Image analysis method and image analysis apparatus
An image analysis method includes acquiring images of spatially different analysis regions. Each of the images of the analysis regions is constituted by pixels including a plurality of data acquired simultaneously or time-serially. The method further includes obtaining a cross-correlation between two analysis regions by using data of pixels of images of the analysis regions.
1. An image analysis method comprising:
acquiring images of spatially different analysis regions, each of the images of the analysis regions being constituted by pixels including a plurality of data acquired simultaneously or time-serially, respectively; and
obtaining a cross-correlation between two analysis regions by using data of pixels of the images of the analysis regions,
wherein each image of the analysis regions is a two-dimensional image, the two analysis regions, between which the cross-correlation is obtained, comprise an analysis region 1 and an analysis region 2 , and the obtaining the cross-correlation performs correlation calculation by using equation (1) and fitting for the correlation calculation result by using equation (2) to obtain the cross-correlation between the two-dimensional analysis regions:
G
s
(
ξ
,
ψ
)
=
∑
I
1
(
x
,
y
)
*
I
2
(
x
+
ξ
,
y
+
ψ
)
/
M
12
(
∑
I
1
(
x
,
y
)
/
M
1
)
(
∑
I
2
(
x
,
y
)
/
M
2
)
(
1
)
where G s is a spatial cross-correlation value of RICS, I 1 is data of a pixel of an image of the analysis region 1 , I 2 is data of a pixel of an image of the analysis region 2 , x and y are the spatial coordinates of a measurement point, ξ and ψ are the changes of the spatial coordinates from the measurement point, M 12 is the number of times of sum-of-product calculation of data of the analysis region 1 and the analysis region 2 , M 1 is the total number of data of the analysis region 1 , and M 2 is the total number of data of the analysis region 2
G
s
(
ξ
,
ψ
)
=
S
(
ξ
,
ψ
)
*
G
(
ξ
,
ψ
)
S
(
ξ
,
ψ
)
=
exp
(
-
1
2
*
[
(
2
ξ
δ
r
W
0
)
2
+
(
2
ψ
δ
r
W
0
)
2
]
(
1
+
4
D
(
τ
p
ξ
+
τ
l
ψ
)
W
0
2
)
)
G
(
ξ
,
ψ
)
=
1
N
(
(
1
+
4
D
(
τ
p
ξ
+
τ
l
ψ
)
W
0
2
)
-
1
*
(
1
+
4
D
(
τ
p
ξ
+
τ
l
ψ
)
W
Z
2
)
-
1
/
2
)
(
2
)
where Gs is a spatial correlation value of RICS, S is an influence of a scan in RICS analysis, G is an influence of a time delay in RICS analysis, D is a diffusion constant, δ r is a pixel size, N is the number of molecules, ξ and ψ are the changes of spatial coordinates from a measurement point, W 0 is a radius of an excitation laser beam in a lateral direction, W z is a radius of an excitation laser beam in a longitudinal direction, τ p is a pixel time, and τ l is a line time.
2. The method of claim 1 , wherein the acquiring images of analysis regions comprising:
acquiring an image of an observation region including the analysis regions, the image of the observation region being constituted by pixels including a plurality of data acquired simultaneously or time-serially, respectively;
setting the analysis regions for the image of the observation region; and
extracting data of pixels corresponding to the analysis regions from the image of the observation region.
3. The method of claim 2 , wherein the acquiring the image of the observation region acquires images of frames of the observation region.
4. The method of claim 3 , wherein the obtaining the cross-correlation obtains the cross-correlation by using any one of a fluorescence intensity, a pixel time, a line time, a frame time, a pixel positional relationship, a pixel size, and a statistical value thereof.
5. The method of claim 1 , wherein the acquiring the images of the analysis regions acquires images of the analysis regions respectively by using optical systems.
6. The method of claim 5 , wherein the acquiring the images of the analysis regions simultaneously acquires images of the analysis regions.
7. The method of claim 5 , wherein the acquiring the images of the analysis regions acquires images of frames of the analysis regions.
8. The method of claim 7 , wherein the obtaining the cross-correlation obtains the cross-correlation by using any one of a fluorescence intensity, a pixel time, a line time, a frame time, a pixel positional relationship, a pixel size, and a statistical value thereof.
9. The method of claim 1 , wherein the obtaining the cross-correlation obtains the cross-correlation by using any one of an average value, a maximum value, a minimum value, a relative difference, and an absolute difference of the data.
10. The method of claim 1 , wherein the obtaining the cross-correlation obtains the cross-correlation by using reconstructed data obtained by reconstructing the data.
11. An image analysis method comprising:
acquiring images of spatially different analysis regions, each of the images of the analysis regions being constituted by pixels including a plurality of data acquired simultaneously or time-serially, respectively; and
obtaining a cross-correlation between two analysis regions by using data of pixels of the images of the analysis regions,
wherein each image of the analysis regions is a three-dimensional image, the two analysis regions, between which the cross-correlation is obtained, are an analysis region 1 and an analysis region 2 , and the obtaining the cross-correlation performs correlation calculation by using equation (3) and fitting for the correlation calculation result by using equation (4) to obtain the cross-correlation between the three-dimensional analysis regions:
G
s
(
ξ
,
ψ
,
η
)
=
∑
I
1
(
x
,
y
,
z
)
*
I
2
(
x
+
ξ
,
y
+
ψ
,
z
+
η
)
/
M
12
(
∑
I
1
(
x
,
y
,
z
)
/
M
1
)
(
∑
I
2
(
x
,
y
,
z
)
/
M
2
)
(
3
)
where Gs is a spatial cross-correlation value of RICS, I 1 is data of a pixel of an image of the analysis region 1 , I 2 is data of a pixel of an image of the analysis region 2 , x, y, and z are the spatial coordinates of a measurement point, ξ, ψ, and η are the changes of the spatial coordinates from the measurement point, M 12 is the number of times of sum-of-product calculation of data of the analysis region 1 and the analysis region 2 , M 1 is the total number of data of the analysis region 1 , and M 2 is the total number of data of the analysis region 2
G
s
(
ξ
,
ψ
,
η
)
=
S
(
ξ
,
ψ
,
η
)
*
G
(
ξ
,
ψ
,
η
)
S
(
ξ
,
ψ
,
η
)
=
exp
(
-
1
2
*
[
(
2
ξ
δ
r
W
0
)
2
+
(
2
ψ
δ
r
W
0
)
2
+
(
2
η
δ
r
W
0
)
2
]
(
1
+
4
D
(
τ
p
ξ
+
τ
l
ψ
+
τ
f
η
)
W
0
2
)
)
G
(
ξ
,
ψ
,
η
)
=
1
N
(
(
1
+
4
D
(
τ
p
ξ
+
τ
l
ψ
+
τ
f
η
)
W
0
2
)
-
1
*
(
1
+
4
D
(
τ
p
ξ
+
τ
l
ψ
+
τ
f
η
)
W
Z
2
)
-
1
/
2
)
(
4
)
where Gs is a spatial correlation value of RICS, S is an influence of a scan in RICS analysis, G is an influence of a time delay in RICS analysis, D is a diffusion constant, δ r is a pixel size, N is the number of molecules, ξ, ψ, and η are the changes of spatial coordinates, W 0 is a radius of an excitation laser beam in a lateral direction, W z is a radius of an excitation laser beam in a longitudinal direction, τ p is a pixel time, τ l is a line time, and τ f is a frame time.
12. An image analysis apparatus comprising:
an analysis region image acquisition unit configured to acquire images of spatially different analysis regions, each of the images of the analysis regions being constituted by pixels including a plurality of data acquired simultaneously or time-serially, respectively; and
a correlation analysis unit configured to obtain a cross-correlation between two analysis regions by using data of pixels of the images of the analysis regions,
wherein each image of the analysis regions is a two-dimensional image, the two analysis regions, between which the cross-correlation is obtained, are an analysis region 1 and an analysis region 2 , and the correlation analysis unit performs correlation calculation by using equation (5) and fitting for the correlation calculation result by using equation (6) to obtain the cross-correlation between the two-dimensional analysis regions:
G
s
(
ξ
,
ψ
)
=
∑
I
1
(
x
,
y
)
*
I
2
(
x
+
ξ
,
y
+
ψ
)
/
M
12
(
∑
I
1
(
x
,
y
)
/
M
1
)
(
∑
I
2
(
x
,
y
)
/
M
2
)
(
5
)
where G s is a spatial cross-correlation value of RICS, I 1 is data of a pixel of an image of the analysis region 1 , I 2 is data of a pixel of an image of the analysis region 2 , x and y are the spatial coordinates of a measurement point, ξ and ψ are the changes of the spatial coordinates from the measurement point, M 12 is the number of times of sum-of-product calculation of data of the analysis region 1 and the analysis region 2 , M 1 is the total number of data of the analysis region 1 , and M 2 is the total number of data of the analysis region 2
G
s
(
ξ
,
ψ
)
=
S
(
ξ
,
ψ
)
*
G
(
ξ
,
ψ
)
S
(
ξ
,
ψ
)
=
exp
(
-
1
2
*
[
(
2
ξ
δ
r
W
0
)
2
+
(
2
ψ
δ
r
W
0
)
2
]
(
1
+
4
D
(
τ
p
ξ
+
τ
l
ψ
)
W
0
2
)
)
G
(
ξ
,
ψ
)
=
1
N
(
(
1
+
4
D
(
τ
p
ξ
+
τ
l
ψ
)
W
0
2
)
-
1
*
(
1
+
4
D
(
τ
p
ξ
+
τ
l
ψ
)
W
Z
2
)
-
1
/
2
)
(
6
)
where G s is a spatial correlation value of RICS, S is an influence of a scan in RICS analysis, G is an influence of a time delay in RICS analysis, D is a diffusion constant, δ r is a pixel size, N is the number of molecules, ξ and ψ are the changes of spatial coordinates from a measurement point, W 0 is a radius of an excitation laser beam in a lateral direction, W z is a radius of an excitation laser beam in a longitudinal direction, τ p is a pixel time, and τ l is a line time.
13. The apparatus of claim 12 , wherein the analysis region image acquisition unit comprising:
an observation region image acquisition unit configured to acquire an image of an observation region including the analysis regions, the image of the observation region being constituted by pixels including a plurality of data acquired simultaneously or time-serially, respectively;
an analysis region setting unit configured to set the analysis regions for the image of the observation region; and
a data extraction unit configured to extract data of pixels corresponding to the analysis regions from the image of the observation region.
14. The apparatus of claim 13 , wherein the observation region image acquisition unit acquires images of frames of the observation region.
15. The apparatus of claim 14 , wherein the correlation analysis unit obtains the cross-correlation by using any one of a fluorescence intensity, a pixel time, a line time, a frame time, a pixel positional relationship, a pixel size, and a statistical value thereof.
16. The apparatus of claim 12 , wherein the analysis region image acquisition unit includes optical systems configured to respectively acquire images of the analysis regions.
17. The apparatus of claim 16 , wherein the analysis region image acquisition unit simultaneously acquires images of the analysis regions.
18. The apparatus of claim 16 , wherein the analysis region image acquisition unit acquires images of frames of the analysis regions.
19. The apparatus of claim 16 , wherein the correlation analysis unit obtains the cross-correlation by using any one of a fluorescence intensity, a pixel time, a line time, a frame time, a pixel positional relationship, a pixel size, and a statistical value thereof.
20. The apparatus of claim 12 , wherein the correlation analysis unit obtains the cross-correlation by using any one of an average value, a maximum value, a minimum value, a relative difference, and an absolute difference of the data.
21. The apparatus of claim 12 , wherein the correlation analysis unit obtains the cross-correlation by using reconstructed data obtained by reconstructing the data.
22. An image analysis apparatus comprising:
an analysis region image acquisition unit configured to acquire images of spatially different analysis regions, each of the images of the analysis regions being constituted by pixels including a plurality of data acquired simultaneously or time-serially, respectively; and
a correlation analysis unit configured to obtain a cross-correlation between two analysis regions by using data of pixels of the images of the analysis regions,
wherein each image of the analysis region is a three-dimensional image, the two analysis regions, between which the cross-correlation is obtained, are an analysis region 1 and an analysis region 2 , and the correlation analysis unit performs correlation calculation by using equation (7) and fitting for the correlation calculation result by using equation (8) to obtain the cross-correlation of the three-dimensional analysis regions:
G
s
(
ξ
,
ψ
,
η
)
=
∑
I
1
(
x
,
y
,
z
)
*
I
2
(
x
+
ξ
,
y
+
ψ
,
z
+
η
)
/
M
12
(
∑
I
1
(
x
,
y
,
z
)
/
M
1
)
(
∑
I
2
(
x
,
y
,
z
)
/
M
2
)
(
7
)
where G s is a spatial cross-correlation value of RICS, I 1 is data of a pixel of an image of the analysis region 1 , I 2 is data of a pixel of an image of the analysis region 2 , x, y, and z are the spatial coordinates of a measurement point, ξ, ψ, and η are the changes of the spatial coordinates from the measurement point, M 12 is the number of times of sum-of-product calculation of data of the analysis region 1 and the analysis region 2 , M 1 is the total number of data of the analysis region 1 , and M 2 is the total number of data of the analysis region 2
G
s
(
ξ
,
ψ
,
η
)
=
S
(
ξ
,
ψ
,
η
)
*
G
(
ξ
,
ψ
,
η
)
S
(
ξ
,
ψ
,
η
)
=
exp
(
-
1
2
*
[
(
2
ξ
δ
r
W
0
)
2
+
(
2
ψ
δ
r
W
0
)
2
+
(
2
η
δ
r
W
0
)
2
]
(
1
+
4
D
(
τ
p
ξ
+
τ
l
ψ
+
τ
f
η
)
W
0
2
)
)
G
(
ξ
,
ψ
,
η
)
=
1
N
(
(
1
+
4
D
(
τ
p
ξ
+
τ
l
ψ
+
τ
f
η
)
W
0
2
)
-
1
*
(
1
+
4
D
(
τ
p
ξ
+
τ
l
ψ
+
τ
f
η
)
W
Z
2
)
-
1
/
2
)
(
8
)
where G s is a spatial correlation value of RIGS, S is an influence of a scan in RIGS analysis, G is an influence of a time delay in RIGS analysis, D is a diffusion constant, δ r is a pixel size, N is the number of molecules, ξ, ψ, and η are the changes of spatial coordinates, W 0 is a radius of an excitation laser beam in a lateral direction, W z is a radius of an excitation laser beam in a longitudinal direction, τ p is a pixel time, τ l is a line time, and τ f is a frame time.