3D wavelet-based filter and method
View Patent ↗A 3D wavelet-based filter for visualizing and locating structural features of a user-specified linear size in 2D or 3D image data. The only input parameter is a characteristic linear size of the feature of interest, and the filter output contains only those regions that are correlated with the characteristic size, thus denoising the image.
1. A method in a computer system for filtering 2D or 3D image data, comprising:
providing a 3D continuous wavelet transform having a single unknown parameter which is a wavelet width, (a), necessary for transforming a dataset;
receiving an input value for the wavelet width, (a);
using the 3D continuous wavelet transform and the input value of the wavelet width, (a), to transform a set of up to 3D image data into a correlation image representing correlation strengths, with respect to the wavelet width, (a), as a function of spatial position; and
graphically rendering the correlation image to be viewed by a user, whereby high correlation structural features can be discernable by the user in the correlation image.
2. The method of claim 1 ,
wherein the wavelet width, (a), is a characteristic linear dimension of a known structural feature of interest.
3. The method of claim 1 ,
wherein the wavelet width, (a), is measured in voxels.
4. The method of claim 1 ,
wherein the input value for the wavelet width is provided by a user.
5. The method of claim 1 ,
wherein the 3D continuous wave transform is adapted to produce only positive correlations.
6. The method of claim 1 ,
wherein the 3D continuous wave transform has at least partial invariance to rigid body rotations.
7. The method of claim 6 ,
wherein rotational invariance is approximated in the 3D continuous wave transform by using only cubical wavelets and averaging over angles.
8. The method of claim 1 , wherein the 3D continuous wave transform is constructed from three 1D wavelet kernels, Ψ, each defined as follows:
Ψ
(
ζ
)
=
1
a
′
for
ζ
≤
1
2
and
Ψ
(
ζ
)
=
-
1
2
a
′
for
1
2
<
ζ
≤
3
2
where ζ=(x−x′)/a′ for the x-domain (a′=a), ζ=(y−y′)/a′ for the y-domain (a′=b), and ζ=(z−z′)/a′ for the z-domain (a′=c), and a=b=c.
9. The method of claim 1 ,
further comprising, upon viewing the correlation image and determining that the graphic rendering is sub-optimal, adjusting the input value of the wavelet width, (a) to graphically re-render the correlation image.
10. The method of claim 1 ,
wherein the 3D continuous wave transform is the function W(x,y,z,a), with:
W
(
x
,
y
,
z
,
a
)
=
1
4
(
W
sym
(
x
,
y
,
z
,
a
,
0
,
x
)
+
W
sym
(
x
,
y
,
z
,
a
,
π
/
4
,
x
)
+
W
sym
(
x
,
y
,
z
,
a
,
π
/
4
,
y
)
+
W
sym
(
x
,
y
,
z
,
a
,
π
/
4
,
z
)
)
W
sym
(
x
,
y
,
z
,
a
,
ϕ
,
i
)
=
1
6
R
i
-
1
(
ϕ
)
∑
x
,
y
,
z
perm
W
_
(
x
,
y
,
z
,
a
,
a
,
a
,
ϕ
,
i
)
;
W
_
(
x
,
y
,
z
,
a
,
b
,
c
,
ϕ
,
i
)
=
H
[
∫
Ψ
(
z
-
z
′
c
)
H
[
∫
Ψ
(
y
-
y
′
b
)
H
[
∫
Ψ
(
x
-
x
′
a
)
R
i
(
ϕ
)
f
(
x
′
,
y
′
,
z
′
)
ⅆ
x
′
]
ⅆ
y
′
]
ⅆ
z
′
]
where H[q]=q for q>0 and H[q]=0 for q≦0, to produce only positive correlations; and
Ψ
(
ζ
)
=
1
a
′
for
ζ
≤
1
2
and
Ψ
(
ζ
)
=
-
1
2
a
′
for
1
2
<
ζ
≤
3
2
where ζ=(x−x′)/a′for the x-domain (a′=a), ζ=(y−y′)/a′ for the y-domain (a′=b), and ζ=(z−z′)/a′ for the z-domain (a′=c), and a=b=c.
11. A computer system for filtering 2D or 3D image data, comprising:
means for receiving an input value for a wavelet width, (a);
a 3D continuous wave transform component having a single unknown parameter which is a wavelet width, (a), necessary for transforming a dataset, wherein upon receiving the input value of the wavelet width, (a) the transform component is adapted to transform a set of up to 3D image data into a correlation image representing correlation strengths, with respect to the wavelet width, (a), as a function of spatial position; and
means for graphically rendering the correlation image to be viewed by a user, whereby high correlation structural features can be discernable by the user in the correlation image.
12. The computer system of claim 11 ,
wherein the wavelet width, (a), is a characteristic linear dimension of a known structural feature of interest.
13. The computer system of claim 11 ,
wherein the wavelet width, (a), is measured in voxels.
14. The computer system of claim 11 ,
wherein the input value for the wavelet width is provided by a user.
15. The computer system of claim 11 ,
wherein the 3D continuous wave transform is adapted to produce only positive correlations.
16. The computer system of claim 11 ,
wherein the 3D continuous wave transform has at least partial invariance to rigid body rotations.
17. The computer system of claim 16 ,
wherein rotational invariance is approximated in the 3D continuous wave transform by using only cubical wavelets and averaging over angles.
18. The computer system of claim 11 , wherein the 3D continuous wave transform is constructed from three 1D wavelet kernels, Ψ, each defined as follows:
Ψ
(
ζ
)
=
1
a
′
for
ζ
≤
1
2
and
Ψ
(
ζ
)
=
-
1
2
a
′
for
1
2
<
ζ
≤
3
2
where ζ=(x−x′)/a′ for the x-domain (a′=a), ζ=(y−y′)/a′ for the y-domain (a′=b), and ζ=(z−z′)/a′ for the z-domain (a′=c), and a=b=c.
19. The computer system of claim 11 ,
wherein the 3D continuous wave transform is the function W(x,y,z,a), with:
W
(
x
,
y
,
z
,
a
)
=
1
4
(
W
sym
(
x
,
y
,
z
,
a
,
0
,
x
)
+
W
sym
(
x
,
y
,
z
,
a
,
π
/
4
,
x
)
+
W
sym
(
x
,
y
,
z
,
a
,
π
/
4
,
y
)
+
W
sym
(
x
,
y
,
z
,
a
,
π
/
4
,
z
)
)
W
sym
(
x
,
y
,
z
,
a
,
ϕ
,
i
)
=
1
6
R
i
-
1
(
ϕ
)
∑
x
,
y
,
z
perm
W
_
(
x
,
y
,
z
,
a
,
a
,
a
,
ϕ
,
i
)
;
W
_
(
x
,
y
,
z
,
a
,
b
,
c
,
ϕ
,
i
)
=
H
[
∫
Ψ
(
z
-
z
′
c
)
H
[
∫
Ψ
(
y
-
y
′
b
)
H
[
∫
Ψ
(
x
-
x
′
a
)
R
i
(
ϕ
)
f
(
x
′
,
y
′
,
z
′
)
ⅆ
x
′
]
ⅆ
y
′
]
ⅆ
z
′
]
where H[q]=q for q>0 and H[q]=0 for q≦0, to produce only positive correlations; and
Ψ
(
ζ
)
=
1
a
′
for
ζ
≤
1
2
and
Ψ
(
ζ
)
=
-
1
2
a
′
for
1
2
<
ζ
≤
3
2
where ζ=(x−x′)/a′ for the x-domain (a′=a), ζ=(y−y′)/a′ for the y-domain (a′=b), and ζ=(z−z′)/a′ for the z-domain (a′=c), and a=b=c.
20. An article of manufacture comprising:
a computer readable medium having computer readable program code means embodied therein for filtering 2D or 3D image data, the computer readable program code means in said article of manufacture comprising:
computer readable program code means for causing a computer to receive an input value for a wavelet width, (a);
computer readable program code means for causing the computer to include the input value for the wavelet width (a) to a 3D continuous wave transform where only the wavelet width, (a), is unknown, and to use the 3D continuous wave transform to transform a set of up to 3D image data into a correlation image representing correlation strengths, with respect to the wavelet width, (a), as a function of spatial position; and
computer readable program code means for graphically rendering the correlation image to be viewed by a user, whereby high correlation structural features can be discernable by the user in the correlation image.