[Insight-users] itk::Transform, how do to a FORWARD transform?

[Jakub Bican]

Hi.

ITK transforms are usually one-way transforms, no
matter which direction you use them for. Transform just takes point from
input space and returns corresponding point from output space. So, if you
use CartesianToPolar transform (
http://insight-journal.org/InsightJournalManager/view_reviews.php?back=publications.php%3Fjournalid%3D6%26order%3Drating%26revision_display%3Dcombined&pubid=130),
you can transform POINTS from cartesian space to polar space.

The other thing is how transforms are used in registration framework and by
ResampleImageFilter to resample IMAGES. In these cases, transforms are used
to map points from output image space to input image space to guarantee that
the output image space is fully covered. Input space of a transform
corresponds to output image's space and output space of transform
corresponds to input image's space.

So if you want to transform image from cartesian coordinates to polar
coordinates, you need to use ResampleImageFilter with PolarToCartesian
transform. As resample filter is filling values into output image, it asks
transform to give for the current voxel of the output image coordinates of
corresponding point in the input image. This is what is called BACKWARD
MAPPING. If we would like to use FORWARD mapping, we would result with
output with discontinuities.

HTH

    Jakub



2007/3/11, Ali - < saveez at hotmail.com>:
>
> Hi,
>
> For whatever reason, itk::Transform only likes backward transforms
> (mapping from
> output to input). This is not just confusing for newbies, but sort of a
> bad base for many
> other things.
>
> Assume you want to do a Cartesian-to-polar transform. One way is to
> sub-class from
> itk::Transform and call the class like itk::CartesianToPolarTransform and,
> in a funny way,
> ask your users with a big notice to use this class for the *backward*
> transform.
>
> One more serious problem with this is that the backward transform does not
> always work
> the way that it is expected to.
>
> How is it possible to the itk::transform in a FORWARD way?
>
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