Calculating the motion vector field for a reconstructed CT scan image
A method for calculating a motion vector field (MVF) in a reconstructed CT scan image, comprises: determining a region of interest (ROI) based on a vessel centreline in a first reconstructed CT scan image, wherein a motion vector field (MVF) for the ROI is to be calculated; determining at least two time control points for calculating the MVF; calculating a motion level factor of the ROI; calculating motion amounts of the MVF corresponding to each of the time control points; determining the direction of the MVF of the ROI; and calculating the MVF of the ROI according to the motion level factor, the motion amounts of the MVF corresponding to each of the time control points and the direction of the MVF.
1. A method for calculating the motion vector field (MVF) in a reconstructed Computed Tomography (CT) scan image, comprises:
determining a region of interest (ROI) based on a vessel centreline in a first reconstructed CT scan image, wherein a motion vector field (MVF) for the ROI is to be calculated;
determining time control points for calculating the MVF;
calculating a motion level factor of the ROI;
calculating motion amounts of the MVF corresponding to each of the time control points;
determining the direction of the MVF of the ROI;
calculating the MVF of the ROI according to the motion level factor, the motion amounts of the MVF corresponding to each of the time control points and the direction of the MVF; and
reconstructing a target reconstructed image by performing a motion compensation on the first reconstructed CT scan image according to the MVF of the ROI.
2. The method of claim 1 , further comprises:
determining an extension factor for adjusting the MVF after the direction of the MVF is determined; and then
calculating the MVF of the ROI according to the motion level factor, the motion amounts of the MVF corresponding to each of the time control points, the direction of the MVF and the extension factor.
3. The method of claim 2 , wherein, a formula for calculating the MVF of the ROI according to the motion level factor, the motion amounts of the MVF corresponding to each of the time control points, the direction of the MVF and the extension factor is as following:
C t n ,x =ω×c t n ,x =ω×η×φ×c′ t n ,x ,
C t n ,y =ω×c t n ,y =ω×η×φ×c′ t n ,y ,
wherein, c′ t n ,x ,c′ t n ,y are the motion amounts of the MVF corresponding to the time control points t n ,
C t n ,x ,C t n ,y are the motion vector corresponding to the time control points t n , and the MVF of the ROI comprises the motion vectors corresponding to each of the time control points,
ω is the extension factor,
η is the direction of the MVF, and
φ is the motion level factor.
4. The method of claim 2 , wherein, determining the extension factor for adjusting the MVF comprises:
calculating an initial MVF according to the motion level factor, the motion amounts of the MVF corresponding to each of the time control points and the direction of the MVF;
setting at least two assumed extension factor with equal intervals, and calculating extended MVFs extended from the initial MVF by each of the assumed extension factors;
reconstructing extended images corresponding to each of the assumed extension factors by performing motion compensations on the ROI with each of the extended MVFs, and calculating the edge gradient standard deviations of each of the extended images;
fitting a standard deviation variation curve based on each of the assumed extension factors and the edge gradient standard deviations corresponding to each of the assumed extension factors; and
determining an extension factor which corresponds to the maximum edge gradient standard deviation along the standard deviation variation curve as the extension factor.
5. The method of claim 1 , wherein, calculating the motion level factor of the ROI comprises:
calculating the edge gradient standard deviation of the ROI; and
determining the motion level factor based on the edge gradient standard deviation and a preset threshold.
6. The method of claim 5 , wherein, the edge gradient standard deviation of the ROI is calculated based on the absolute value of the edge gradient, and a formula for calculating the absolute value of the edge gradient of the ROI is as follows:
E
(
a
,
b
)
=
f
(
a
,
b
)
-
f
(
a
+
1
,
b
)
Δ
x
+
f
(
a
,
b
)
-
f
(
a
,
b
+
1
)
Δ
y
wherein, E(a,b) is the absolute value of the edge gradient on the pixel (a,b);
Δx is the pixel sampling interval on the X-axis, and Δy is the pixel sampling interval on the Y-axis;
a is the X-axis index of the pixel (a,b), and b is the Y-axis index of the pixel (a,b); and
f(a,b) is the value of the pixel (a,b) on the image of the ROI.
7. The method of claim 4 , wherein, a formula for determining the motion level factor based on the edge gradient standard deviation and the preset threshold is:
φ
=
{
0
StdE
≥
φ
Th
φ
Th
-
StdE
StdE
<
φ
Th
wherein, φ Th is the preset threshold, StdE is the edge gradient standard deviation, and φ is the motion level factor.
8. The method of claim 1 , wherein, calculating the motion amounts of the MVF corresponding to each of the time control points comprises:
determining the range of the projection data corresponding to each of the time control points based on the projection angle for acquiring the projection data;
calculating the derivatives of the projection data corresponding to each of the time control points with respect to the MVF as the motion amount of the MVF corresponding to each of the time control point, by the following formula:
c
t
n
,
x
′
=
∂
τ
_
∂
x
t
n
=
∑
t
β
∈
t
n
(
∂
p
∂
u
∂
u
∂
x
+
∂
p
∂
v
∂
v
∂
x
)
×
∂
M
(
t
β
,
x
,
y
,
c
t
β
,
x
,
y
)
∂
x
,
c
t
n
,
y
′
=
∂
τ
_
∂
y
t
n
=
∑
t
β
∈
t
n
(
∂
p
∂
u
∂
u
∂
y
+
∂
p
∂
v
∂
v
∂
y
)
×
∂
M
(
t
β
,
x
,
y
,
c
t
β
,
x
,
y
)
∂
y
,
wherein, {right arrow over (τ)} is the MVF,
x,y are coordinates of a reconstructed point on the reconstructed CT scan image f(L),
β is the projection angle,
t β is the collecting time of the projection data of the projection angle β, and the collecting time t β is within the range of the time control point t n ,
p is the projection data,
u,v are parameters regarding channel and slice direction of the detector,
M(t,x,y,c t,x,y ) is corrected coordinates of the reconstructed point, c t,x is the X-axis projection value of the motion vector at time t, and c t,y is the Y-axis projection value of the motion vector at time t, and
c′ t n ,x ,c′ t n ,y are the motion amount of the MVF corresponding to the time control point t n .
9. The method of claim 1 , wherein, determining the direction of the MVF of the ROI comprises:
setting at least two assumed directions;
calculating estimated MVFs in each of the assumed directions with the motion amounts of the MVF corresponding to each of the time control points;
performing motion compensations on the ROI with the estimated MVFs in each of the assumed directions, so as to reconstruct estimated images in each of the assumed directions;
calculating the edge gradient standard deviations of each of the estimated images; and
determining the assumed direction which corresponds to the maximum edge gradient standard deviation among the edge gradient standard deviations of each of the estimated images, as the direction of the MVF of the ROI.
10. A device for calculating the motion vector field (MVF) in a reconstructed Computed Tomography (CT) scan image, the device comprises a processor which invokes machine readable instructions corresponding to a control logic for calculating a MVF in a reconstructed CT scan image stored on a storage medium and executes the machine readable instructions to:
determine a region of interest (ROI) based on a vessel centreline in a first reconstructed CT scan image, wherein a motion vector field (MVF) for the ROI is to be calculated;
determine at least two time control points for calculating the MVF;
calculate a motion level factor of the ROI;
calculate motion amounts of the MVF corresponding to each of the time control points;
determine the direction of the MVF of the ROI;
calculate the MVF of the ROI according to the motion level factor, the motion amounts of the MVF corresponding to each of the time control points and the direction of the MVF; and
reconstruct a target reconstructed image by performing a motion compensation on the first reconstructed CT scan image according to the MVF of the ROI.
11. The device according to claim 10 , wherein said machine readable instructions further cause the processor to:
determine an extension factor for adjusting the MVF after the direction of the MVF is determined; and then
calculate the MVF of the ROI according to the motion level factor, the motion amounts of the MVF corresponding to each of the time control points, the direction of the MVF and the extension factor.
12. The device according to claim 11 , wherein a formula for calculating the MVF of the ROI according to the motion level factor, the motion amounts of the MVF corresponding to each of the time control points, the direction of the MVF and the extension factor is as following:
C t n ,x =ω×c t n ,x =ω×η×φ×c′ t n ,x ,
C t n ,y =ω×c t n ,y =ω×η×φ×c′ t n ,y ,
wherein, c′ t n ,x ,c′ t n ,y are the motion amounts of the MVF corresponding to the time control point t n ,
C t n ,x ,C t n ,y are the motion vectors corresponding to the time control point t n , and the MVF of the ROI comprises the motion vectors corresponding to each of the time control points,
ω is the extension factor,
η is the direction of the MVF, and
φ is the motion level factor.
13. The device according to claim 11 , wherein said machine readable instructions further cause the processor to:
calculate an initial MVF according to the motion level factor, the motion amounts of the MVF corresponding to each of the time control points and the direction of the MVF;
set at least two assumed extension factors with equal intervals;
calculate extended MVFs extended from the initial MVF by each of the assumed extension factors;
reconstruct extended images corresponding to each of the assumed extension factors by performing motion compensations on the ROI with each of the extended MVFs;
calculate the edge gradient standard deviations of each of the extended images;
fit a standard deviation variation curve based on each of the assumed extension factors and the edge gradient standard deviations corresponding to each of the assumed extension factors; and
determine an extension factor which corresponds to the maximum edge gradient standard deviation along the standard deviation variation curve as the extension factor.
14. The device according to claim 10 , wherein said machine readable instructions further cause the processor to:
calculate the edge gradient standard deviation of the ROI; and
determine the motion level factor based on the edge gradient standard deviation and a preset threshold.
15. The device according to claim 14 , wherein the edge gradient standard deviation of the ROI is calculated based on the absolute value of the edge gradient, and a formula for calculating the absolute value of the edge gradient of the ROI is as follows:
E
(
a
,
b
)
=
f
(
a
,
b
)
-
f
(
a
+
1
,
b
)
Δ
x
+
f
(
a
,
b
)
-
f
(
a
,
b
+
1
)
Δ
y
wherein, E(a,b) is the absolute value of the edge gradient on the pixel (a,b);
Δx is the pixel sampling interval on the X-axis, and Δy is the pixel sampling interval on the Y-axis;
a is the X-axis index of the pixel (a,b), and b is the Y-axis index of the pixel (a,b); and
f(a,b) is the value of the pixel (a,b) on the image of the ROI.
16. The device according to claim 14 , wherein a formula for determining the motion level factor based on the edge gradient standard deviation and the preset threshold is:
φ
=
{
0
StdE
≥
φ
Th
φ
Th
-
StdE
StdE
<
φ
Th
wherein, φ Th , is the preset threshold, StdE is the edge gradient standard deviation, and φ is the motion level factor.
17. The device according to claim 10 , wherein said machine readable instructions further cause the processor to:
determine the range of the projection data corresponding to each of the time control points based on the projection angle for acquiring the projection data;
calculate the derivatives of the projection data corresponding to each of the time control points with respect to the MVF as the motion amount of the MVF corresponding to each of the time control points, by the following formula:
c
t
n
,
x
′
=
∂
τ
_
∂
x
t
n
=
∑
t
β
∈
t
n
(
∂
p
∂
u
∂
u
∂
x
+
∂
p
∂
v
∂
v
∂
x
)
×
∂
M
(
t
β
,
x
,
y
,
c
t
β
,
x
,
y
)
∂
x
,
c
t
n
,
y
′
=
∂
τ
_
∂
y
t
n
=
∑
t
β
∈
t
n
(
∂
p
∂
u
∂
u
∂
y
+
∂
p
∂
v
∂
v
∂
y
)
×
∂
M
(
t
β
,
x
,
y
,
c
t
β
,
x
,
y
)
∂
y
,
wherein, {right arrow over (τ)} is the MVF,
x,y are coordinates of a reconstructed point on the reconstructed CT scan image f(L),
β is the projection angle,
t β is the collecting time of the projection data of the projection angle β, and the collecting time t β is within the range of the time control point t n ,
p is the projection data,
u,v are parameters regarding channel and slice direction of the detector,
M(t,x,y,c t,x,y ) are corrected coordinates of the reconstructed point, c t,x is the X-axis projection value of the motion vector at time t, and c t,y is the Y-axis projection value of the motion vector at time t, and
c′ t n ,x ,c′ t n ,y are the motion amount of the MVF corresponding to the time control point t n .
18. The device according to claim 10 , wherein said machine readable instructions further cause the processor to:
set at least two assumed directions;
calculate estimated MVFs in each of the assumed directions with the motion amounts of the MVF corresponding to each of the time control points;
perform motion compensations on the ROI with the estimated MVFs in each of the assumed directions, so as to reconstruct estimated images on each of the assumed directions;
calculate the edge gradient standard deviations of each of the estimated images; and
determine the assumed direction which corresponds to the maximum edge gradient standard deviation among the present edge gradient standard deviations of each of the estimated images, as the direction of the MVF of the ROI.