[Insight-users] Convert Rigid3DTransform To VersorRigid3DTransform

[Hans Johnson]

Bill,

Thanks.  I have that page printed on my desk and have been referencing it.

The code I have supplied in my previous message is producing a
VersorRigid3DTransformation that produces different resampling results than
the original Rigid3DTransform.

=========  From itkVersor.h  ============
205   /** Set the versor using an orthogonal matrix.
206    *  Based on code from:
207    *  http://www.euclideanspace.com/maths/geometry/rotations/
208    *  conversions/matrixToQuaternion/index.htm
209    */
210   void Set( const MatrixType & m );

========  From itkVersorRigid3DTransform.h ================
116 
117   /** This method must be made protected here because it is not a safe
way of
118    * initializing the Versor */
119   virtual void SetRotationMatrix(const MatrixType & matrix)
120     { this->Superclass::SetRotationMatrix( matrix ); }


The comment in line 117 of itkVersorRigid3DTransform.h is concerning to me.
I would think that this would be a safe way to initialize the rotation part
of the itkVersor3DTransform, as long as the input matrix was tested to be
orthogonal.

========  From itkVersorRigid3DTransform.h ================
 70 // Check if input matrix is orthogonal to within tolerance
 71 template<class TScalarType>
 72 bool
 73 Rigid3DTransform<TScalarType>
 74 ::MatrixIsOrthogonal(
 75  const MatrixType & matrix,
 76  double tolerance )
 77 {
 78   typename MatrixType::InternalMatrixType test =
 79     matrix.GetVnlMatrix() * matrix.GetTranspose();
 80 
 81   if( !test.is_identity( tolerance ) )
 82     {    
 83     return false;
 84     }
 85 
 86   return true;
 87 }


The itkVersorRigid3DTransform has 6 total parameters.  The last three are
the translation, and the first 3 are the rotation.  The versor is a unit
quaternion, so one of the 4 quaternion parameters can be computed from the
other 3.  I am not sure if I am placing the proper 3 parameters in the first
three locations of the itk::VersorRigid3DTransform.

I would like to see the following code work, or an explanation of why this
will not work:

itk::VersorRigid3DTransform<double>::Pointer
    ConvertToVersorRigid3D( itk::Rigid3DTransform<double>::Pointer RT)
{
   if(! RT->MatrixIsOrthogonal(RT->GetRotationMatrix()))
  { 
   throw exception...
  }
  itk::VersorRigid3DTransform<double>::Pointer returnVersorRigid3D=
       itk::VersorRigid3DTransform<double>::New();
  returnVersorRigid3D->SetFixedParameters(RT->GetFixedParameters());
  returnVersorRigid3D->SetRotationMatrix( RT->GetRotationMatrix() );
  returnVersorRigid3D->SetTranslation( RT->GetTranslation() );
  return returnVersorRigid3D;
}



Thanks,
Hans




On 12/16/08 11:02 PM, "Bill Lorensen" <bill.lorensen at gmail.com> wrote:

> Hans,
> 
> Here's a wikipedia entry:
> http://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles
> 
> Bill
> 
> On Tue, Dec 16, 2008 at 10:20 PM, Hans Johnson <hans-johnson at uiowa.edu> wrote:
>> Hello All,
>> 
>> I have a program that generates rho, phi, theta rotation euler angles, and I
>> can easily generate the rotation matrix for creating the Rigid3DTransform.
>> 
>> I now need to convert Rigid3DTransform to VersorRigid3DTransform so that I
>> can initialize a mutual information registration with it.
>> 
>> Could anyone provide some advice on how to perform this conversion?
>> 
>> Thanks,
>> Hans
>> 
>> PS: The following code does not work.
>> ===========================
>> typedef itk::Rigid3DTransform<double> RigidTransformType;
>> typedef itk::VersorRigid3DTransform<double> VersorTransformType;
>> 
>> VersorTransformType::Pointer
>> ConvertToVersorRigid3D(RigidTransformType::Pointer RT)
>> {
>>   VersorTransformType::Pointer VT=VersorTransformType::New();
>>   VT->SetFixedParameters(RT->GetFixedParameters());
>> 
>>   itk::Matrix<double,3,3> R=RT->GetRotationMatrix();
>>   RigidTransformType::TranslationType T=RT->GetTranslation();
>> 
>>   VersorTransformType::ParametersType p;
>>   p.SetSize(6);
>>   itk::Versor<double> v;
>>   v.Set(R);
>>   //Get the first 3 elements of the versor;
>>   p[0]=v.GetRight()[0];
>>   p[1]=v.GetRight()[1];
>>   p[2]=v.GetRight()[2];
>>   p[3]=T[0];
>>   p[4]=T[1];
>>   p[5]=T[2];
>>   VT->SetParameters(p);
>>   return VT;
>> }
>> 
>> 
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