Optimal registration of multiple deformed images using a physical model of the imaging distortion
Methods and systems for image registration implementing a feature-based strategy that uses a retinal vessel network to identify features, uses an affine registration model estimated using feature correspondences, and corrects radial distortion to minimize the overall registration error. Also provided are methods and systems for retinal atlas generation. Further provided are methods and systems for testing registration methods.
1. A method for image distortion correction, comprising:
receiving a target image and a reference image;
correcting radial distortion in the target image and the reference image according to a distortion parameter;
detecting feature correspondence points in the distortion corrected target image and the distortion corrected reference image;
initializing an affine registration model with the feature correspondence points;
minimizing vessel centerline error measure (CEM) between the distortion corrected target image and the distortion corrected reference image to determine an optimal distortion parameter and an optimal affine registration model;
correcting radial distortion in the target image and the reference image according to the optimal distortion parameter;
applying an affine transform to the optimally distortion corrected target image and the optimally distortion corrected reference image according to the optimal affine registration model;
combining the transformed optimally distortion corrected target image and the transformed optimally distortion corrected reference image into a montage image; and
outputting the montage image.
2. The method of claim 1 , wherein the target image and the reference image are retinal images.
3. The method of claim 2 , wherein feature correspondence points comprise measurements derived from vessel lines, vessel line branch points, and vessel crossings.
4. The method of claim 1 , wherein detecting feature correspondence points in the distortion corrected target image and the distortion corrected reference image further comprises:
for each feature correspondence point, determining a spatial and vector space correlation; and
determining two feature correspondence points having the highest spatial and vector space correlation.
5. The method of claim 2 , wherein correcting radial distortion further comprises:
determining a point u on the target image;
transforming point u as a function of position off of an optical axis to determine a distorted point ν; and
correcting for distortion by estimating {circumflex over (ν)} from u using
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wherein k n is the distortion parameter and r is the distance from an optical axis center to u.
6. The method of claim 5 , wherein k n is determined by a bisection search over an interval that is determined from properties of an imaged object and an image acquisition system.
7. The method of claim 5 , wherein an optimal affine registration model for k n is determined by a minimization method to find minimum vessel centerline error measure (CEM) between the target image and the reference image.
8. The method of claim 7 , wherein
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wherein N is a vessel line length and ν (r) is a closest point in the reference image after transforming a point ν (t) in the target image.
9. The method of claim 1 , wherein if two pixels overlap in the montage image creating an overlap pixel, then determine an intensity of the overlap pixel by a distance weighted blending scheme.
10. A computer readable storage medium storing computer executable instructions thereon for image distortion correction, the computer executable instructions comprising:
receiving a target image and a reference image;
correcting radial distortion in the target image and the reference image according to a distortion parameter;
detecting feature correspondence points in the distortion corrected target image and the distortion corrected reference image;
initializing an affine registration model with the feature correspondence points;
minimizing vessel centerline error measure (CEM) between the distortion corrected target image and the distortion corrected reference image to determine an optimal distortion parameter and an optimal affine registration model;
correcting radial distortion in the target image and the reference image according to the optimal distortion parameter;
applying an affine transform to the optimally distortion corrected target image and the optimally distortion corrected reference image according to the optimal affine registration model;
combining the transformed optimally distortion corrected target image and the transformed optimally distortion corrected reference image into a montage image; and
outputting the montage image.
11. The computer readable storage medium of claim 10 , wherein the target image and the reference image are retinal images.
12. The computer readable storage medium of claim 11 , wherein feature correspondence points comprise measurements derived from vessel lines, vessel line branch points, and vessel crossings.
13. The computer readable storage medium of claim 10 , wherein detecting feature correspondence points in the distortion corrected target image and the distortion corrected reference image further comprises:
for each feature correspondence point, determining a spatial and vector space correlation; and
determining two feature correspondence points having the highest spatial and vector space correlation.
14. The computer readable storage medium of claim 11 , wherein correcting radial distortion further comprises:
determining a point u on the target image;
transforming point u as a function of position off of an optical axis to determine a distorted point ν; and
correcting for distortion by estimating {circumflex over (ν)} from u using
υ
^
=
u
·
(
1
+
∑
n
=
1
∞
k
n
r
2
n
)
,
wherein k n is the distortion parameter and r is the distance from an optical axis center to u.
15. The computer readable storage medium of claim 14 , wherein k n is determined by a bisection search over an interval that is determined from properties of an imaged object and an image acquisition system.
16. The computer readable storage medium of claim 14 , wherein an optimal affine registration model for k n is determined by a minimization method to find minimum vessel centerline error measure (CEM) between the target image and the reference image.
17. The computer readable storage medium of claim 16 , wherein
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1
N
∑
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=
0
N
-
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∑
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N
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,
wherein N is a vessel line length and ν (r) is a closest point in the reference image after transforming a point ν (t) in the target image.
18. The computer readable storage medium of claim 10 , wherein if two pixels overlap in the montage image creating an overlap pixel, then determine an intensity of the overlap pixel by a distance weighted blending scheme.
19. A system for image distortion correction, comprising:
a memory, configured for storing image data; and
a processor, coupled to the memory, configured for
receiving a target image and a reference image,
correcting radial distortion in the target image and the reference image according to a distortion parameter,
detecting feature correspondence points in the distortion corrected target image and the distortion corrected reference image,
initializing an affine registration model with the feature correspondence points,
minimizing vessel centerline error measure (CEM) between the distortion corrected target image and the distortion corrected reference image to determine an optimal distortion parameter and an optimal affine registration model,
correcting radial distortion in the target image and the reference image according to the optimal distortion parameter,
applying an affine transform to the optimally distortion corrected target image and the optimally distortion corrected reference image according to the optimal affine registration model,
combining the transformed optimally distortion corrected target image and the transformed optimally distortion corrected reference image into a montage image, and
outputting the montage image.
20. The system of claim 19 , wherein the target image and the reference image are retinal images.
21. The system of claim 20 , wherein feature correspondence points comprise measurements derived from vessel lines, vessel line branch points, and vessel crossings.
22. The system of claim 19 , wherein detecting feature correspondence points in the distortion corrected target image and the distortion corrected reference image further comprises:
for each feature correspondence point, determining a spatial and vector space correlation; and
determining two feature correspondence points having the highest spatial and vector space correlation.
23. The system of claim 22 , wherein correcting radial distortion further comprises:
determining a point u on the target image;
transforming point u as a function of position off of an optical axis to determine a distorted point ν; and
correcting for distortion by estimating {circumflex over (ν)} from u using
υ
^
=
u
·
(
1
+
∑
n
=
1
∞
k
n
r
2
n
)
,
wherein k n is the distortion parameter and r is the distance from an optical axis center to u.
24. The system of claim 23 , wherein k n is determined by a bisection search over an interval that is determined from properties of an imaged object and an image acquisition system.
25. The system of claim 23 , wherein an optimal affine registration model for k n is determined by a minimization method to find minimum vessel centerline error measure (CEM) between the target image and the reference image.
26. The system of claim 25 , wherein
C
E
M
=
1
N
∑
n
=
0
N
-
1
υ
n
(
r
)
-
υ
^
n
=
1
N
∑
n
=
0
N
-
1
υ
n
(
r
)
-
υ
n
(
t
)
M
,
wherein N is a vessel line length and ν (r) is a closest point in the reference image after transforming a point ν (t) in the target image.
27. The system of claim 19 , wherein if two pixels overlap in the montage image creating an overlap pixel, then determine an intensity of the overlap pixel by a distance weighted blending scheme.