System and method for efficient feature estimation for medical images
View Patent ↗A method for estimating feature values from a digitized image includes calculating a gradient of an image, defining a filter weighting function, convolving the gradient with the filter weighting function, integrating over a subdomain of the convolved gradient to calculate components of a cost matrix Φ, wherein the cost matrix minimizes a distance metric in a frequency domain of the image, solving for the eigenvalues of the cost matrix, and calculating one or more features from the cost matrix eigenvalues. One or more predesigned bandpass filters can be applied to the image, and cost matrix eigenvalues are analyzed to select one or more appropriate bandpass filters to be applied to the image.
1. A method for estimating feature values from a digitized image, comprising the steps of:
using a computer to perform the following steps of:
providing a digitized image f(x) comprising a plurality of intensities corresponding to a domain of points on a n-dimensional grid;
calculating a gradient of said image;
defining a filter weighting function;
convolving said gradient with said filter weighting function;
integrating over a subdomain of said convolved gradient to calculate components of a cost matrix Φ, wherein said cost matrix minimizes a distance metric in a frequency domain of said image;
solving for the eigenvalues of said cost matrix; and
calculating one or more features from said cost matrix eigenvalues.
2. The method of claim 1 , further comprising designing one or more bandpass filters to be applied to said image; and
analyzing said cost matrix eigenvalues to select one or more appropriate bandpass filters to be applied to said image.
3. The method of claim 1 , wherein a component Φ ij of said cost matrix is proportional to
∫
∫
R
(
∂
f
(
x
)
∂
x
i
∘
w
(
x
)
)
(
∂
f
(
x
)
∂
x
j
∘
w
(
x
)
)
ⅆ
x
i
ⅆ
x
j
,
wherein x=(x 1 , x 2 , . . . , x n ) is a point vector representing the image grid, R is the n-dimensional domain over which the integration is performed,
∂
f
∂
x
i
and
∂
f
∂
x
j
represents components of the gradient of the image intensities, w(x) represents the filter weighting function, and the symbol ∘ represents convolution.
4. The method of claim 3 , further comprising calculating a signal direction θ(x) from said cost matrix by accumulating rotation angles
θ
ij
(
x
)
=
{
1
2
tan
-
1
(
2
Φ
ij
Φ
ii
-
Φ
jj
)
}
,
wherein θ ij (x) denotes the rotation angle within the hyperplane that contains coordinate axes i and j, Φ ij , Φ ii , and Φ jj are components of the cost matrix, and the angle accumulation is over all hyperplanes in a rotation matrix that diagonalizes said cost matrix.
5. The method of claim 3 , wherein said features include a signal anisotropy A(x) defined as
A
(
x
)
=
(
λ
max
-
λ
min
λ
max
+
λ
min
)
2
,
wherein λ max and λ min are the maximum and minimum eigenvalues, respectively, of the cost matrix Φ.
6. The method of claim 3 , wherein said features include a signal energy E(x)defined as
E
(
x
)
=
∑
i
=
1
n
λ
i
k
,
wherein the λ i are the eigenvalues of the cost matrix Φ, and k is a positive integer.
7. The method of claim 2 , wherein a sum of said lowpass and said one or more bandpass filters is substantially flat in the frequency domain, at least up to a high frequency cutoff.
8. The method of claim 1 , wherein said weighting function is proportional to
exp
(
-
x
·
x
T
2
σ
)
,
wherein x is a point in the image domain, and σ is a pre-determined constant based on the desired frequency spectrum of said weighting function.
9. A computer implemented method for estimating feature values from a digitized image, the method performed by the computer comprising the steps of:
providing a digitized image comprising a plurality of intensities corresponding to a domain of points on a n-dimensional grid;
convolving a gradient of said image;
integrating said convolved gradient over a subdomain of said image to calculate components of a cost matrix, wherein said cost matrix minimizes a distance metric in a frequency domain of said image;
solving for the eigenvalues of said cost matrix;
designing one or more bandpass filters to be applied to said image; and
analyzing said cost matrix eigenvalues to select one or more appropriate bandpass filters to be applied to said image.
10. The method of claim 9 , further comprising calculating one or more features from said cost matrix eigenvalues.
11. The method of claim 9 , further comprising defining a filter weighting function in said image domain, wherein said gradient is convolved with said filter weighting function.
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 estimating feature values from a digitized image, said method comprising the steps of:
providing a digitized image f(x) comprising a plurality of intensities corresponding to a domain of points on a n-dimensional grid;
calculating a gradient of said image;
defining a filter weighting function;
convolving said gradient with said filter weighting function;
integrating over a subdomain of said convolved gradient to calculate components of a cost matrix Φ, wherein said cost matrix minimizes a distance metric in a frequency domain of said image;
solving for the eigenvalues of said cost matrix; and
calculating one or more features from said cost matrix eigenvalues.
13. The computer readable program storage device of claim 12 , the method further comprising designing one or more bandpass filters to be applied to said image; and
analyzing said cost matrix eigenvalues to select one or more appropriate bandpass filters to be applied to said image.
14. The computer readable program storage device of claim 12 , wherein a component Φ ij of said cost matrix is proportional to
∫
∫
R
(
∂
f
(
x
)
∂
x
i
∘
w
(
x
)
)
(
∂
f
(
x
)
∂
x
j
∘
w
(
x
)
)
ⅆ
x
i
ⅆ
x
j
,
wherein x=(x 1 , x 2 , . . . , x n ) is a point vector representing the image grid, R is the n-dimensional domain over which the integration is performed,
∂
f
∂
x
i
and
∂
f
∂
x
j
represents components of the gradient of the image intensities, w(x) represents the filter weighting function, and the symbol ∘ represents convolution.
15. The computer readable program storage device of claim 14 , the method further comprising calculating a signal direction θ(x) from said cost matrix by accumulating rotation angles
θ
ij
(
x
)
=
{
1
2
tan
-
1
(
2
Φ
ij
Φ
ii
-
Φ
jj
)
}
,
wherein θ ij (x) denotes the rotation angle within the hyperplane that contains coordinate axes i and j, Φ ij , Φ ii , and Φ jj are components of the cost matrix, and the angle accumulation is over all hyperplanes in a rotation matrix that diagonalizes said cost matrix.
16. The computer readable program storage device of claim 14 , wherein said features include a signal anisotropy A(x) defined as
A
(
x
)
=
(
λ
max
-
λ
min
λ
max
+
λ
min
)
2
,
wherein λ max and λ min are the maximum and minimum eigenvalues, respectively, of the cost matrix Φ.
17. The computer readable program storage device of claim 14 , wherein said features include a signal energy E(x) defined as
E
(
x
)
=
∑
i
=
1
n
λ
i
k
,
wherein the λ i are the eigenvalues of the cost matrix Φ, and k is a positive integer.
18. The computer readable program storage device of claim 13 , wherein a sum of said lowpass and said one or more bandpass filters is substantially flat in the frequency domain, at least up to a high frequency cutoff.
19. The computer readable program storage device of claim 12 , wherein said weighting function is proportional to
exp
(
-
x
·
x
T
2
σ
)
,
wherein x is a point in the image domain, and σ is a pre-determined constant based on the desired frequency spectrum of said weighting function.