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Shearing matrix composition in Affine DTI 3D Transform #488

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o-fares opened this issue Oct 3, 2022 · 0 comments
Open

Shearing matrix composition in Affine DTI 3D Transform #488

o-fares opened this issue Oct 3, 2022 · 0 comments

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@o-fares
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o-fares commented Oct 3, 2022

Hello,

I am working on affine registration with Affine DTI Transform. In the source article, the shearing matrix is defined as :
(1 gx*gz 0)
(gy 1 0)
(0 gz 1)

On the Simple Elastix website, it is written that the shearing matrix G is written as Gx Gy Gz.
Is it possible to have the shape and content of these three matrices ? I would need them to be sure of the range of the shearing angles (possibly arctan(gx) for the x dimension for example)

Additionnally, with a matrix T of the form T(x)=RGS(x−c)+t+c , is it possible to recover the initial parameters (3 rotation angles, 3 translation values, 3 shearing and 3 scaling)? If yes, is there an unique solution, or different possible solutions with a link between them?

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