System and method for automatic segmentation of vessels in breast MR sequences
A method for segmenting digitized images includes providing a digitized image, selecting a point with a median enhancement greater than a predefined threshold, wherein a contrast enhancing agent was applied to the subject matter of said digitized image prior to acquisition of said image, defining a shape matrix for the selected point in said image from moments of the intensities in a window of points about said selected point, calculating eigenvalues of said shape matrix, determining an eccentricity of a structure underlying said point from said eigenvalues, and segmenting said image based on said eccentricity values, wherein the steps of defining a shape matrix, calculating eigenvalues of said shape matrix, and determining the eccentricity of the underlying structure are repeated for all points in said image.
1. A computer-implemented method of segmenting digitized images, the method performed by said computer comprising the steps of:
providing a digitized image comprising a plurality of intensities corresponding to a domain of points on a 3-dimensional grid;
defining a shape matrix for a selected point in said image from moments of the intensities in a window of points about said selected point;
calculating eigenvalues of said shape matrix;
determining an eccentricity of a structure underlying said point from said eigenvalues, and
segmenting said image based on said eccentricity values, wherein the steps of defining a shape matrix, calculating eigenvalues of said shape matrix, and determining the eccentricity of the underlying structure are repeated for all points in said image.
2. The method of claim 1 , wherein said selected point has a median enhancement greater than a predefined threshold, wherein a contrast enhancing agent was applied to the subject matter of said digitized image prior to acquisition of said image.
3. The method of claim 2 , wherein said median enhancement is calculated by taking a difference of a median value of said contrast enhanced image and a median value of a pre-contrast enhanced image, and normalizing said difference to be within a predefined range.
4. The method of claim 1 , wherein said shape matrix S α is defined as
S
α
=
(
μ
xx
,
α
μ
xy
,
α
μ
xz
,
α
μ
xy
,
α
μ
yy
,
α
μ
yz
,
α
μ
xz
,
α
μ
yz
,
α
μ
zz
,
α
)
,
wherein
μ
xx
,
α
=
m
2
,
0
,
0
,
α
m
0
,
0
,
0
,
α
-
m
1
,
0
,
0
,
α
2
m
0
,
0
,
0
,
α
2
,
μ
xy
,
α
=
m
1
,
1
,
0
,
α
m
0
,
0
,
0
,
α
-
m
1
,
0
,
0
,
α
m
0
,
1
,
0
,
α
m
0
,
0
,
0
,
α
2
,
μ
yy
,
α
=
m
0
,
2
,
0
,
α
m
0
,
0
,
0
,
α
-
m
0
,
1
,
0
,
α
2
m
0
,
0
,
0
,
α
2
,
μ
xz
=
m
1
,
0
,
1
,
α
m
0
,
0
,
0
,
α
-
m
1
,
0
,
0
,
α
m
0
,
0
,
1
,
α
m
0
,
0
,
0
,
α
2
,
μ
yz
,
α
=
m
0
,
1
,
1
,
α
m
0
,
0
,
0
,
α
-
m
0
,
1
,
0
,
α
m
0
,
0
,
1
,
α
m
0
,
0
,
0
,
α
2
,
μ
zz
,
α
=
m
0
,
0
,
2
,
α
m
0
,
0
,
0
,
α
-
m
0
,
0
,
1
,
α
2
m
0
,
0
,
0
,
α
2
,
wherein moments m p,q,r,α are defined as
m p,q,r,α ( x 0 , y 0 , z 0 )=∫ R 3 ( x−x 0 ) p ( y−y 0 ) q ( z−z 0 ) r ƒ( x, y, z ) α w ( x−x 0 , y−y 0 , z−z 0 ) dxdydz,
wherein ƒ is the image intensity function, w is a window function with compact support, p, q, r≧0 and α≧1.
5. The method of claim 4 , wherein the integral is calculated by a sum over a finite neighborhood about each point.
6. The method of claim 4 , wherein said window function is defined by
w
(
x
,
y
,
z
)
=
{
1
if
{
x
∈
[
-
N
x
v
x
,
N
x
v
x
]
y
∈
[
-
N
y
v
y
,
N
y
v
y
]
z
∈
[
-
N
z
v
z
,
N
z
v
z
]
,
0
otherwise
wherein ν x , ν y , ν z are image point spacings, N x , N y , N z are non-negative integers defined wherein a window size contains a largest diameter of interest.
7. The method of claim 4 , further comprising computing said moments using nearest neighbor interpolation, and correcting said shape matrix according to
S
^
α
+
1
12
(
v
x
2
0
0
0
v
y
2
0
0
0
v
z
2
)
,
wherein ν x , ν y , ν z are image point spacings.
8. The method of claim 4 , further comprising computing said moments using trilinear interpolation.
9. The method of claim 8 , wherein α=1, and correcting said shape matrix according to
S
^
α
+
1
6
(
v
x
2
0
0
0
v
y
2
0
0
0
v
z
2
)
,
wherein ν x , ν y , ν z are image point spacings.
10. A computer implemented method of segmenting digitized images, the method performed by said computer comprising the steps of:
providing a digitized image comprising a plurality of intensities corresponding to a domain of points on an 3-dimensional grid;
defining a shape matrix for a selected point in said image from moments of the intensities in a window of points about said selected point, wherein said shape matrix S α is defined as
S
α
=
(
μ
xx
,
α
μ
xy
,
α
μ
xz
,
α
μ
xy
,
α
μ
yy
,
α
μ
yz
,
α
μ
xz
,
α
μ
yz
,
α
μ
zz
,
α
)
,
wherein
μ
xx
,
α
=
m
2
,
0
,
0
,
α
m
0
,
0
,
0
,
α
-
m
1
,
0
,
0
,
α
2
m
0
,
0
,
0
,
α
2
,
μ
xy
,
α
=
m
1
,
1
,
0
,
α
m
0
,
0
,
0
,
α
-
m
1
,
0
,
0
,
α
m
0
,
1
,
0
,
α
m
0
,
0
,
0
,
α
2
,
μ
yy
,
α
=
m
0
,
2
,
0
,
α
m
0
,
0
,
0
,
α
-
m
0
,
1
,
0
,
α
2
m
0
,
0
,
0
,
α
2
,
μ
xz
,
α
=
m
1
,
0
,
1
,
α
m
0
,
0
,
0
,
α
-
m
1
,
0
,
0
,
α
m
0
,
0
,
1
,
α
m
0
,
0
,
0
,
α
2
,
μ
yz
,
α
=
m
0
,
1
,
1
,
α
m
0
,
0
,
0
,
α
-
m
0
,
1
,
0
,
α
m
0
,
0
,
1
,
α
m
0
,
0
,
0
,
α
2
,
μ
zz
,
α
=
m
0
,
0
,
2
,
α
m
0
,
0
,
0
,
α
-
m
0
,
0
,
1
,
α
2
m
0
,
0
,
0
,
α
2
,
wherein moments m p,q,r,α are defined as
m p,q,r,α ( x 0 , y 0 , z 0 )=∫ R 3 ( x−x 0 ) p ( y−y 0 ) q ( z−z 0 ) r ƒ( x, y, z ) α w ( x−x 0 , y−y 0 , z−z 0 ) dxdydz,
wherein ƒ is the image intensity function, w is a window function with compact support, p, q, r≧0 and α≧1;
calculating eigenvalues of said shape matrix; and
determining an eccentricity of a structure underlying said point from said eigenvalues.
11. The method of claim 10 , further comprising repeating the steps of defining a shape matrix, calculating eigenvalues of said shape matrix, and determining the eccentricity of the underlying structure for all points in said image, and segmenting said image based on said eccentricity values.
12. A program storage device readable by a computer, tangibly embodying a program of instructions executable by the computer to perform the method steps for segmenting digitized images, comprising the steps of:
providing a digitized image comprising a plurality of intensities corresponding to a domain of points on a 3-dimensional grid;
defining a shape matrix for a selected point in said image from moments of the intensities in a window of points about said selected point;
calculating eigenvalues of said shape matrix;
determining an eccentricity of a structure underlying said point from said eigenvalues, and
segmenting said image based on said eccentricity values, wherein the steps of defining a shape matrix, calculating eigenvalues of said shape matrix, and determining the eccentricity of the underlying structure are repeated for all points in said image.
13. The computer readable program storage device of claim 12 , wherein said selected point has a median enhancement greater than a predefined threshold, wherein a contrast enhancing agent was applied to the subject matter of said digitized image prior to acquisition of said image.
14. The computer readable program storage device of claim 13 , wherein said median enhancement is calculated by taking a difference of a median value of said contrast enhanced image and a median value of a pre-contrast enhanced image, and normalizing said difference to be within a predefined range.
15. The computer readable program storage device of claim 12 , wherein said shape matrix S α is defined as
S
α
=
(
μ
xx
,
α
μ
xy
,
α
μ
xz
,
α
μ
xy
,
α
μ
yy
,
α
μ
yz
,
α
μ
xz
,
α
μ
yz
,
α
μ
zz
,
α
)
,
wherein
μ
xx
,
α
=
m
2
,
0
,
0
,
α
m
0
,
0
,
0
,
α
-
m
1
,
0
,
0
,
α
2
m
0
,
0
,
0
,
α
2
,
μ
xy
,
α
=
m
1
,
1
,
0
,
α
m
0
,
0
,
0
,
α
-
m
1
,
0
,
0
,
α
m
0
,
1
,
0
,
α
m
0
,
0
,
0
,
α
2
,
μ
yy
,
α
=
m
0
,
2
,
0
,
α
m
0
,
0
,
0
,
α
-
m
0
,
1
,
0
,
α
2
m
0
,
0
,
0
,
α
2
,
μ
xz
,
α
=
m
1
,
0
,
1
,
α
m
0
,
0
,
0
,
α
-
m
1
,
0
,
0
,
α
m
0
,
0
,
1
,
α
m
0
,
0
,
0
,
α
2
,
μ
yz
,
α
=
m
0
,
1
,
1
,
α
m
0
,
0
,
0
,
α
-
m
0
,
1
,
0
,
α
m
0
,
0
,
1
,
α
m
0
,
0
,
0
,
α
2
,
μ
zz
,
α
=
m
0
,
0
,
2
,
α
m
0
,
0
,
0
,
α
-
m
0
,
0
,
1
,
α
2
m
0
,
0
,
0
,
α
2
,
wherein moments m p,q,r,α are defined as
m p,q,r,α ( x 0 , y 0 , z 0 )=∫ R 3 ( x−x 0 ) p ( y−y 0 ) q ( z−z 0 ) r ƒ( x, y, z ) α w ( x−x 0 , y−y 0 , z−z 0 ) dxdydz,
wherein ƒ is the image intensity function, w is a window function with compact support, p, q, r≧0 and α≧1.
16. The computer readable program storage device of claim 15 , wherein the integral is calculated by a sum over a finite neighborhood about each point.
17. The computer readable program storage device of claim 15 , wherein said window function is defined by
w
(
x
,
y
,
z
)
=
{
1
if
{
x
∈
[
-
N
x
v
x
,
N
x
v
x
]
y
∈
[
-
N
y
v
y
,
N
y
v
y
]
z
∈
[
-
N
z
v
z
,
N
z
v
z
]
0
otherwise
,
wherein ν x , ν y , ν z are image point spacings, N x , N y , N z are non-negative integers defined wherein a window size contains a largest diameter of interest.
18. The computer readable program storage device of claim 15 , the method further comprising computing said moments using nearest neighbor interpolation, and correcting said shape matrix according to
S
^
α
+
1
12
(
v
x
2
0
0
0
v
y
2
0
0
0
v
z
2
)
,
wherein ν x , ν y , ν z are image point spacings.
19. The computer readable program storage device of claim 15 , the method further comprising computing said moments using trilinear interpolation.
20. The computer readable program storage device of claim 19 , wherein α=1, and correcting said shape matrix according to
S
^
α
+
1
6
(
v
x
2
0
0
0
v
y
2
0
0
0
v
z
2
)
,
wherein ν x , ν y , ν z are image point spacings.