System and method for contour tracking in cardiac phase contrast flow MR images
View Patent ↗A method for tracking a contour in cardiac phase contrast flow magnetic resonance (MR) images includes estimating a global translation of a contour in a reference image in a time sequence of cardiac phase contrast flow MR images to a contour in a current image in the time sequence of images by finding a 2-dimensional translation vector that maximizes a similarity function of the contour in the reference image and the current image calculated over a bounding rectangle containing the contour in the reference image, estimating an affine transformation of the contour in the reference image to the contour in the current image, and performing a constrained local deformation of the contour in the current image.
1. A method for tracking a contour in cardiac phase contrast flow magnetic resonance (MR) images, said method comprising the steps of:
estimating a global translation of a contour in a reference image in a time sequence of cardiac phase contrast flow MR images to a contour in a current image in said time sequence of images by finding a 2-dimensional translation vector that maximizes a similarity function of the contour in the reference image and the current image calculated over a bounding rectangle containing the contour in the reference image;
estimating an affine transformation of the contour in the reference image to the contour in the current image; and
performing a constrained local deformation of the contour in the current image.
2. The method of claim 1 , wherein said contour represents a boundary of a vessel or a valve in a vessel, and tracking said boundary tracks motion of said boundary in said time sequence of images.
3. The method of claim 1 , wherein the 2-dimensional translation vector is determined by sampling all possible solutions over a search space defined by the bounding rectangle and the maximum possible displacements of the contour.
4. The method of claim 3 , further comprising finding a second 2-dimensional translation vector that maximizes a similarity function of the contour in the current image and a previous image calculated over a bounding rectangle containing the contour in the previous image, comparing with the 2-dimensional translation vector that maximizes a similarity function of the contour in the reference image and the current image, and selecting a 2-dimensional translation vector that generates a larger similarity measure.
5. The method of claim 1 , wherein when the cardiac phase contrast flow MR images are phase images, the similarity function is defined as
S
(
Δ
x
,
Δ
y
)
=
∑
(
x
,
y
)
∈
R
w
(
x
,
y
;
Δ
x
,
Δ
y
)
cos
(
2
Δ
θ
(
x
,
y
;
Δ
x
,
Δ
y
)
)
,
wherein (Δx,Δy) is a sample 2D translation vector, (x,y) is a point in the reference image bounding rectangle, R represents the bounding rectangle,
w
(
x
,
y
;
Δ
x
,
Δ
y
)
=
M
c
(
x
+
Δ
x
,
y
+
Δ
y
)
M
r
(
x
,
y
)
∑
(
x
,
y
)
∈
R
M
c
(
x
+
Δ
x
,
y
+
Δ
y
)
M
r
(
x
,
y
)
,
wherein M r (x,y) and M c (x,y) represent a magnitude of an image gradient at point (x,y) in the reference frame and the current frame, respectively, and
Δθ( x,y;Δx,Δy )=θ c ( x+Δx,y+Δy )−θ r ( x,y ),
wherein θ r (x,y) and θ c (x,y) represent the edge orientation of the image gradient at point (x,y) in the reference frame and current frame, respectively.
6. The method of claim 1 , wherein when the cardiac phase contrast flow MR images are anatomy images, the similarity function is defined as
S
(
Δ
x
,
Δ
y
)
=
∑
(
x
,
y
)
∈
R
w
(
x
,
y
;
Δ
x
,
Δ
y
)
cos
(
Δ
θ
(
x
,
y
;
Δ
x
,
Δ
y
)
)
,
wherein (Δx,Δy) is a sample 2D translation vector, (x,y) is a point in the reference image bounding rectangle, R represents the bounding rectangle,
w
(
x
,
y
;
Δ
x
,
Δ
y
)
=
M
c
(
x
+
Δ
x
,
y
+
Δ
y
)
M
r
(
x
,
y
)
∑
(
x
,
y
)
∈
R
M
c
(
x
+
Δ
x
,
y
+
Δ
y
)
M
r
(
x
,
y
)
,
wherein M r (x,y) and M c (x,y) represent a magnitude of an image gradient at point (x,y) in the reference frame and the current frame, respectively, and
Δθ( x,y;Δx,Δy )=θ c ( x+Δx,y+Δy )−θ r ( x,y ),
wherein θ r (x,y) and θ c (x,y) represent the edge orientation of the image gradient at point (x,y) in the reference frame and current frame, respectively.
7. The method of claim 1 , wherein the 2D translation vector is restricted to integer point shifts.
8. The method of claim 1 , wherein estimating an affine transformation comprises dividing the contour in the reference image into a plurality of overlapped local regions R k each having a center point (x k , y k ) representing its position, identifying, for each local region, a corresponding position (x′ k , y′ k ) in the current image by searching for a region R′ k that best matches R k according to a similarity function, wherein the search is confined within a small neighborhood centered at (x k +Δx k , y k +Δy k ), and estimating an affine transformation parameter vector a from a=(X T X) −1 X T y, wherein y=[x′ 1 y′ 1 . . . x′ K y′ K ] T denotes a collection of coordinates of the position points in the current image, and
X
=
[
x
1
y
1
1
0
0
0
0
0
0
x
1
y
1
1
⋮
⋮
⋮
⋮
⋮
⋮
x
K
y
K
1
0
0
0
0
0
0
x
K
y
K
1
]
is a matrix of coordinates of the position points in the reference image wherein each region corresponds to a row.
9. The method of claim 8 , wherein when the cardiac phase contrast flow MR images are phase images, the similarity function is defined as
S
(
Δ
x
,
Δ
y
)
=
∑
(
x
,
y
)
∈
R
w
(
x
,
y
;
Δ
x
,
Δ
y
)
cos
(
2
Δ
θ
(
x
,
y
;
Δ
x
,
Δ
y
)
)
,
wherein (Δx,Δy) is a sample 2D translation vector, (x,y) is a contour position point in the reference image, R represents the small neighborhood about (x,y),
w
(
x
,
y
;
Δ
x
,
Δ
y
)
=
M
c
(
x
+
Δ
x
,
y
+
Δ
y
)
M
r
(
x
,
y
)
∑
(
x
,
y
)
∈
R
M
c
(
x
+
Δ
x
,
y
+
Δ
y
)
M
r
(
x
,
y
)
,
wherein M r (x,y) and M c (x,y) represent a magnitude of an image gradient at point (x,y) in the reference frame and the current frame, respectively, and
Δθ( x,y;Δx,Δy )=θ c ( x+Δx,y+Δy )−θ r ( x,y ),
wherein θ r (x,y) and θ c (x,y) represent the edge orientation of the image gradient at point (x,y) in the reference frame and current frame, respectively.
10. The method of claim 8 , wherein when the cardiac phase contrast flow MR images are anatomy images, the similarity function is defined as
S
(
Δ
x
,
Δ
y
)
=
∑
(
x
,
y
)
∈
R
w
(
x
,
y
;
Δ
x
,
Δ
y
)
cos
(
Δθ
(
x
,
y
;
Δ
x
,
Δ
y
)
)
,
wherein (Δx,Δy) is a sample 2D translation vector, (x,y) is a contour position point in the reference image, R represents the small neighborhood about (x,y),
w
(
x
,
y
;
Δ
x
,
Δ
y
)
=
M
c
(
x
+
Δ
x
,
y
+
Δ
y
)
M
r
(
x
,
y
)
∑
(
x
,
y
)
∈
R
M
c
(
x
+
Δ
x
,
y
+
Δ
y
)
M
r
(
x
,
y
)
,
wherein M r (x,y) and M c (x,y) represent a magnitude of an image gradient at point (x,y) in the reference frame and the current frame, respectively, and
Δθ( x,y;Δx,Δy )=θ c ( x+Δx,y+Δy )−θ r ( x,y ),
wherein θ r (x,y) and θ c (x,y) represent the edge orientation of the image gradient at point (x,y) in the reference frame and current frame, respectively.
11. The method of claim 8 , wherein performing a constrained local deformation of the contour comprises initializing a point (x k (s),y k (s)) on the contour in the current frame k corresponding to a point ({tilde over (x)}(s),{tilde over (y)}(s)) in the reference frame from
[
x
k
(
s
)
y
k
(
s
)
]
=
[
x
~
(
s
)
y
~
(
s
)
1
0
0
0
0
0
0
x
~
(
s
)
y
~
(
s
)
1
]
a
k
wherein a k is the estimated affine transformation for the k th frame, and deforming the contour using a gradient vector flow snake with high viscosity.
12. A method for tracking a contour in cardiac phase contrast flow magnetic resonance (MR) images, said method comprising the steps of:
estimating a global translation of a contour in a reference image in a time sequence of cardiac phase contrast flow MR images to a contour in a current image in said time sequence of images;
estimating an affine transformation of the contour in the reference image to the contour in the current image by dividing the contour in the reference image into a plurality of overlapped local regions R k each having a center point (x k ,y k ) representing its position, for each local region, searching for a corresponding position (x′ k ,y′ k ) in the current image in a region R′ k that best matches R k according to a similarity function, wherein the search is confined within a small neighborhood centered at (x k +Δx k ,y k +Δy k ), and estimating an affine transformation parameter vector a from the center point positions in the reference image and the current image; and
performing a constrained local deformation of the contour in the current image.
13. The method of claim 12 , wherein estimating the global translation of the contour in the reference image comprises finding a 2-dimensional translation vector that maximizes a similarity function of the contour in the reference image and the current image calculated over a bounding rectangle containing the contour in the reference image.
14. The method of claim 12 , wherein estimating an affine transformation parameter vector a comprises calculating a=(X T X) −1 X T y, wherein y=[x′ 1 y′ 1 . . . x′ K y′ K ] T denotes a collection of coordinates of the position points in the current image, and
X
=
[
x
1
y
1
1
0
0
0
0
0
0
x
1
y
1
1
⋮
⋮
⋮
⋮
⋮
⋮
x
K
y
K
1
0
0
0
0
0
0
x
K
y
K
1
]
is a matrix of coordinates of the position points in the reference image wherein each region corresponds to a row.