[Insight-developers] Centered Transforms

[Stephen R. Aylward]

Cool idea...  I do all conversions between transforms via center, matrix, and offset - that is what led to the recent changes so that those terms were handled consistently.   Also added matrix to parameter converts for quaternion and other transforms.  Since center of rotation is not a parameter for most transforms, you must use center et al.

The problem with incorporating scales in transforms is that scales are quite application specific.  The transorms can possibly report which params are translation, rotation, scale, or skew related....it is a bit unclear which categories should be used...we can keep thinking about this...

Stephen
-----Original Message-----

From:  "Blezek, Daniel J \(Research\)" <blezek at crd.ge.com>
Subj:  RE: [Insight-developers] Centered Transforms
Date:  Thu Mar 10, 2005 2:45 pm
Size:  4K
To:  "Stephen R. Aylward" <aylward at unc.edu>,   "Miller, James V \(Research\)" <millerjv at crd.ge.com>
cc:  "Insight-developers \(E-mail\)" <insight-developers at itk.org>

Stephen,  I suppose by opening my mouth, I get some of the blame.  Well here goes anyway.

I've been looking at the transforms as well, and on think that could use some revamping is setting scales for optimizers.  It would be great if the transforms provided some runtime clue as to which parameters related to translation, so a framework to swap transformation types like what you describe (and I'd love to know how you do it) can generically set a translation scale factor for any transform.

-dan

-----Original Message-----
From: insight-developers-bounces at itk.org
[mailto:insight-developers-bounces at itk.org]On Behalf Of Stephen R.
Aylward
Sent: Monday, March 07, 2005 4:59 PM
To: Miller, James V (Research)
Cc: Insight-developers (E-mail)
Subject: Re: [Insight-developers] Centered Transforms


Hi,

Yup - the terms center, offset, and translation aren't my favorite 
either (I didn't pick them, I am following the ITK standard)...it was 
decided quite some time ago to call "translation" the component of the 
transform that defines the shift to be applied after rotation about a 
center of rotation.   The offset vector defines the amount of shift to 
apply after a rotation when a center of rotation has not used.

Center (of rotation) must be maintained since it is not specifically 
being optimized during registration.  That is, it must be stored since 
it isn't being passed.

Furthermore, since center isn't being optimized, rotation can only 
decoupled from shifting during registration if the optimizers update 
translation instead of offset during registration.   So, translation is 
a parameter of the optimizer instead of offset.

So, the optimizers drove the addition of the concepts of center of 
rotation and translation in the transforms.

Having a center of rotation greatly simplifies certain registration 
optimizations compared to image alignment when rotation were limited to 
being about the origin.  ITK began years ago by having registration 
optimization temporarily move the origin of an image to the center of 
the image during registration, and then move the origin back after 
registration, but that really is a hack - the origin really shouldn't 
move during registration...so, we added the concept of a center of 
rotation...

I hope this clarifies things a bit.   I don't like classes that have 
redundant/linked variables that must be kept in sync, but there is no 
way that Bill would let us remove the Get/SetOffset functions :)   And, 
actually, I don't think we should either... :)

So this is the rock and the hard place that we are between...   With 
that in mind...any ideas/suggestions?   I've been working with the 
transforms quite a bit - switching between them within a single 
application and composing them in chains while using center of rotation. 
   This has revealed some inconsistencies in how offset and translation 
are handled (not surprisingly) as well as inconsistencies in their APIs. 
   This lead to the development of the MatrixOffsetTransform base class 
that we are adding to make sure all of the affine, similarity, rigid, 
translation, and rotation transforms handle these concepts consistently. 
   I just want to make sure we all agree on which is the lessor of the 
evils :)

Sorry for the long email...just looking for someone I can share the 
blame with when we ultimately pick a standard... :)   Anyone.... 
Anyone... :)

Thanks,
Stephen


Miller, James V (Research) wrote:
> I don't think I am going to be of much help since I do not 
> understand the difference between an "offset" and a "translation".
> 
> Skimming through the headers, it looks like transforms like the 
> affine transform are defined by equations
> 
> y = Ax + b
> 
> where A is the "matrix" stored in the transform and "b" is the offset.
> 
> To me, it looks like the only things that need to be STORED are the
> matrix and offset.  With the "center" and "translation" being computations
> based on A and b.  Conversely, you could argue that one would want to
> set the center and translation. In doing so, the matrix A and offset b
> would have to be updated. However, I would favor not storing the center and
> translation if there are truly secondary parameters completely defined by
> A and b.
> 
> 
> 
> 
> 
> -----Original Message-----
> From: insight-developers-bounces at itk.org
> [mailto:insight-developers-bounces at itk.org]On Behalf Of Stephen R.
> Aylward
> Sent: Monday, March 07, 2005 1:15 PM
> To: Insight-developers (E-mail)
> Subject: [Insight-developers] Centered Transforms
> 
> 
> 
> When someone updates the center of rotation or matrix for a transform, 
> either the translation or the offset must be implicitly updated for 
> consistency.   This implicit update is necessary since translation and 
> offset are related to one another via the transform matrix and the 
> 
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