3D tissue model formation from non-parallel 2D images
Biopsy of the prostate using 2D transrectal ultrasound (TRUS) guidance is the current gold standard for diagnosis of prostate cancer; however, the current procedure is limited by using 2D biopsy tools to target 3D biopsy locations. We have discovered a technique for patient-specific 3D prostate model reconstruction from a sparse collection of non-parallel 2D TRUS biopsy images. Our method can be easily integrated with current TRUS biopsy equipment and could be incorporated into current clinical biopsy procedures for needle guidance without the need for expensive hardware additions. We have demonstrated the model reconstruction technique using simulated biopsy images from 3D TRUS prostate images of 10 biopsy patients. This technique of model reconstruction is not limited to the prostate, but can be applied to the reconstruction of any tissue acquired with non-parallel 2-dimensional ultrasound images.
1. A method for reconstructing a three dimensional model of an object, comprising the steps of:
receiving a plurality of two dimensional images;
segmenting a two dimensional object boundary in each of the two dimensional images, wherein the two dimensional object boundary in each of the two dimensional images is segmented using a deformable contour; and
performing three dimensional fitting of the segmented two dimensional object boundaries using a radial basis function.
2. The method according to claim 1 , wherein the plurality of two dimensional images are ultrasound images.
3. The method according to claim 1 , wherein the plurality of two dimensional images are transrectal ultrasound (TRUS) images.
4. The method according to claim 3 , wherein the TRUS images are formed from signals obtained by a two dimensional TRUS probe.
5. The method according to claim 4 , wherein the two dimensional TRUS probe is mounted on a rotational mover.
6. The method according to claim 1 , wherein a three dimensional position and an orientation of each of the plurality of two dimensional images are recorded.
7. The method according to claim 1 , wherein the plurality of two dimensional images are in transverse axial planes or oblique sagittal and approximately orthogonal planes.
8. The method according to claim 1 , wherein the deformable contour is a dynamic deformable contour.
9. The method according to claim 8 , wherein the dynamic deformable contour is obtained by dynamically moving each vertex which satisfies a first equation, f i tot =w i int f i int +w i img f i img +w i d v i wherein f i int is an internal or curvature force to maintain contour smoothness, f i img is an image or external force used to drive contour an edge, v i is a damping force based on a vertex velocity, and w i int , w i img , and w i d are weighting parameters.
10. The method according to claim 1 , wherein the step of performing three dimensional fitting using a radial basis function comprises the step of interpolating the segmented two dimensional object boundaries in the plurality of two dimensional images using the radial basis function.
11. The method according to claim 10 ,
wherein the segmented two dimensional object boundaries in the plurality of two dimensional images are interpolated according to a second equation,
s
(
x
)
=
p
1
(
x
)
+
∑
i
=
1
n
λ
i
ϕ
(
x
-
x
i
)
,
x
∈
3
,
λ
i
∈
where s(x) is surface approximation of the object, p 1 is a first order polynomial, and φ(r)=r for biharmonic splines.
12. The method according to claim 11 ,
wherein λi where i=1 . . . n are determined so that s(x) satisfies an third equation, s(xi)=f(xi), i=1, 2, . . . , n and a fourth equation,
∑
j
=
1
n
λ
j
q
(
x
i
)
=
0
,
forallq
∈
π
1
3
where π 1 3 are all three-variable first-order polynomials.
13. The method according to claim 11 ,
wherein an input smoothing constant ρ is obtained by minimizing a fifth equation,
ρ
s
2
+
1
n
∑
i
=
1
n
(
s
(
x
i
)
-
f
(
x
i
)
)
2
where ρ≧0 and ∥s∥ 2 is a measure of an energy in a second derivative of s, and
wherein λi where i=1 . . . n are determined so that s(x) satisfies a fifth equation, s(xi)=f(xi)+ρλi, i=1, 2, . . . , n and a fourth equation,
∑
j
=
1
n
λ
j
q
(
x
i
)
=
0
,
forallq επ 1 3 where π 1 3 are all three-variable first-order polynomials.
14. The method according to claim 1 , wherein the radial basis function is a polyharmonic radial basis function.
15. A non-transitory machine-readable medium storing a computer program for reconstructing a three dimensional model of an object, the computer program operable for:
receiving a plurality of two dimensional images;
segmenting the two dimensional object boundary in each of the two dimensional images, wherein the two dimensional object boundary in each of the two dimensional images is segmented using a deformable contour; and
performing three dimensional fitting of the segmented two dimensional object boundaries using a radial basis function.
16. The machine-readable medium according to claim 15 , wherein the plurality of two dimensional images are ultrasound images.
17. The machine-readable medium according to claim 15 , wherein the plurality of two dimensional images are transrectal ultrasound (TRUS) images.
18. The machine-readable medium according to claim 17 , wherein the TRUS images are formed from signals obtained by a two dimensional TRUS probe.
19. The machine-readable medium according to claim 18 , wherein the two dimensional TRUS probe is mounted on a rotational mover.
20. The machine-readable medium according to claim 15 , wherein a three dimensional position and an orientation of each of the plurality of two dimensional images are recorded.
21. The machine-readable medium according to claim 15 , wherein the plurality of two dimensional images are in transverse axial planes or oblique sagittal and approximately orthogonal planes.
22. The machine-readable medium according to claim 15 , wherein the deformable contour is a dynamic deformable contour.
23. The machine-readable medium according to claim 22 , wherein the dynamic deformable contour is obtained by dynamically moving each vertex which satisfies a first equation, f i tot =w i int f i int +w i img f i img +w i d v i wherein f i int is an internal or curvature force to maintain contour smoothness, f i img is an image or external force used to drive contour an edge, v i is a damping force based on a vertex velocity, and w i int , w i img , and w i d are weighting parameters.
24. The machine-readable medium according to claim 15 , wherein the step of performing three dimensional fitting using a radial basis function comprises the step of interpolating the segmented two dimensional object boundaries in the plurality of two dimensional images using the radial basis function.
25. The machine-readable medium according to claim 24 ,
wherein the segmented two dimensional object boundaries in the plurality of two dimensional images are interpolated according to a second equation,
s
(
x
)
=
p
1
(
x
)
+
∑
i
=
1
n
λ
i
ϕ
(
x
-
x
i
)
,
x
∈
3
,
λ
i
∈
where s(x) is surface approximation of the object, ρ 1 is a first order polynomial, and φ(r)=r for biharmonic splines.
26. The machine-readable medium according to claim 25 ,
wherein λi where i=1 . . . n are determined so that s(x) satisfies an third equation, s(xi)=f(xi), i=1, 2, . . . , n and a fourth equation,
∑
j
=
1
n
λ
j
q
(
x
i
)
=
0
,
forallq επ 1 3 where π 1 3 are all three-variable first-order polynomials.
27. The machine-readable medium according to claim 25 ,
wherein an input smoothing constant ρ is obtained by minimizing a fifth equation,
ρ
s
2
+
1
n
∑
i
=
1
n
(
s
(
x
i
)
-
f
(
x
i
)
)
2
where ρ≧0 and ∥s∥ 2 is a measure of an energy in a second derivative of s, and
wherein λi, where i=1 . . . n are determined so that s(x) satisfies a fifth equation, s(xi)=f(xi)+ρλi, i=1, 2, . . . , n and a fourth equation,
∑
j
=
1
n
λ
j
q
(
x
i
)
=
0
,
forallq επ 1 3 where π 1 3 are all three-variable first-order polynomials.
28. The machine-readable medium according to claim 15 , wherein the radial basis function is a polyharmonic radial basis function.
29. A method for reconstructing a three dimensional model of an object, comprise the steps of:
receiving a plurality of two dimensional images;
segmenting a two dimensional object boundary in each of the two dimensional images; and
performing three dimensional fitting of the segmented two dimensional object boundaries using a radial basis function, wherein the step of perfoming three dimensional fitting using a radial basis function comprises the step of interloping the segmented two dimensional object boundaries in the plurality of two dimensional images using the radial basis function.
30. The method according to claim 29 , wherein the two dimensional object boundary in each of the two dimensional images is segmented using a deformable contour.
31. A non-transitory machine-readable storing a computer program for reconstructing a three dimensional model of an object, the computer program operable for:
receiving a plurality of two dimensional images;
segmenting a two dimensional object boundary in each of the two dimensional images; and
performing three dimensional fitting of the segmented two dimensional object boundaries using a radial basis function, wherein the step of performing three dimensional fitting using a radial basis function comprises the step of interpolating the segmented two dimensional object boundaries in the plurality of two dimensional images using the radial basis function.
32. The machine-readable medium according to claim 31 , wherein the two dimensional object boundary in each of the two dimensional images is segmented using a deformable contour.