How do I determine the angle, scale and translation between two images after imregister?

I have one rotated, scaled, translated image and a fixed image. The output of imregister, t is shown:

[movingregistered] = imregister(fixed,moving,'similarity',optimizer,metric,'DisplayOptimization',1);

t = [1.001092e+00    -6.373544e-04   0.000000e+00;...
     6.373544e-04    1.001092e+00    0.000000e+00;...
     -1.351965e+00   5.672809e-01    1.000000e+00];

I need accurate subpixel knowledge of the offset and rotation of two images. Is t rotated about center pixel or upper left pixel (1,1). It is not sufficient to show the images "look" registered :) Using R2012B

What is the definition of the 9 elements of t?

Thanks, Howard

[Matt J]

Your code doesn't show how t was produced. It appears nowhere in your call to imregister. Did you call imregister with a 2nd output arg that you aren't showing?

Answer 1

[Sean de Wolski]

You can use imregtform to get the transformation matrix:

doc imregtform

[Matt J]

The OP is using R2012B, which does not include imregtform. :-(

But it's great to discover that the issue is fixed in R2013!

[Sean de Wolski]

Ah!

Well, good reason to upgrade :)

[Matt J]

Well, if I could allow myself to vent for just a moment, I really think they should back-patch this into R2012 or whenever imregister was introduced. A registration routine without the ability to return the transformation parameters is like a 3-wheeled car.

[Sean de Wolski]

@Matt J: http://www.3wheelers.com/

You can go into imregister and add the transformation matrix as an output.

[Matt J]

You can go into imregister and add the transformation matrix as an output.

That was easier than I thought!

[Matt J]

Actually, not so easy. The toolbox installs with permission barriers on imregister and its directory. I guess I could de-activate those, but I would have prefered to make my own separate local copy. No good, though, because imregister relies on private directory files.

[Sean de Wolski]

You could make a local copy in that directory. That way it has access to the private files.

[Matt J]

yes, I've done that now. I'm vaguely nervous, though, about tampering with factory-installed MATLAB directories. I'll be happier once I've upgraded to a version with imregtform!

Answer 2

[Matt J]

Is t rotated about center pixel or upper left pixel (1,1).

After some experimentation with code (below) that duplicates the relevant portions of IMREGISTER, I think I can safely say that the rotation is about the upper left pixel.

    M=100;N=M;

    A=zeros(M);
      A(1:M+1:50*(M+1))=1;

      %30 degree rotation
      t=[    0.8660   -0.5000         0
             0.5000    0.8660         0
               0         0    1.0000];

    B = imtransform(A, maketform('affine',t), 'XData', [1 N], 'YData', [1 M], ...
       'Size', [M N]);

    figure;imagesc(A)
    figure; imagesc(B+A)

Answer 3

[Howard]

If I use imtransform and then imregister I get transform matrix t which do not agree. What's up with that?

    M=100;N=M;    A=zeros(M);
    A(1:M+1:50*(M+1))=1;      %
    t=[    1.0   0         0
           0    1.0         0
         1.1     0    1.0000];    
    B = imtransform(A, maketform('affine',t), 'XData', [1 N], 'YData', [1 M], ...
         'Size', [M N]);    
    figure; imagesc(B+A)
    fixed = A;
    moving = B;
     [optimizer,metric] = imregconfig('monomodal');   %try monomodal
     [movingregistered] = imregister(fixed,moving,'similarity',optimizer,metric,'DisplayOptimization',1, 'PyramidLevels',3);

But the output of imregister has a very different transform with cos values > 1.0

Use the resulting tform struct with imtransform.

t = [1.010712e+00    7.025940e-04    0.000000e+00;...
     -7.025940e-04   1.010712e+00    0.000000e+00;...
     1.817039e-01    -9.390789e-01   1.000000e+00];

[Matt J]

This seems like a different question than what you originally posted. First, please confirm whether that question is still open. I thought I provided pretty convincing evidence that the rotation was about the upper left corner. If you agree, please Accept-click that answer and start a new question. If you don't agree, please explain why the question is unanswered.