[Insight-users] Understanding why the direction of the transform mapping is from fixed to moving image

[Charl Botha]

2009/8/17 Anja Ende <anja.ende at googlemail.com>:
> "If we have used the Transform that maps coordinates from the moving
> image physical space
> into the fixed image physical space, then the resampling process could
> not guarantee that every
> pixel in the grid of the fixed image was going to receive one and only
> one value".
>
> Would anyone be kind enough to explain this a bit?

Mapping the moving image onto the fixed image is much easier when you
simply have to iterate over the pixels / voxels of the fixed image,
and for each pixel / voxel you have a vector pointing to the position
in the moving domain that you have to interpolate.  For example, for a
2D case, you'd have a stock-standard double nested loop (rows /
columns) for the fixed image, at each position you'd look up the
corresponding vector, use that to determine the position in the moving
space, interpolate the moving image pixel, then put that at your
current position in the fixed image.

Having it the other way around, would result in a really complex
compositing process transferring information from the moving image
(which would now have the stock-standard nested loop) to the fixed
image, as each contribution from the moving image would potentially
end up between pixel positions, and would then carefully need to be
distributed over the fixed image grid positions it covers.  Also
multiple contributions would often fall in the same small area,
meaning one would also have to take care of compositing everything,
somewhat like splatting in volume rendering.

Choosing between these two options, the former is clearly the more
straight-forward approach.

I hope this helps a bit!

Regards,
Charl