[Insight-users] Centered Affine Transform
Luis Ibanez
luis.ibanez at kitware.com
Tue Jul 20 01:14:57 EDT 2004
Hi Lucas,
You seem to exhibit the symptoms of
"CRSCS"
Also known as
"Coordinate Reference System Confusion Syndrome" :-)
Here are some questions for
further verification of the diagnosis:
1) Are you representing your object as a region in an image ?
2) Are you applying a transform to this object by resampling
the image using the itkResampleImageFilter, connecting
the CenteredAffineTransform and extracting the output image ?
3) Are you often under the impresion that objects in the
image move in the oposite direction to what you expect ?
If so, the source of your confusion may be originated on
the fact that the ResampleImage filter visit points from
the Output image space and map them into the input image
space. That makes that if you provide a transform with
a translation with *positive* values in X and Y, then in
the resampled image, your object seems to have moved in
the *negative* direction in X and Y. In other words, the
transform does not describe the movement of objects, it
describes the movements of the coordinate system frame.
The most effective treatment against "CRSCS" is the
following procedure:
1) Find a quite place, away from any source of distraction.
2) Ingest a moderate amount of coffee.
3) Read from the ITK Software Guide the following section
Chapter 6, Section 6.7 "Geometric Transformation"
pdf-pages 199-218.
4) Perform the excercises in this section. The source
code will be found in the directory
Insight/Examples/Filtering
Please let us know if you have further questions,
Thanks
Luis
----------------------
Lucas Lorenzo wrote:
> Hi Luis,
>
>>
>> Hi Lucas,
>>
>> Please post numbers :-)
>
>
> My original object is center is located at point (175 mm ; 168 mm). So
> that's the center of rotation.
>
>>
> a) For translation I'm using (43.54 mm , -17.81 mm). If for rotation I
> use a matrix [1 0 ; 0 1] then the result is as I expect: the object is
> only translated and the new object center is now at (134.77 mm ; 188.20
> mm). Please, take into account that my object has an irregular shape so
> the coordinates aren't 100 % precise. But this results don't match the
> equation you've posted bellow. Let's do it for the new x coordinate of
> the center:
>
> x' = 1 * (x - Cx) + (Tx + Cx) = 1 * (43.54 - 43.54) + (175 + 43.54)
> = 218.54 mm
>
> where Cx is the original x coordinate for the center and Tx is the x
> component of the translation vector.
>
> b) If instead of using the translation vector specified before I use its
> negative (- 43.54 mm , 17.81 mm) then the equation makes sense, but now
> the results are not what I expect. Now the new center is 218.54 mm
> instead of 131.46 mm.
>
> c) if for rotation I use a matrix [0 -1 ; 1 0] (we are rotating the
> image 90 degrees) around center (174.765 mm, 175.242 mm) and I use a
> translation vector of (43.5537 mm, -17.8095 mm), then the object is
> rotated according to what I expect but the new center is translated to
> location (218.54 mm , 152 mm).
> If I apply the equations then the new center will be at (218.3187 mm ,
> 157.4325 mm).
>
> d) if for rotation I use a matrix [0 -1 ; 1 0] (we are rotating the
> image 90 degrees) around center (183.42 mm, 176.236 mm) and I use a
> translation vector of (-44.1889 mm, 17.5775 mm), then the object is
> rotated according to what I expect but the new center is translated to
> location (156.93 mm , 143.67 mm).
> If I apply the equations then the new center will be at (139.24 mm ,
> 193.8 mm).
>
>
> Again I have to be doing something wrong.
>
> Thanks for your help,
>
> Lucas
>
>
>
>> What are the coordinates of the center of the object ?
>> What is the translation that you are applyng ?
>>
>>
>> TheCenteredAffineTransform transforms a point P into
>> a point P' by using the following expression
>>
>>
>> P' = R * ( P - C ) + ( T + C )
>>
>> In dimension N: C is a N dimensional point with
>> the coordinates of the center of rotation, P is
>> the N dimensional point to be transformed, P' is
>> the resulting N dimensional point, T is the N
>> dimensional translation Vector.
>>
>>
>> Regards,
>>
>>
>>
>> Luis
>>
>>
>>
>> ----------------------
>> Lucas Lorenzo wrote:
>>
>>> Hi Luis,
>>> I'm selecting the spatial coordinates of the center of the object I'm
>>> interested in.
>>> Lucas
>>> On Jul 16, 2004, at 5:06 PM, Luis Ibanez wrote:
>>>
>>>> Hi Lucas,
>>>>
>>>>
>>>> What center of rotation did you selected ?
>>>>
>>>> Luis
>>>>
>>>>
>>>> ---------------------
>>>> Lucas Lorenzo wrote:
>>>>
>>>>> Hi Luis,
>>>>> I've been running some tests so as to understand a little bit
>>>>> better what's this transform doing and it is clear to me now that
>>>>> it is applying the translation first and then it is rotating the
>>>>> translated image with respect to the specified center of rotation.
>>>>> My understanding is that it should perform these operations but in
>>>>> reverse order.
>>>>> Please let me know if this is wrong.
>>>>> Thanks,
>>>>> Lucas
>>>>> On Jul 16, 2004, at 2:14 PM, Lucas Lorenzo wrote:
>>>>>
>>>>>> Hi Luis,
>>>>>>
>>>>>> thanks for your feedback.
>>>>>>
>>>>>> 1) Till now the way I was setting the parameters was using the
>>>>>> m_Transform->SetParameters(m_TransformParameters);
>>>>>>
>>>>>> 2) I have a 2D image so my understanding is that I'm going to have
>>>>>> 8 parameters for this transformation where the first 4 parameters
>>>>>> define the rotation, shear, and scaling; the next two define the
>>>>>> center of rotation and the last two define the translation to be
>>>>>> applied with respect to the center of rotation (after the image
>>>>>> has been rotated).
>>>>>>
>>>>>> Please, let me know where am I making a mistake.
>>>>>>
>>>>>> Thanks,
>>>>>>
>>>>>> Lucas
>>>>>>
>>>>>>
>>>>>> On Jul 16, 2004, at 1:17 PM, Luis Ibanez wrote:
>>>>>>
>>>>>>>
>>>>>>> Hi Lucas,
>>>>>>>
>>>>>>> It is likely that you are misinterpreting
>>>>>>> the encoding of the parameters in this
>>>>>>> transform.
>>>>>>>
>>>>>>> Please post the values of the parameters
>>>>>>> that you are providing, and post also
>>>>>>> what you are expecting to be the effect.
>>>>>>>
>>>>>>> Note that you have:
>>>>>>>
>>>>>>> - Center of rotation
>>>>>>> - Translation
>>>>>>> - Offset
>>>>>>> - Rotation matrix
>>>>>>>
>>>>>>>
>>>>>>> When you use this transform you should only
>>>>>>> care about SetCenter(), SetTranlation() and
>>>>>>> Rotation. Never touch the Offset directly.
>>>>>>>
>>>>>>>
>>>>>>> A code snippet illustrating the calls that
>>>>>>> you are making on the transform will also
>>>>>>> be very useful....
>>>>>>>
>>>>>>>
>>>>>>> Thanks
>>>>>>>
>>>>>>>
>>>>>>> Luis
>>>>>>>
>>>>>>>
>>>>>>> ----------------------
>>>>>>> Lucas Lorenzo wrote:
>>>>>>>
>>>>>>>> Hi Gavin,
>>>>>>>> thanks a lot for your answer.
>>>>>>>> I'm setting the parameters using
>>>>>>>> m_Transform->SetParameters(m_TransformParameters);
>>>>>>>> So, afterwards I'm adding
>>>>>>>> m_Transform->ComputeOffset();
>>>>>>>> But still the results are not as expected (after rotation the
>>>>>>>> object is not been translated to the desired location). Is
>>>>>>>> there anything wrong in what I'm doing ?
>>>>>>>> Thanks,
>>>>>>>> Lucas
>>>>>>>> On Jul 15, 2004, at 10:07 PM, Gavin Baker wrote:
>>>>>>>>
>>>>>>>>>
>>>>>>>>> Hi Lucas,
>>>>>>>>>
>>>>>>>>> On Thu, Jul 15, 2004 at 06:01:26PM -0600, Lucas Lorenzo wrote:
>>>>>>>>>
>>>>>>>>>> I'm trying to use a Centered Affine Transform. So first I'm
>>>>>>>>>> taking a
>>>>>>>>>> look at the following example:
>>>>>>>>>>
>>>>>>>>>> Examples/Registration/ImageRegistration9.cxx.
>>>>>>>>>>
>>>>>>>>>> I'm a little bit confused on how to use the ComputeOffset()
>>>>>>>>>> method
>>>>>>>>>> because I don't see where it is been used in this example and
>>>>>>>>>> when
>>>>>>>>>> reading the online documentation my understanding is that it is
>>>>>>>>>> mandatory to use this particular method.
>>>>>>>>>>
>>>>>>>>>> Could anyone please help me to get a better understanding on
>>>>>>>>>> this issue
>>>>>>>>>> ?
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> When using the centered affine transform, there is an implicit
>>>>>>>>> translation
>>>>>>>>> due to the center. The offset takes into account the affect of
>>>>>>>>> any
>>>>>>>>> rotations you specify on this center, to give a new
>>>>>>>>> translation. The
>>>>>>>>> ComputeOffset() method recalcuates this offset (which need only
>>>>>>>>> be done
>>>>>>>>> once), and needs to be updated before applying the transform.
>>>>>>>>>
>>>>>>>>> This was discussed a while ago:
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> http://public.kitware.com/pipermail/insight-users/2003-October/
>>>>>>>>> 005230.html
>>>>>>>>>
>>>>>>>>> http://public.kitware.com/pipermail/insight-users/2003-October/
>>>>>>>>> 005272.html
>>>>>>>>>
>>>>>>>>>> From the comments at the top of ImageRegistration9.cxx (from
>>>>>>>>>> the Software
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Guide) show:
>>>>>>>>>
>>>>>>>>> // Note that the final total offset of
>>>>>>>>> the transform
>>>>>>>>> // is to be computed as a combination of the shift due
>>>>>>>>> rotation plus the
>>>>>>>>> // explicit translation set on the transform.
>>>>>>>>> //
>>>>>>>>>
>>>>>>>>> General usage would be:
>>>>>>>>>
>>>>>>>>> xform->Translate( delta );
>>>>>>>>> xform->Rotate( theta );
>>>>>>>>> // ...
>>>>>>>>> xform->ComputeOffset();
>>>>>>>>>
>>>>>>>>> resample->Update();
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> ComputeOffset() is actually called explicitly in all the
>>>>>>>>> CenteredAffineTransform methods that affect the transform, but
>>>>>>>>> (obviously)
>>>>>>>>> not any AffineTransform methods. It isn't called automagically
>>>>>>>>> (after each
>>>>>>>>> change) since it only needs to be done once, although it
>>>>>>>>> probably wouldn't
>>>>>>>>> hurt if it were.
>>>>>>>>>
>>>>>>>>> :: Gavin
>>>>>>>>>
>>>>>>>>> --
>>>>>>>>> Gavin Baker Complex
>>>>>>>>> Systems Group
>>>>>>>>> http://www.cs.mu.oz.au/~gavinb The University of
>>>>>>>>> Melbourne
>>>>>>>>> _______________________________________________
>>>>>>>>> Insight-users mailing list
>>>>>>>>> Insight-users at itk.org
>>>>>>>>> http://www.itk.org/mailman/listinfo/insight-users
>>>>>>>>>
>>>>>>>> Lucas Lorenzo
>>>>>>>> University of Utah
>>>>>>>> Nora Eccles Harrison CardioVascular Research and Training Institute
>>>>>>>> Fellows Room
>>>>>>>> 95 South 2000 East
>>>>>>>> Salt Lake City, UT 84112-5000
>>>>>>>> e-mail: lucas at cvrti.utah.edu
>>>>>>>> telephone: 801-587-9536
>>>>>>>> _______________________________________________
>>>>>>>> Insight-users mailing list
>>>>>>>> Insight-users at itk.org
>>>>>>>> http://www.itk.org/mailman/listinfo/insight-users
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>> Lucas Lorenzo
>>>>>>
>>>>>> University of Utah
>>>>>> Nora Eccles Harrison CardioVascular Research and Training Institute
>>>>>> Fellows Room
>>>>>> 95 South 2000 East
>>>>>> Salt Lake City, UT 84112-5000
>>>>>>
>>>>>> e-mail: lucas at cvrti.utah.edu
>>>>>> telephone: 801-587-9536
>>>>>>
>>>>>>
>>>>> Lucas Lorenzo
>>>>> University of Utah
>>>>> Nora Eccles Harrison CardioVascular Research and Training Institute
>>>>> Fellows Room
>>>>> 95 South 2000 East
>>>>> Salt Lake City, UT 84112-5000
>>>>> e-mail: lucas at cvrti.utah.edu
>>>>> telephone: 801-587-9536
>>>>
>>>>
>>>>
>>>>
>>>>
>>>>
>>> Lucas Lorenzo
>>> University of Utah
>>> Nora Eccles Harrison CardioVascular Research and Training Institute
>>> Fellows Room
>>> 95 South 2000 East
>>> Salt Lake City, UT 84112-5000
>>> e-mail: lucas at cvrti.utah.edu
>>> telephone: 801-587-9536
>>> _______________________________________________
>>> Insight-users mailing list
>>> Insight-users at itk.org
>>> http://www.itk.org/mailman/listinfo/insight-users
>>
>>
>>
>>
>> _______________________________________________
>> Insight-users mailing list
>> Insight-users at itk.org
>> http://www.itk.org/mailman/listinfo/insight-users
>>
> Lucas Lorenzo
>
> University of Utah
> Nora Eccles Harrison CardioVascular Research and Training Institute
> Fellows Room
> 95 South 2000 East
> Salt Lake City, UT 84112-5000
>
> e-mail: lucas at cvrti.utah.edu
> telephone: 801-587-9536
>
>
More information about the Insight-users
mailing list