Methods and systems for registration of images
View Patent ↗A method for registering images, for example medical images, includes acquiring a first image. A second image is acquired. A deformation field for registering the second image to the first image is calculated. The deformation field includes a sum of a plurality of weighted distortion vectors each of which has a substantially Gaussian distribution. The calculated deformation field is applied to the second image to register it to the first image.
1. A method for registering images, comprising:
acquiring a reference image;
acquiring a moving image;
calculating an initial degree of registration between the reference and moving images;
calculating a gradient field for the reference image;
generating an incremental deformation based on the calculated gradient;
calculating a second degree of registration between an incrementally deformed reference image and the moving image;
determining whether the second degree of registration is greater than the initial degree of registration;
when the second degree of registration is greater than the initial degree of registration, applying an inverse of the incremental deformation to the moving image;
determining whether a second degree of registration is maximized, wherein a similarity function is used to determine whether the second degree of registration is greater than the initial degree of registration and to determine whether the second degree of registration is maximized, wherein the similarity function is optimized uses the equation:
{
ϕ
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=
ϕ
0
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δ
1
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δ
2
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1
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…
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ϕ
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∂
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(
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wherein ε>0 is sufficiently small to provide for the invertibility of δ k , id denotes the identity of mapping and δ ∞ represents δ n for a value n sufficiently large to attain convergence criteria.
2. The method of claim 1 , wherein the steps of generating an incremental deformation, calculating a second degree of registration and applying the inverse of the incremental deformation to the moving image when the second degree of registration is greater than the initial degree of registration, are repeated until the degree of registration is maximized.
3. The method of claim 1 , wherein the similarity function is a mean square error function representing a stun of absolute differences between the intensities of the moving image and the reference image.
4. The method of claim 1 , wherein a gradient field for an image is calculated only once.
5. A method for registering images, comprising:
acquiring a reference image;
acquiring a moving image;
calculating a gradient field for the reference image;
generating an incremental deformation based on the calculated gradient;
temporarily applying the generated incremental deformation to the reference image to determine whether the generated incremental deformation has increased a degree of registration between the reference and moving images; and
when the incremental deformation has increased the degree of registration between the images, applying an inverse of the incremental deformation to the moving image;
wherein a similarity function is used to determine whether the degree of registration has been increased and to determine whether the degree of registration is maximized; and
wherein a deformation field is initially unknown and is expressed according to the function: φ: 3 → 3 , the reference image I 1 is represented by a scalar function I 1 : 3 → and the moving image I 2 is represented by a scalar function I 2 : 3 → , and the similarity function is denoted by S, and wherein a displacement u({right arrow over (x)}) is solved for at each point {right arrow over (x)}ε 3 such that φ({right arrow over (x)})={right arrow over (x)}+u({right arrow over (x)}).
6. A method for registering images, comprising:
acquiring a reference image:
acquiring a moving image;
calculating a gradient field for the reference image;
generating an incremental deformation based on the calculated gradient;
temporarily applying the generated incremental deformation to the reference image to determine whether the generated incremental deformation has increased a degree of registration between the reference and moving images; and
when the incremental deformation has increased the degree of registration between the images, applying an inverse of the incremental deformation to the moving image;
wherein a similarity function is used to determine whether the degree of registration has been increased and to determine whether the degree of registration is maximized; and
wherein the similarity function is optimized using the equation:
{
ϕ
*
=
ϕ
0
·
δ
1
-
1
·
δ
2
-
1
·
…
·
δ
∞
-
1
ϕ
k
=
id
+
ɛ
∂
∂
δ
S
(
I
1
·
δ
,
I
2
·
ϕ
0
·
δ
1
-
1
·
δ
2
-
1
·
…
·
δ
k
-
1
-
1
)
|
δ
=
id
wherein ε>0 is sufficiently small to provide for the invertibility of δ k , id denotes the identity of mapping and δ ∞ represents δ n for a value rt sufficiently large to attain convergence criteria.