Probabilistic minimal path for automated esophagus segmentation
View Patent ↗A segmentation of the esophagus from image data by specifying only the two end points is disclosed. Surrounding structures are used as high-level constraints to construct shape and appearance models. Prior shape information is integrated for the segmentation of a new esophagus using a Bayesian formulation. This permits to automatically select the proper models. Given the end points, a shortest path algorithm provides the optimal esophagus according to the Bayesian formulation.
1. A method to process an image that includes a first object, and a second object and a third object, comprising:
segmenting by a processor of the second object and the third object in the image;
determining by the processor of a centerline for the first object in the image, wherein the centerline is related to one or more training images which include labels for the the second object and the third object and wherein the centerline is related to the segmentation of the second object and the third object in the image;
generating an outer boundary relative to the centerline of the first object;
determining a first probability of an element of the image to be part of a centerline of the first object given the one or more training images wherein each training image is registered to the second and third object in a reference image, wherein the first probability is determined by the processor evaluating an expression
p
C
(
x
❘
{
C
1
,
…
,
C
N
}
)
=
∏
i
=
1
N
p
(
x
❘
C
i
)
;
wherein p C (x|{C 1 , . . . , C N }) represents the first probability, p(x|C i ) represents a conditional probability of an element x of the image being part of a centerline given a training image C i , and iε {1, . . . , N};
determining a second probability of an intensity of an element inside the first object given the one or more training images wherein the second probability is determined b the processor evaluating an expression
p
(
I
❘
{
C
1
,
…
,
C
N
}
)
=
∏
i
=
1
N
p
(
I
❘
C
i
)
.
wherein p(I|{C 1 , . . . , C N }) represents the second probability, p(I|C i ) represents a conditional probability of an element of the image having an intensity I given a training image C i ;
combining the first and second probability in a single term; and
optimizing the single term.
2. The method of claim 1 , wherein the first and second probability are combined as:
p
C
(
x
❘
I
(
x
)
)
=
∏
i
=
1
N
p
(
x
❘
C
i
)
︸
location
p
(
C
i
❘
I
(
x
)
)
︸
appearance
.
3. The method of claim 2 , further comprising:
expressing the combination of the first and the second probability as an energy term
E
(
C
)
=
-
log
p
(
C
❘
I
)
=
-
∫
C
log
(
∑
i
=
1
N
p
(
C
(
s
)
❘
C
i
)
p
(
C
i
❘
I
(
C
(
s
)
)
)
)
ⅆ
s
;
︸
g
(
C
(
s
)
)
wherein C represents a centerline of the first object and s is a variable representing a location on C;
identifying two extreme points of the first object; and
applying a minimal path algorithm using the two extreme points to minimize the energy term.
4. The method as claimed in claim 1 , wherein the first object is an esophagus, the second object is an aorta and the third object is a left atrium.
5. The method of claim 4 , further comprising adjusting an energy tell for detected air holes in the esophagus.
6. The method of claim 1 , wherein determining the outer boundary of the first object comprises:
defining the outer boundary of the first object as a series of slices of ellipses;
initializing a center of the ellipses on the centerline of the first object;
expressing a region-based criterion for an ellipse in each slice as an energy term based on intensity likelihoods inside and outside an ellipse;
adding a regularization term between neighboring ellipses in the energy term;
combining energy terms of a plurality of ellipses in the series of slices with ellipses in a combined energy expression; and
minimizing the combined energy expression.
7. A system to process an image from image data, comprising:
a processor;
application software operable on the processor to:
process an image that includes a first object and a second object and a third object, comprising:
segmenting the second object and the third object in the image;
determining a centerline for the first object in the image, wherein the centerline is related to one or more training images which include labels for the second object and the third object and wherein the centerline is related to the segmentation of the second object and the third object in the image;
generating an outer boundary relative to the centerline of the first object;
determining a first probability of an element of the image to be part of a centerline of the first object given the one or more training images wherein each training image is registered to the second and third object in a reference image, wherein the first probability is determined b the processor evaluating expression
p
C
(
x
❘
{
C
1
,
…
,
C
N
}
)
=
∏
i
=
1
N
p
(
x
❘
C
i
)
;
wherein p C (x|{C 1 , . . . , C N }) represents the first probability, p(x|C i ) represents a conditional probability of an element x of the image being part of a centerline given a training image C i , and iε {1, . . . , N};
determining a second probability of an intensity of an element inside the first object given the one or more training images, wherein the second probability is determined by the processor evaluating an expression
p
(
I
❘
{
C
1
,
…
,
C
N
}
)
=
∏
i
=
1
N
p
(
I
❘
C
i
)
.
wherein p(I |{C 1 , . . . , C N }) represents the second probability, p(I |C i ) represents a conditional probability of an element of the image having an intensity I given a training image C i ;
combining the first and second probability in a single term; and
optimizing the single term.
8. The system of claim 7 , wherein the first and second probability are combined as:
p
C
(
x
❘
I
(
x
)
)
=
∏
i
=
1
N
p
(
x
❘
C
i
)
︸
location
p
(
C
i
❘
I
(
x
)
)
︸
appearance
.
9. The system of claim 8 , further comprising:
expressing the combination of the first and the second probability as an energy term
E
(
C
)
=
-
log
p
(
C
❘
I
)
=
-
∫
C
log
(
∑
i
=
1
N
p
(
C
(
s
)
❘
C
i
)
p
(
C
i
❘
I
(
C
(
s
)
)
)
)
︸
g
(
C
(
s
)
)
ⅆ
s
;
wherein C represents a centerline of the first object and s is a variable representing a location on C;
identifying two extreme points of the first object; and
applying a minimal path algorithm using the two extreme points to minimize the energy term.
10. The system as claimed in claim 7 , wherein the first object is an esophagus, the second object is an aorta and the third object is a left atrium.
11. The system of claim 10 , further comprising adjusting an energy term for detected air holes in the esophagus.
12. The system of claim 7 , wherein determining the outer boundary of the first object comprises:
defining the outer boundary of the first object as a series of slices of ellipses;
initializing a center of the ellipses on the centerline of the first object;
expressing a region-based criterion for an ellipse in each slice as an energy term based on intensity likelihoods inside and outside an ellipse;
adding a regularization term between neighboring ellipses in the energy term;
combining energy terms of a plurality of ellipses in the series of slices with ellipses in a combined energy expression; and
minimizing the combined energy expression.