[Insight-users] Moving image and fixed image

[Luis Ibanez]

Hi Bjorn,

As you pointed out,
the use of the terms "fixed" and "moving" is a bit arbitrary.

Here is the rationale for ITK:

   Let's call M(x) the moving Image
   Let's call F(x) the fixed Image
   Let's call T(x) the spatial transform

"x" being an N-D vector that indicates the position of a pixel.

When a Metric is computed in the registration framework,
the three elements { F(x), M(x), T(x) }  are involved:

Metrics are computed in such a way that the coordinate
system of the "fixed" image is used as the reference.

That is, ALL the pixels in the "fixed" image are visited
and for each one of them, its coordinates are mapped
through the transform into the space of the "moving" image.
The resulting point on the moving image is interpolated
(since in general it will not fall on top of one of the
grid points).

For example, the MeanSquare metric is computed as:

  Sum( ( F(x) - M(T(x)) )^2 ) / NumberOfPixelsIn( F(x) )

where x going over the domain of F(x) (All the pixels
of F() are visited).

The transform T() maps points from the coordinate system
of the "fixed" image, to the coordinate system of the
"moving" image:

              x' = T( x )

   x' = point in the moving image coordinate system
   x  = point in the fixed image coordinate system

So, the notion of "fixed" comes from the fact that this
F(x) image is the one from which we map points into the
other space.

Just for the record: previous to this we used to have
"Reference" and "Target" images and run into similar
discussion about the ambiguity of the naming.


The description below is the bogus one:
 >
 >http://www.itk.org/Doxygen/html/classitk_1_1ImageRegistrationMethod.html)
 > it reads:
 > "This class uses the coordinate system of the Fixed image and searchs
 > for a transform that will map the Moving image on top of the Fixed
 > image."

I'll fix this one. Thank you for pointing this out.

--

Please let us know if this helps to clarify a bit the
naming convention.


Thanks

   Luis


=================================================================

Bjorn Hanch Sollie wrote:
> Hi all!
> 
> "Moving image" and "fixed image" are terms used by the ITK
> registration framework to denote the two images to be registered.
> Unfortunately, there is contradictory usage of the two terms in the
> documentation, as it is not clear what image is transformed to the
> other. In the description of ImageRegistrationMethod
> (http://www.itk.org/Doxygen/html/classitk_1_1ImageRegistrationMethod.html)
> it reads:
> "This class uses the coordinate system of the Fixed image and searchs
> for a transform that will map the Moving image on top of the Fixed
> image."
> 
> In the description of MutualInformationImageToImageMetric, however
> (http://www.itk.org/Doxygen/html/classitk_1_1MutualInformationImageToImageMetric.html)
> it reads:
> "The Transform is used to map points from the fixed image to the
> moving image domain."
> 
> Can anyone please explain what is correct usage of these terms?  What
> image is mapped to the other?  (And what is the correct usage in the
> case of MutualInformationImageToImageMetric?)
> 
> Thanks in advance!
> 
> -Bjorn
>