[Insight-developers] ImageRegistration9

[Luis Ibanez]

Hi Gunnar,

Thanks for your detailed report.

You are right, the current output of this example
differs now from what ikt was at the time the
comments where written for the Software Guide.

Please log this as a bug in the database, you may
want to specify that it is a "documentation" bug.

I agree with you in that SVD is a better way of
estimating the rotation angle. The way to go is
to include your VNL lines for angle estimation
into the example itself. This will certainly be
useful to other users.

We will update the comments accordingly for the next
edition of the Software Guide (as you probably know,
the Software Guide is for the most part, generated
out of the C++ comments in the Examples).


Please let us know if you encounter any other
inconsistency.


Thanks,


    Luis


------------------------
Gunnar Farneback wrote:
> A few questions and notes about
> Examples/Registration/ImageRegistration9.
> 
> 1. The comments about testing it on two images say:
> 
>   //  The second image is the result of intentionally rotating the first
>   //  image by $10$ degrees and then translating by $(-13,-17)$.  Both images
>   //  have unit-spacing and are shown in Figure
>   //  \ref{fig:FixedMovingImageRegistration9}. We execute the code using the
>   //  following parameters: step length=1.0, translation scale= 0.0001 and
>   //  maximum number of iterations = 300. With these images and parameters
>   //  the registration takes $240$ iterations and produces
>   //
>   //  \begin{center}
>   //  \begin{verbatim}
>   //   239 44.3138   
>   //  [0.984935, -0.172989, 0.172608, 0.984926, 
>   //    123.249, 147.12, 9.58612, 17.9202]
>   //  \end{verbatim}
>   //  \end{center}
> 
> I can't quite reproduce this. With default parameter settings I end
> with
> 
> 237   50.7402   [0.986115, -0.170693, 0.168981, 0.985808, 111.202, 131.578, 12.4614, 16.0768]
> 
> which is close but the difference is larger than I would expect from
> pure numerical variations. These numbers also seem to agree with a
> random Dashboard I checked.
> 
> If I instead use the parameters indicated in the text I don't even get
> close to the expected values.
> 
> Am I doing something wrong or has something changed since the
> comments were written?
> 
> 2. Later in the code there is a comment:
> 
>   //  The second component of the matrix values is usually associated with
>   //  $\sin{\theta}$.
> 
> This is only valid if there's no significant scaling in the transform.
> On the other hand it's not difficult to compute the rotation angle and
> scaling parameters properly from the singular value decomposition of
> the matrix, like this:
> 
>   vnl_matrix<double> p(2, 2);
>   p[0][0] = (double) finalParameters[0];
>   p[0][1] = (double) finalParameters[1];
>   p[1][0] = (double) finalParameters[2];
>   p[1][1] = (double) finalParameters[3];
>   vnl_svd<double> svd(p);
>   vnl_matrix<double> r(2, 2);
>   r = svd.U() * vnl_transpose(svd.V());
>   double angle = asin(r[1][0]);
>   
>   std::cout << " Scale 1         = " << svd.W(0)                 << std::endl;
>   std::cout << " Scale 2         = " << svd.W(1)                 << std::endl;
>   std::cout << " Angle (radians) = " << angle                    << std::endl;
>   std::cout << " Angle (degrees) = " << angle * 45.0 / atan(1.0) << std::endl;
> 
> Unless someone thinks it's a bad idea to add this information to the
> final output, I'll add a complete patch to the bug tracker.
> 
> 3. Using the code above the affine parameters I get compute to a
>    rotation of 9.77 degrees and scaling parameters 1.00135 and
>    0.999613. The rotation angle doesn't look quite as impressive as
>    the one in the code comments:
> 
>   // In this case the value $0.1729$ corresponds to a rotation 
>   //  of $9.95$ degrees, which is approximately the intentional misalignment of 
>   //  $10.0$ degrees.
> 
> /Gunnar
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