Image analysis method and image analysis apparatus
An image analysis method includes acquiring an image of at least one frame that comprises pixels, setting at least one analytic region for the image of at least one frame, extracting data on the pixel corresponding to each analytic region, setting time intervals for data pairs for use in correlation calculations, performing a correlation calculation for each of the time intervals by use of the extracted data, and performing a fitting for each of the correlation calculation results.
1. An image analysis method comprising:
acquiring an image of at least one frame that comprises pixels;
setting at least one analytic region for the image of at least one frame;
extracting data on the pixel corresponding to each analytic region;
setting time intervals for data pairs for use in correlation calculations;
performing a correlation calculation for each of the time intervals by use of the extracted data; and
performing a fitting for each of the correlation calculation results,
wherein the acquiring the image of the at least one frame acquires images of frames, and
the setting the at least one analytic region sets analytic regions for the image of each frame, the analytic regions being the same regions in the image of each frame, respectively,
wherein the performing the correlation calculation includes performing the correlation calculation by use of pairs of data on the pixels in different analytic regions in the images of different frames.
2. The image analysis method according to claim 1 , wherein the image of the analytic region is a two-dimensional image, and
the performing the correlation calculation performs the correlation calculation by use of the following equation:
G
2
ddc
(
ξ
,
ψ
)
=
∑
I
1
f
i
(
x
,
y
)
*
I
2
f
j
(
x
+
ξ
,
y
+
ψ
)
/
M
12
ij
(
∑
I
1
f
i
(
x
,
y
)
/
M
1
i
)
(
∑
I
2
f
j
(
x
,
y
)
/
M
2
j
)
where G 2ddc is a cross-correlation value between the analytic region A 1 of the frame f i and the analytic region A 2 of the same f j , I 1fi is data, for example, fluorescence intensity data on the pixels of the image of the analytic region A 1 of the frame f i , I 2fj is data, for example, fluorescence intensity data on the pixels of the image of the analytic region A 2 of the frame f j , x, y are spatial coordinates of a measurement point, ξ, ψ are variations of the spatial coordinates from the measurement point, M 12ij is the number of product-sum calculations of the data on the pixels of the images of the analytic region A 1 of the frame f i and the analytic region A 2 of the frame f j , M 1i , is the total number of data on the pixels of the image of the analytic region A 1 of the frame f i , and M 2j is the total number of data on the pixels of the image of the analytic region A 2 of the frame f j .
3. The image analysis method according to claim 1 , wherein the image of the analytic region is a three-dimensional image,
the performing the correlation calculation performs the correlation calculation by use of the following equation:
G
3
ddc
(
ξ
,
ψ
,
η
)
=
∑
I
1
f
i
(
x
,
y
,
z
)
*
I
2
f
j
(
x
+
ξ
,
y
+
ψ
,
z
+
η
)
/
M
12
i
j
(
∑
I
1
f
i
(
x
,
y
,
z
)
/
M
1
i
)
(
∑
I
2
f
j
(
x
,
y
,
z
)
/
M
2
j
)
where G 3ddc is a cross-correlation value between the analytic region A 1 of the frame f i and the analytic region A 2 of the same f j , I 1fi is data, for example, fluorescence intensity data on the pixels of the image of the analytic region A 1 of the frame f i , I 2fj is data, for example, fluorescence intensity data on the pixels of the image of the analytic region A 2 of the frame f j , x, y, z are spatial coordinates of a measurement point, ξ, ψ, η are variations of the spatial coordinates from the measurement point, M 12ij is the number of product-sum calculations of the data on the pixels of the images of the analytic region A 1 of the frame f i and the analytic region A 2 of the frame f j , M 1i , is the total number of data on the pixels of the image of the analytic region A 1 of the frame f i , and M 2j is the total number of data on the pixels of the image of the analytic region A 2 of the frame f j .
4. The image analysis method according to claim 3 , wherein the performing the fitting performs the fitting by use of the following equation:
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
)
where G s is a spatial correlation value of RIGS, S is the influence of a scan in an analysis of the RIGS, G is the influence of a time delay in the analysis of the RIGS, D is a diffusion constant, δ r is a pixel size, N is the number of molecules, ξ, ψ, η are variations of spatial coordinates, W 0 is the lateral radius of an excitation laser beam, W Z is the longitudinal radius of the excitation laser beam, τ p is a pixel time, τ l is a line time, and τ f is a frame time.
5. The image analysis method according to claim 1 , further comprising estimating the number of molecules of a molecular species of each component in the analytic region by performing the fitting, and calculating the ratio of the molecular species by use of the following equation:
P
N
i
=
N
i
∑
k
=
1
m
N
k
×
100
%
where N i is the number of molecules of the molecular species of an i-component, P Ni is the ratio of the number of molecules N i in the molecular species of the i-component, N k is the number of molecules of the molecular species of a k-component, and m is the number of components in the multicomponent analysis.
6. The image analysis method according to claim 1 , further comprising reconstructing data on the pixels in the analytic region, wherein the performing the correlation calculation performs the correlation calculation by use of the reconstructed data.
7. The image analysis method according to claim 1 , wherein the image of each frame comprises pixels the data of which are acquired in a time-series manner by light scanning.
8. The image analysis method according to claim 1 , further comprising displaying a correlation calculation result.
9. An image analysis apparatus comprising:
an image acquiring section to acquire an image of at least one frame that comprises pixels;
an analytic region setting section to set at least one analytic region for the image of at least one frame;
a data extracting section to extract data on the pixel corresponding to each analytic region;
a time interval setting section to set time intervals for data pairs for use in correlation calculations; and
an analytic processing section to perform a correlation calculation for each of the time intervals by use of the extracted data, and a fitting for each of the correlation calculation results,
wherein the image acquiring section acquires images of frames, and
the analytic region setting section sets analytic regions for the image of each frame, the analytic regions being the same regions in the image of each frame, respectively,
wherein the analytic processing section performs the correlation calculation by use of pairs of data on the pixels in different analytic regions in the images of different frames.
10. The image analysis apparatus according to claim 9 , wherein the image of the analytic region is a two-dimensional image, and
the analytic processing section performs the correlation calculation by use of the following equation:
G
2
ddc
(
ξ
,
ψ
)
=
∑
I
1
f
i
(
x
,
y
)
*
I
2
f
j
(
x
+
ξ
,
y
+
ψ
)
/
M
12
i
j
(
∑
I
1
f
i
(
x
,
y
)
/
M
1
i
)
(
∑
I
2
f
j
(
x
,
y
)
/
M
2
j
)
where G 2ddc is a cross-correlation value between the analytic region A 1 of the frame f i and the analytic region A 2 of the same f j , I 1fi is data, for example, fluorescence intensity data on the pixels of the image of the analytic region A 1 of the frame f i , I 2fj is data, for example, fluorescence intensity data on the pixels of the image of the analytic region A 2 of the frame f j , x, y are spatial coordinates of a measurement point, ξ, ψ are variations of the spatial coordinates from the measurement point, M 12ij is the number of product-sum calculations of the data on the pixels of the images of the analytic region A 1 of the frame f i and the analytic region A 2 of the frame f j , M 1i is the total number of data on the pixels of the image of the analytic region A 1 of the frame f i , and M 2j is the total number of data on the pixels of the image of the analytic region A 2 of the frame f j .
11. The image analysis apparatus according to claim 9 , wherein the image of the analytic region is a three-dimensional image,
the analytic processing section performs the correlation calculation by use of the following equation:
G
3
ddc
(
ξ
,
ψ
,
η
)
=
∑
I
1
f
i
(
x
,
y
,
z
)
*
I
2
f
j
(
x
+
ξ
,
y
+
ψ
,
z
+
η
)
/
M
12
i
j
(
∑
I
1
f
i
(
x
,
y
,
z
)
/
M
1
i
)
(
∑
I
2
f
j
(
x
,
y
,
z
)
/
M
2
j
)
where G 3ddc is a cross-correlation value between the analytic region A 1 of the frame f i and the analytic region A 2 of the same f j , I 1fi is data, for example, fluorescence intensity data on the pixels of the image of the analytic region A 1 of the frame f i , I 2fj is data, for example, fluorescence intensity data on the pixels of the image of the analytic region A 2 of the frame f j , x, y, z are spatial coordinates of a measurement point, ξ, ψ, η are variations of the spatial coordinates from the measurement point, M 12ij is the number of product-sum calculations of the data on the pixels of the images of the analytic region A 1 of the frame f i and the analytic region A 2 of the frame f j , M 1i is the total number of data on the pixels of the image of the analytic region A 1 of the frame f i , and M 2j is the total number of data on the pixels of the image of the analytic region A 2 of the frame f j .
12. The image analysis apparatus according to claim 11 , wherein the analytic processing section performs the fitting by use of the following equation:
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
)
where G s is a spatial correlation value of RIGS, S is the influence of a scan in an analysis of the RIGS, G is the influence of a time delay in the analysis of the RIGS, D is a diffusion constant, δ r is a pixel size, N is the number of molecules, ξ, ψ, η are variations of spatial coordinates, W 0 is the lateral radius of an excitation laser beam, W Z is the longitudinal radius of the excitation laser beam, τ p is a pixel time, τ l is a line time, and τ f is a frame time.
13. The image analysis apparatus according to claim 9 , the analytic processing section estimates the number of molecules of a molecular species of each component in the analytic region by performing the fitting, and calculates the ratio of the molecular species by use of the following equation:
P
N
i
=
N
i
∑
k
=
1
m
N
k
×
100
%
where N i is the number of molecules of the molecular species of an i-component, P Ni is the ratio of the number of molecules N i in the molecular species of the i-component, N k is the number of molecules of the molecular species of a k-component, and m is the number of components in the multicomponent analysis.
14. The image analysis apparatus according to claim 9 , the analytic processing section reconstructs data on the pixels in the analytic region, and performs the correlation calculation by use of the reconstructed data.
15. The image analysis apparatus according to claim 9 , wherein the image of each frame comprises pixels the data of which are acquired in a time-series manner by light scanning.
16. The image analysis apparatus according to claim 9 , further comprising a displaying section to display a correlation calculation result.