[Insight-users] Re: VersorRigid3DTransform

[Luis Ibanez]

Hi Radhika,

Please consult the Doxygen documentation for the
list of methods avilable for every ITK class.

Answers to your questions can easily be found there.

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

1) has a SetCenter() method


2) The Set/Get Parameters manage 9 elements.

    3 for the versor, 3 for translation and
    3 for the center of rotation
http://www.itk.org/Insight/Doxygen/html/classitk_1_1VersorRigid3DTransform.html#z1257_0


3) Offset is computed as the result of rotating
    the center and adding the translation:

    P' = R * ( P - C ) + C + T

    Offset = - R * C + C + T

    P' = R * P + Offset

    R  = rotation matrix
    P  = input point
    P' = output point
    C  = center of rotation
    T  = translation


4) Yes there is a way of printing the translation:

             GetTranslation()

     Please check the Doxygen page for details.



Regards,


    Luis



-------------------------------------

Radhika Sivaramakrishna wrote:
> Hi Luis,
> 
> Thanks for the explanation. It was helpful.
> I had some further questions.
> How do I set the center of rotation to something other than the origin? I
> can do this by explicitly setting the values in finalParameters but how do I
> do it using versors and setting the rotation angle explicitly?
> Also is the optimization done in a 9-parameter space including center of
> rotation or is it a 6-parameter space?
> 
> Also, when the offset is printed out (for example in the example given under
> CenteredTransform), is this always given as though the rotation were about
> the origin rather than the center of rotation?
> Is there a way to print out the true translation?
> 
> Radhika
> 
> ----- Original Message ----- 
> From: "Luis Ibanez" <luis.ibanez at kitware.com>
> To: "Radhika Sivaramakrishna" <radshashi at earthlink.net>
> Cc: <insight-users at itk.org>
> Sent: Wednesday, December 31, 2003 11:42 AM
> Subject: Re: VersorRigid3DTransform
> 
> 
> 
>>Hi Radhika,
>>
>>A) The memory problem that you are encountering is
>>    due to the fact that the "ParameterType" used by
>>    ITK transform for representing the array of
>>    parameters is indeed a vnl_vector<>.
>>
>>    This is a variable size vector that by default has
>>    size=0. You must replace the declaration:
>>
>>TransformType::ParametersType finalParameters;
>>
>>    with something like:
>>
>>TransformType::ParametersType finalParameters(
>>                      transform->GetNumberOfParameters() );
>>
>>    or something like:
>>
>>TransformType::ParametersType finalParameters =
>>                      transform->GetParameters();
>>
>>     In both cases the vector-size of finalParameters
>>     will take the correct value.
>>
>>
>>
>>B)  The value that you provided for the parameter[0]
>>     doesn't correspond to 10 degrees.  A Versors is
>>     a unit quaternion. The magnitude of the three
>>     versor components is equal to sin(angle/2).
>>
>>     You probably computed
>>
>>        parameter[0] = 0.174532 = sin( 10 )
>>
>>     while you should do
>>
>>        parameter[0] = 0.087155 = sin( 10 / 2 )
>>
>>
>>C) Yes there is a better way of initializing the transform.
>>    Please look at the methods of the Versor class:
>>http://www.itk.org/Insight/Doxygen/html/classitk_1_1Versor.html
>>
>>    You can simply do:
>>
>>       TransformType::VersorType  versor;
>>       versor.SetRotationAroundX( 10.0 * PI / 180.0 );
>>       transform->SetRotation( versor );
>>
>>    or you could do
>>
>>       TransformType::AxisType axis;
>>       axis[0] = 1.0;
>>       axis[1] = 0.0;
>>       axis[2] = 0.0;
>>
>>       transform->SetRotation( axis, 10.0 * PI / 180.0 );
>>
>>
>>
>>Please let us know if you have further questions,
>>
>>
>>    Thanks
>>
>>
>>      Luis
>>
>>
>>-------------------------------
>>Radhika Sivaramakrishna wrote:
>>
>>
>>>Hi Luis,
>>>I was trying to use the VersorRigid3DTransform to artificially transform
> 
> a
> 
>>>given image by 10 degrees about the center of the image only in the
>>>X-direction (ie no rotation in Y and Z) and no translation either. I am
>>>doing this to get a better understanding of this transform because I
> 
> will
> 
>>>need to use it to register a large number of unknown cases.
> 
> Unfortunately, I
> 
>>>am running into some problems.
>>>I modified the example in ImageRegistration8.cxx to do this.
>>>
>>>Here is what I did:
>>>
>>>I read in the fixed and moving image (in my case both are from the same
>>>file). Since no registration is required this time, I only defined a
>>>Transform of type VersorRigid3DTransform.
>>>
>>>I then set the finalparameters of my transform directly in the following
>>>way:
>>>
>>>TransformType::ParametersType finalParameters;
>>>
>>>
>>>
>>>  finalParameters[0] = 0.174532;
>>>  finalParameters[1] = 0;
>>>  finalParameters[2] = 0;
>>>  finalParameters[3] = 128.0;
>>>  finalParameters[4] = 128.0;
>>>  finalParameters[5] = 82;
>>>  finalParameters[6] = 0;
>>>  finalParameters[7] = 0;
>>>  finalParameters[8] = 0;
>>>
>>>since I want a 10 degree rotation in X, my image is of size 256x256x164.
>>>
>>>I then did the usual resampling and casting to create my final image.
>>>However a memory error is reported when I try to set the finalParameters
>>>directly. Can you tell me what the problem is?
>>>
>>>Is there a better way of artificially creating a known transformation?
>>>
>>>Also, when I get to the actual image registration stage, what is the
> 
> best
> 
>>>optimizer for this transform? Is it the VersorTransformOptimizer?
>>>
>>>Thanks
>>>Radhika
>>>
>>>
>>>
>>
>>
>>
> 
> 
>