect
to
1,
and
K
is
can
be
directly
formulated
as
r(X)
Sdc,
(X)

(A)
the
local
curvature
of
the
front.
The
latter
parameter
actsas
a
to
measure
thedifference
between
the
transformed
shape
and
regularizationterm.
its
target
representation.
A
natural
energy
function
can
be
The
term
(vg
=
±
1)
in
the
PDE
specifies
thedirection
formulated
by
summing
up
the
squared
difference
betweenof
the
front
propagation
either
moving
inward
or
outward
(g
the
two
representations
as
follows:
is
used
to
refer
to
the
intensity
gray
level
model
associated
with
a
function
Og
which
will
evolve
according
to
the
above
E1
X08:
r2
dQ
(3)
PDE).
The
problem
can
be
reformulated
asclassification
ofeach
point
at
the
evolving
front
(points
of
the
narrowbandwhere
6'
is
added
to
reduce
the
complexity
of
the
problem
region).
If
the
point
belongs
to
the
associated
object,
the
frontas
shown
in
[9]
where
E
is
the
widthparameterof
the
band
expands,
otherwise
(the
background)
it
contracts.
around
the
shape
contour.
Itis
straightforward
to
show
that
The
point
classification
is
based
on
the
Bayesian
decision
the
given
measure
r
satisfies
the
relation:
r
<
(sOb'(X)

[8]
at
point
X.
The
term
(vg)
for
each
point
is
replaced
by
the
/a
(A))
where
s
=
max(sx,
sy).
Hence
another
energycan
function
vg
(X)
defined
as
follows:
be
obtained
which
is
always
less
than
or
equal
to
El:
7 1
Y
f
1if
woPo(I(X))
._
wbPb(I(X))
V
'AC)A
)2,7
A
9g X)
{
+i1
otherwise
(2)
F
=]6d(q5c,q5j)
(sqc(X)

q1(A))2dQ
(4)
where
wr
is
the
region
prior
probability
and
p(.)
is
the
cor
The
above
energy
functionhas
a
big
advantage
since
it
allows
responding
probabilitydensity
function
(pdf)
for
theobject
the
use
of
inhomogeneous
scales.
Alsoadding
theindicator
(o)
and
the
background
(b).
We
characterize
each
region
by
function
6'
makes
the
comparison
limited
to
a
band
around
the
1187
shapes
contours.
This
is
very
important
to
make
the
perfect
where
q
S1
bi
(Ai)
represents
the
transformed
signed
alignment
with
almost
zero
energy
when
E
+
0.
Then
we
distance
map
marked
by
t.
We
define
w
[wl
...
wN]T
to
be
will
obtain
identical
optimization
parameters
for
both
E1
and
the
weighting
coefficient
vector.
By
varying
these
weights,
E.
Gradient
descent
is
used
to
handle
the
optimization
to
(P
can
cover
all
values
of
the
training
distance
maps
and
estimate
the
transformation
parameters.
Unfortunately,
the
hence
the
shape
model
changes
according
to
all
the
given
function
s(sz,
sy)
=
max(sz,
sy)
is
not
differentiable
at
the
shapes.
In
[10],
principal
component
analysis
is
used
to
get
line
(s,
=
sy).
So
we
use
a
smeared
version
of
that
function
eigenshapes
and
a
limited
number
of
them
is
used
to
build
based
on
its
srcinal
definition:
the
model.
The
shape
variability
is
restricted
to
theselected
eigen
shapes
while
in
the
proposedapproach
all
the
training
s(sz,
sy)
=
max(sx,
sy)
=
sxH(sxsy)+b(1H,(ssy))
shapes
are
taken
into
consideration
to
enhance
the
results.
(5)
Basedon
the
above
formulation,
the
functionreturns
s
x
if
s
sy
>
0,
otherwise
it
resultsin
sy.
The
smeared
heaviside
MODELS
step
function
H
(defined
in
[9])
is
used
to
get
a
smooth
transi
tion
around
the
line
sx
=
sy
and
hence
the
function
is
differ
The
shape
model
is
fittedto
the
image
volume
by
means
entiable
everywhere.
The
function
derivativeswill
be
directly
of
registration
using
a
transformation
A
(defined
as
before)
calculated
as
follows
aS
=
HE
(sxsy)
±
(sYsy)
E
(s

registeringtheintensity
model
Og
to
the
shape
model
Op.
As
sy)
and
as
=
HE
(sy

s)
+
(sy

sx)&
(sy

sm).
stated
in
section
IV,
the
registration
is
formulated
as
an
energy
minimization
problem
as
follows:
IVB.
Mean
Shape
Estimation
E(5g,
qOp)
6
q5g,qp)r2dQ.
(9)
Registering
the
mean
shape
OM
with
the
shapei
repre
Q
sented
by
Xi~
means
sjq5M
q Xi(Ai)
where
i

1..N
and
sent(dby
i
as
show
above
So
ther
transforatn
where
r
=sg
qp(A)
is
the
dissimilarity
measure.
The
par=ameters
shou
minimize
b
the
n
eneg
.fu
tion:
transformation
A
and
the
weight
vector
w
should
minimize
the
objective
function
E:
using
the
gradient
descent
flow.
A
N
closed
form
solution
for
the
weight
vector
is
used
as
shown
E(qM,
X
qN)
Sf
6
(qM,
qi)r
2dQ
(6)
in
[1
1].
The
shape
parameters
and
the
transfornation
give
the
i=l
steady
state
shape
as
the
segmentation
results.
where
ri
=
siM

i(Ai),
is
the
dissimilarity
measure.
Rotation
and
translation
do
not
have
any
effect
on
the
valueVII.
EXPERIMENTAL
RESULTS
of
the
signed
distance
map
but
scaling
will
result
in
increas
A
39
data
sets
are
used
to
builda
kidneyshape
contours
ing/decreasing
projections
in
each
direction
which
motivates
(Fig.
1.
(a)).
The
alignment
and
mean
shape
calculations
the
use
of
the
smeared
max
function.
are
carried
out
to
remove
thedifferences
between
thetraining
The
minimizationof
the
energy
with
respect
to
the
transfor
instances
(Fig.
1.
(b)
and
(c)).
Image
statistics
are
used
to
ini
mations
parameters
is
done
through
the
gradient
descent.
The
tialize
the
intensity
segmentation
level
set
function
Og
using
mean
level
set
function
OM
evolves
according
its
calculus
of
the
well
known
stochastic
expectation
maximization
(SEM).
variation
using
the
following
PDE:
Automatic
seed
initialization
is
usedbased
on
the
region
pa
rameters
estimated
by
the
SEM.
A
similar
approach
to
that
in
N
N
[9]
but
the
contour
seeds
are
decided
basedon
the
Bayesian
=2
EXdi
siridQ
[
0
',rfdQ.
(7)
decision
rule.
The
contour
evolves
and
reaches
the
steady
at
Oml
2
state
to
mark
the
object
region.This
results
in
segmenting
some
parts
of
the
background
as
kidney
or
at
the
same
time
V.
THE
SHAPE
MODEL
LEVEL
SET
FUNCTION
missing
kidney
tissues.
This
motivates
the
incorporation
of
VThe
hape
model
SA
MOquired
LEE
capture
the
variationsinthe
the
shape
model
Op
by
estimating
the
weight
and
the
global
The
shape
model
is
required
to
capture
the
variations
in
the
transformationparameters.
Some
examples
of
the
shape
seg
training
set.
For
this
purpose,
Each
curve/surface
is
trans
mentation
results
are
illustratedin
Fig.
2.
The
approach
pro
formed
to
the
domain
of
the
mean
function
b
M
by
its
cor
videssuccessful
results
since
it
can
handle
different
scales,
responding
transformation.
Themodel
is
considered
to
be
a
rotations,
and
translations
in
the
process.
comparison
be
weighted
sum
of
the
transformed
signed
distance
maps
devi
tween
the
proposed
technique
and
that
given
in
[11]
is
illus
ated
from
the
mean
as
follows:
trated
in
3.
The
homogeneous
scales
do
notallow
the
shape
N
model
to
correctly
deform
to
mark
the
correct
boundaries
of
qs=
M
±7E
WiV
tX
(8)
the
kidney
while
this
problem
is
already
solved
by
the
pro
=l
posed
methodology.
1188
(a)
(b)
(c)
Fig.
1.
Trainingcontours
of
39
differentpatients'
kidneys
are
given
in
(a).
Alignment
results
are
visualized
in
(b)
after
removing
the
pose
differences
between
the
subjects.
Averageshape
is
given
in
(c).
figure
The
ultimate
goal
of
the
proposed
algorithms
is
to
suc
network:
transplant
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19901999.
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cessfully
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ing
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