Constrained surface evolutions for prostate and bladder segmentation in CT images
A Bayesian formulation for coupled surface evolutions in level set methods and application to the segmentation of the prostate and the bladder in CT images are disclosed. A Bayesian framework imposing a shape constraint on the prostate is also disclosed, while coupling its shape extraction with that of the bladder. Constraining the segmentation process improves the extraction of both organs' shapes.
1 . A method for segmenting a first structure and a second structure from image data, comprising:
forming an energy function E=f(E data , E coupling ) wherein E data represents a possible segmentation based on the first structure and the second structure and E coupling represents a measure of overlap between the first structure and the second structure; and
minimizing the energy function.
2 . The method as claimed in claim 1 , wherein E=E data +E coupling .
3 . The method as claimed in claim 2 , wherein E data and E coupling are logarithmic expressions.
4 . The method as claimed in claim 1 , wherein the terms E data and E coupling depend on the probability of a level set function of the first structure and of the second structure.
5 . The method as claimed in claim 4 , wherein E coupling depends on a penalty α.
6 . The method as claimed in claim 5 , wherein the term E data is expressed as:
E
data
(
ϕ
1
,
ϕ
2
)
=
-
∫
Ω
H
ɛ
(
ϕ
1
,
x
)
(
1
-
H
ɛ
(
ϕ
2
,
x
)
)
log
p
1
(
I
(
x
)
)
ⅆ
x
-
∫
Ω
H
ɛ
(
ϕ
2
,
x
)
(
1
-
H
ɛ
(
ϕ
1
,
x
)
)
log
p
2
(
I
(
x
)
)
ⅆ
x
-
∫
Ω
(
1
-
H
ɛ
(
ϕ
2
,
x
)
(
1
-
H
ɛ
(
ϕ
1
,
x
)
)
log
p
b
(
I
(
x
)
)
ⅆ
x
and the term E coupling is expressed as:
E coupling (φ 1 ,φ 2 )=α∫ Ω H ε (φ 1,x ) H ε (φ 2,x ) dx.
7 . The method as claimed in claim 2 , wherein a third term E shape is added which expresses a constraint of learned prior shapes.
8 . The method as claimed in claim 7 , wherein the term E shape can be expressed as E shape =−log p(φ|{φ 1 , . . . , φ N }.
9 . The method as claimed in claim 5 , where α is user defined.
10 . The method as claimed in claim 1 wherein the first structure is a prostate and the second structure is a bladder.
11 . A system that can segment a first structure and a second structure from image data, comprising:
a processor;
application software operable on the processor to:
form an energy function E=f(E data , E coupling ) wherein E data represents a possible segmentation based on the first structure and the second structure and E coupling represents a measure of overlap between the first structure and the second structure; and
minimize the energy function.
12 . The system as claimed in claim 11 , wherein E=E data +E coupling .
13 . The system as claimed in claim 12 , wherein. E data and E coupling are logarithmic expressions.
14 . The system as claimed in claim 11 , wherein the terms E data and E coupling depend on the probability of a level set function of the first structure and of the second structure.
15 . The system as claimed in claim 14 , wherein E coupling depends on a penalty α.
16 . The system as claimed in claim 15 , wherein the term E data , is expressed as:
E
data
(
ϕ
1
,
ϕ
2
)
=
-
∫
Ω
H
ɛ
(
ϕ
1
,
x
)
(
1
-
H
ɛ
(
ϕ
2
,
x
)
)
log
p
1
(
I
(
x
)
)
ⅆ
x
-
∫
Ω
H
ɛ
(
ϕ
2
,
x
)
(
1
-
H
ɛ
(
ϕ
1
,
x
)
)
log
p
2
(
I
(
x
)
)
ⅆ
x
-
∫
Ω
(
1
-
H
ɛ
(
ϕ
2
,
x
)
(
1
-
H
ɛ
(
ϕ
1
,
x
)
)
log
p
b
(
I
(
x
)
)
ⅆ
x
and the term E coupling is expressed as:
E coupling (φ 1 ,φ 2 )=α∫ Ω H ε (φ 1,x ) H ε (φ 2,x ) dx.
17 . The system as claimed in claim 12 , wherein a third term E shape is added which expresses a constraint of learned prior shapes.
18 . The system as claimed in claim 17 , wherein the term E shape can be expressed as E shape =−log p(φ|{φ 1 , . . . , φ N }.
19 . The system as claimed in claim 15 , where α is user defined.
20 . The system as claimed in claim 11 wherein the first structure is a prostate and the second structure is a bladder.