How to calculate the reverse 3d affine transform?

Algorithms
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1

Hi all,

I tried to calculate the reverse affine transform matrix and the returned translation vector is always wrong, which bother me a lot. Anyone has any ideas? I appreciate for any suggestions. Thank you!

Here are some details steps I did:
Assume I have two 3d images, A & B. I’ve calculated the transform from A to B and get a 12d vector (V). Now I want to get the transform matrix for B->A directly from the learned 12d vector: V.

I know the first 9 elements corresponding to M matrix, and the last 3 corresponding to the translation vector.

So I calculated the reverse M matrix as reverse(M) and reversed translation vector as -np.matmul(reverse(M), V(-3:)) and it turned out the reversed translation vector is wrong. May anyone know why this happens? Thank you!

2

Have you tried simply negating the translation (instead of multiplying it with the inverse of rotation/scaling/shear)? Have you tried appending 0 0 0 1 as the fourth row and then inverting the resulting 4x4 matrix? If you are using itk::AffineTransform class, you can use GetInverse() method.

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