How to decompose affine matrix to know rotation angle and translation?

I am using affine transformation in the function imregtform in Matlab. The output of the function tform.T gives an affine matrix. Affine matrix consists of translation, rotation, scale, and shear. In matlab affine matrix look like

translation would be e, and f. Now I want to decompose to find the rotation angle. But I don't know which order rotation, scale, and shear should be decomposed? Hence kindly recommend something.

Also if there is any easy way to find the rotation angle please suggest.

Answer 1

[Matt J]

This looks applicable:

https://math.stackexchange.com/questions/612006/decomposing-an-affine-transformation

[arindam mondal]

Thanks, but i am asking the order by which i can decompose the matrix. It means to say which order Matlab combine the shear, scale, and rotation.

[Matt J]

I don't believe imregtform uses a decomposed model to estimate the tform. It estimates a,b,c,d directly.

Regardless, whatever decomposition imregtform uses there is no requirement that you have to work with the same decomposition. Since you are given the final tform, you can decompose any way you wish.

[arindam mondal]

But different way of decomposition gives different rotation angle is it not true?

[Matt J]

Yes, it's true, but what does it matter?