[Insight-users] Translation, Rotation and Scaling

[Luis Ibanez]

Hi Ramon,

When you have Anisotropic Scaling and Rotation,
that is equivalent to providing Shearing.

In other words, you can implement Shearing by
composing Rotation and Anisotropic scaling.

Therefore, you cannot have a transform that has
Anisotropic Scaling and Rotation but not Shearing.

---

Using the Affine transform sounds like the
right thing to do in this case.



    Regards,


          Luis


-----------------------
2009/9/5 Ramón Casero Cañas <ramon.casero at comlab.ox.ac.uk>

> Yang, Jinzhong wrote:
>
>> This is simply an affine transform itk::AffineTransform.
>>
>
>
> Hi Jinzhong,
>
> Am I wrong to say that the affine transform includes translation, rotation
> and anisotropic scaling, as John wants, but also shear, that he doesn't?
>
> John, similarity transformations include isotropic scaling, and in 2D they
> have 4 degrees of freedom (2 for translation + 1 for scaling + 1 for
> rotation).
>
> Affine transformations have 6 degrees of freedom, while the transformation
> you want would have 5 parameters  (2 for translation + 2 for scaling + 1 for
> rotation).
>
> Maybe something you can do is combine an itk::ScaleTransform (anisotropic
> scaling) with an itk::Rigid2DTransform (translation and rotation).
>
> http://www.itk.org/Doxygen/html/classitk_1_1ScaleTransform.html
> http://www.itk.org/Doxygen/html/classitk_1_1Rigid2DTransform.html
>
> although swapping from one optimization to the other may not be worth the
> hassle, and you are better off just using an affine transformation, as
> Jinzhong suggests.
>
> Best regards,
>
> Ramon.
>
> --
> Ramón Casero Cañas, DPhil
>
> Computational Biology, Computing Laboratory
> University of Oxford
> Wolfson Building, Parks Rd
> Oxford OX1 3QD
>
> tlf     +44 (0) 1865 610807
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