[Insight-users] Re: GetJacobian in some transforms

[Luis Ibanez]

Hi Marius,

Yes, that means that if you want to use a Centered rigid
transform in 3D you should use the VersorRigid3DTransform

http://www.itk.org/Insight/Doxygen/html/classitk_1_1VersorRigid3DTransform.html

or the QuaternionRigidTransform

http://www.itk.org/Insight/Doxygen/html/classitk_1_1QuaternionRigidTransform.html


Regards,


    Luis


--------------------
Marius Staring wrote:

> Hi Luis,
> 
> Thank you for your reply. It is very helpfull. I'll read the quaternion 
> tutorials and consider the Versor3DTransform.
> 
> Just one more question about Euler3DTransform: it has no center of 
> rotation, right. So, would that mean that if I wanted to use 
> 3DCenteredTransform's I should use the Versor3DTransform?
> 
> Regards,
> Marius
> 
> At 10:38 12/05/04, you wrote:
> 
>> Hi Marius,
>>
>> The VersorRigid3DTransform has a Center included.
>>
>> This center is not part of the parameter array
>> passed to the optimizer, but it is used during
>> the rotation computation.
>>
>> The center of rotation is extremely important,
>> specially if you are doing image registration.
>>
>> If you want to avoid Versors, you could use the
>> Euler3DTransform which is a rigid 3D transform
>> where rotation are specified as angles around the
>> x,y,z axis.
>>
>> http://www.itk.org/Insight/Doxygen/html/classitk_1_1Euler3DTransform.html
>>
>>
>> I would advice you to do yourself a favor and
>> overcome your fear for Versors. They are the
>> correct representation of rotations in 3D space.
>> Versors are your friends, they are here to help.
>> Euler angles are just a second best. Versors are
>> the right tool for this job. You could use a
>> screwdriver as a hammer but that usually
>> produces very painful results...
>>
>>
>> Please read the tutorials on Quaternions in:
>>
>> http://www.itk.org/cgi-bin/cvsweb.cgi/InsightDocuments/Developer/General/QuaternionsI.pdf?cvsroot=Insight 
>>
>> http://www.itk.org/cgi-bin/cvsweb.cgi/InsightDocuments/Developer/General/QuaternionsII.pdf?cvsroot=Insight 
>>
>>
>>
>>
>>   Regards,
>>
>>
>>     Luis
>>
>>
>> ----------------------
>> Marius Staring wrote:
>>
>>> Hi Luis,
>>> I see. I thought I could also use these classes if I did not wanted 
>>> to use for example a CenteredTransform. So I suppose I better use 
>>> CenteredRigid2DTransform (with maybe center set to 0).
>>> Since we are mailing now anyway: I am looking for a 3D version of 
>>> CenteredRigid2DTransform: a CenteredRigid3DTransform. And I like to 
>>> avoid versors or quaternions. Is that going to be implemented soon?
>>> Thanks for the quick response.
>>> Marius
>>> At 09:49 12/05/04, you wrote:
>>>
>>>> Hi Marius,
>>>>
>>>> Rigid2DTransform and Rigid3DTransform cannot have Jacobians
>>>> because they are base classes for particular parameterizations
>>>> of these transforms.  You will find the Jacobians implemented
>>>> in their derived classes.
>>>>
>>>> http://www.itk.org/Insight/Doxygen/html/classitk_1_1Rigid2DTransform.html 
>>>>
>>>>
>>>> http://www.itk.org/Insight/Doxygen/html/classitk_1_1Rigid3DTransform.html 
>>>>
>>>>
>>>> The Jacobian is computed as the derivatives of the mapped point
>>>> with respect to the transform parameters. Given that there are
>>>> many different ways of parameterizing a rigid transform, those
>>>> Jacobians can only be computed once a particular set of parameters
>>>> has been selected.  For example, rotation can be represented with
>>>> Euler angles or with Versors.
>>>>
>>>> Please don't use the Rigid3DTransform or Rigid2DTransform, use one
>>>> of their derived classes.
>>>>
>>>>
>>>>
>>>>   Regards,
>>>>
>>>>
>>>>     Luis
>>>>
>>>>
>>>> ----------------------
>>>> Marius Staring wrote:
>>>>
>>>>> Hi Luis Ibanez,
>>>>> I am using ITK 1.6 for image registration purposes.
>>>>> I noticed that the GetJacobian() function in some of the transform 
>>>>> classes has not been implemented. See for example Rigid2DTransform 
>>>>> and Rigid3DTransform.
>>>>> Is that going to be implemented soon?
>>>>> With kind regards,
>>>>>
>>>>> Marius Staring
>>>>> Image Science Institute
>>>>> University Medical Center Utrecht, room F01.703
>>>>> Phone: +31 (0)30 250 8562       Fax: +31 (0)30 258 1098
>>>>> email: 
>>>>> <mailto:marius@isi.uu.nl>marius<mailto:marius@isi.uu.nl>@isi.uu.nl 
>>>>> website: http://www.isi.uu.nl/People/Marius/
>>>>
>>>>
>>>>
>>
>>
> 
>