[Insight-users] Rigid3DTransform error Attempting to set a non-orthogonal rotation matrix
Karthik Krishnan
karthik.krishnan at kitware.com
Fri Feb 13 13:11:17 EST 2009
Two points:
1. The Amoeba optimizer, (nor any other optimizer except the
VersorRigid3DTransformOptimizer) does not re-orthogonalize the transform
after every iteration. It simply wobbles using the Neadler mead simplex
algorithm on an array of 12 parameters in your case. The scales help a bit
here, if they are acute enough for instance 1:1000 etc.
2. Why not optimize fewer parameters when you can. (Hint: Use the Versor
transform, with has 6 parameters). I would understand your argument for
using 3x3 matrix, if were to have different scales for the shear components,
or if you needed scaling etc... but your scales aren't different.
On Fri, Feb 13, 2009 at 4:57 AM, Matthias Keil <
matthias.keil at igd.fraunhofer.de> wrote:
> Hi Luis, and all other list members,
>
> sorry for making my point a bit unclear. By saying:
>
> I am using the following parameter values for Rigid3DTransform:
> - first 9 rotation parameters are set to 0.1
> - the three translation parameters are set to 0.001
>
> And the simplex delta parameter values for the optimizer:
> - first 9 values set to 5
> - the last 3 values set to 0 (as there is no translation)
>
> I did not mean that I am constructing a rotation matrix in the format you
> proposed:
>
> When you set the first 9 parameters of the transform to 0.1
> you are construction a rotation Matrix:
>
> 0.1 0.1 0.1
> 0.1 0.1 0.1
> 0.1 0.1 0.1
>
> What I was actually trying to say is that I am initializing the optimizer
> scales of the Rigid3DTransform in the way I mentioned above. I am using the
> Amoeba optimizer to create the actual rotation matrix in all iterations.
> E.g. the rotation matrix computed by Amoeba that is to be applied in the
> first iteration and which fails the orthogonality test is:
>
> 1.0 0.0 0.0
> 0.0 0.996194*72026824951* 0.0871557*36982822418*
> 0.0 -0.0871557*22081661224* 0.996194*72026824951*
>
> This is supposed to be a -5 degree rotation about the x-axis (the first
> step of the Amoeba optimizer). The corresponding rotation matrix should
> actually look like this (I highlighted the differences in the matrix
> elements calculated by Amoeba and by hand):
>
> 1.0 0.0 0.0
> 0.0 0.996194*69809174555* 0.0871557*42747658180*
> 0.0 -0.0871557*42747658180* 0.996194*69809174555*
>
> Please do note especially the difference between the sin(alpha) at column 3
> row 2 and -sin(alpha) at row 3 column 2 in the rotation matrix computed by
> Amoeba.
> This difference is one reason why the matrix resulting from multiplying the
> rotation matrix with its transposed matrix looks like this:
>
> 1.0 0.0 0.0
> 0.0 1.0000000431793548 1.4844458107177161e-008
> 0.0 1.4844458107177161e-008 1.0000000405819116
>
> Comparing this matrix to the identity matrix causes the orthogonality test
> to fail.
>
> The question is now:
> Why do I get a non-orthogonal rotation matrix from the Amoeba optimizer?
>
> If you don't now how to initialize a rotation matrix, then
> you should at least use the Transform Initializer class
>
> Thanks for the hint, I will have a look at it. Although I am not setting
> the transformation by hand but using the Amoeba optimizer instead, as
> mentioned above.
>
> Another potential way of producing a consistent
> rotation matrix is to use an itkVersor, set its axis
> and rotation angle, and then extracts its Matrix.
>
> This would also be a possibility but I think that my scenario using the
> Amoeba optimzer should also work, right?
>
> Best regards,
> Matthias
> Luis Ibanez schrieb:
>
>
> Hi Mathias,
>
> A rigid transform necessarily requires an Orthogonal matrix.
>
>
> If you try to force a non-othogonal matrix into the transform,
> then the transformation will contain Scaling and Shearing
> effect, which is something that a Rigid Transform shouldn't
> include.
>
> The Rigid Transform class is correctly rejecting your Matrix
> as an inappropriate input.
>
>
> When you set the first 9 parameters of the transform to 0.1
> you are construction a rotation Matrix:
>
> 0.1 0.1 0.1
> 0.1 0.1 0.1
> 0.1 0.1 0.1
>
> that is obviously non-orthogonal, and therefore
> it can not be a valid representation of a rotation
> in 3D space.
>
>
> If you don't now how to initialize a rotation matrix, then
> you should at least use the Transform Initializer class, as
> it is illustrated in the examples:
>
>
> Insight/Examples/Registration/
> ImageRegistration12.cxx
> ImageRegistration13.cxx
> ImageRegistration14.cxx
> ImageRegistration6.cxx
> ImageRegistration6o.cxx
> ImageRegistration7.cxx
> ImageRegistration7o.cxx
> ImageRegistration8.cxx
> ImageRegistration9.cxx
> MultiResImageRegistration2.cxx
>
>
>
> Another potential way of producing a consistent
> rotation matrix is to use an itkVersor, set its axis
> and rotation angle, and then extracts its Matrix.
>
>
>
> Regards,
>
>
>
> Luis
>
>
> ---------------------
> Matthias Keil wrote:
>
> Hello,
>
> with regards to this e-mail to the mailing list which unfortunately did not
> get any feedback:
>
>
> http://www.nabble.com/funning-observation-regarding-SetMatrix%28%29-in-VersorRigid3DTransform-class--tp20409801p20409801.html
>
> I am writing to the mailing list hoping to get some more insight into the
> problem.
>
> Using Rigid3DTransform and the Amoeba optimizer for registration of 2
> volumes (one was manually rotated by 5 degrees around the x axis) seems to
> be quite challenging to me. Unfortunately I can't initialize my registration
> in a way which makes it compute any iterations. I do get the error
> "Attempting to set a non-orthogonal rotation matrix" mentioned in the
> subject everytime. As pinpress guessed right, there is a test for the
> identity matrix.
>
> My guess is that in ITK library somewhere, there is a check (e.g., to check
>
> if determinant of the matrix is exactly 1, because it is a "rigid"
> transform), but the tolerance is not set properly which caused the problem
> that I experience.
>
>
> This test is implemented in itkRigid3DTransform.txx line 77.
>
> I am using the following parameter values for Rigid3DTransform:
> - first 9 rotation parameters are set to 0.1
> - the three translation parameters are set to 0.001
>
> And the simplex delta parameter values for the optimizer:
> - first 9 values set to 5
> - the last 3 values set to 0 (as there is no translation)
>
> My question is now as pinpress already asked
>
> However, is such checking necessary?
>
>
> Thanks in advance for any help,
> Matthias
>
> --
> | Dipl.-Ing. Matthias Keil
> |
> | Fraunhofer Institute for Computer Graphics (IGD)
> | Cognitive Computing & Medical Imaging
> | Fraunhoferstraße 5, 64283 Darmstadt, Germany
> |
> | phone : +49 6151 155 212
> | fax : +49 6151 155 480
> | mobile : +49 173 5709746
> | e-mail : matthias.keil at igd.fraunhofer.de
> | skype : matthias.keil.office
> | web : http://www.igd.fraunhofer.de/~makeil<http://www.igd.fraunhofer.de/%7Emakeil>
>
>
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>
> --
> | Dipl.-Ing. Matthias Keil
> |
> | Fraunhofer Institute for Computer Graphics (IGD)
> | Cognitive Computing & Medical Imaging
> | Fraunhoferstraße 5, 64283 Darmstadt, Germany
> |
> | phone : +49 6151 155 212
> | fax : +49 6151 155 480
> | mobile : +49 173 5709746
> | e-mail : matthias.keil at igd.fraunhofer.de
> | skype : matthias.keil.office
> | web : http://www.igd.fraunhofer.de/~makeil <http://www.igd.fraunhofer.de/%7Emakeil>
>
>
> _____________________________________
> Powered by www.kitware.com
>
> Visit other Kitware open-source projects at
> http://www.kitware.com/opensource/opensource.html
>
> Please keep messages on-topic and check the ITK FAQ at:
> http://www.itk.org/Wiki/ITK_FAQ
>
> Follow this link to subscribe/unsubscribe:
> http://www.itk.org/mailman/listinfo/insight-users
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>
--
Karthik Krishnan
R&D Engineer,
Kitware Inc.
Ph: 518 371 3971 x119
Fax: 518 371 3971
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