MATLAB: What are the different elements of the imregtform matrix T

image processingimage registrationimage transformationimregtformMATLAB

I am looking for a way to quantify the ease of producing well alligned images from a number of camera set ups, and I plan to take multiple 2D images and use the imregtform function to assess the scale of transformation required to allign the images to each other.
I am using the code below to get the afine2d "tformestimate" within which there is the matrix T
    [optimizer, metric] = imregconfig('monomodal')
    tformestimate = imregtform(moving, fixed, 'affine', optimizer, metric);
Having looked through the imregtform help section I am not clear on what the different elements of the 3×3 matrix T refer to for each of the transformation types.
Can anyone clarify for each of: 'translation' 'rigid' 'similarity' 'affine' what the 9 different matrix elements refer to?

Best Answer

I'm betting Image Analist will give a much more complete answer than I ever could, but here are my pointers.
The options you are referring to (translation, rigid etc) are restrictions on what the transformation may do. The transformation matrix shows how you can convert one coordinate grid to another. The essence is that [x_new;y_new;1]=T*[x_old;y_old;1];
Working out the parts of that matrix by hand will give you a hint at what they do. It is not so easy as just saying that one element is the rotation around the x-axis or something similar. You can look at the Wikipedia page for a lot more information.
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