The Registration: Landmark-Least Squares algorithm provides a way for registering an image to the reference image by using corresponding points placed in both images. This algorithm works on images requiring rotation and translation, but it does not work on images requiring scaling, because this is a rigid transformation based on two homologous landmark datasets.
The algorithm relates the two corresponding point sets on the image to be registered and on the reference image using the following equation:
where
This algorithm calculates a least-squares solution of R and T, which is based on a singular value decomposition of a 2 x 2 matrix in 2D or a 3 x 3 matrix in 3D. It, first, calculates the centroid p1[i] in the image to be registered:
It, then, calculates the centroid p2[i] in the reference image:
where N = the number of corresponding user points.
The algorithm, next, calculates the difference between the points and the centroid voxel in the image to be registered (q1[i][j]):
and then the difference between the points and centroid voxel in the reference image (q2[i][j]):
The algorithm then performs the following steps:
Image type
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If this is true . . .
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Then . . .
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Comments
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Determinant
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Matrix H
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Success
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Failure
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2D images
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1
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X
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Rotation matrix
R = X | ||
-1
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Has no zero singular values
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X
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Data too noisy
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-1
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Has one singular value
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X
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Data is colinear
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3D images
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1
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X
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-1
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Has no zero singular values
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X
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Data too noisy
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-1
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Has one zero singular value and the other two singular values are unequal
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X
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-1
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Has two equal singular values
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X
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Colinear
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You can apply this algorithm to 2D and 3D grayscale and color images.
The following notes apply:
Refer to the following reference for more information:
"Least-Squares Fitting of Two 3-D Point Sets" by K.S. Arun, T.S. Huang, and S.D. Blostein, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. PAMI-9, No. 5, September, 1987,
pp. 698-700.
To run this algorithm, complete the following steps:
Note: Three-dimensional (3D) images can handle cases that are coplanar but not colinear. |
Tip: Make sure that you delineate the points on the target image in the same order as on the reference image. That is, point 1 on the reference image should correspond to point 1 on the target image, point 2 on the reference image should correspond to point 2 on the target image, etc. |
Register [name of source image] to [name of reference image]
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Displays a set of possible reference images. This box registers the image to be registered to the selected reference image.
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OK
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Applies the algorithm according to the specifications in this dialog box.
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Cancel
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Disregards any changes that you made and closes the dialog box.
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Help
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Displays online help for this dialog box.
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