MATLAB: Inconsistency in the definition of two geometric transformation matrices (tform)

Question

In image processing, when I looked at the literature, I realized that the geometric transformation matrix (tform) in many resources is defined as follows:

However, in Matlab, this matrix is defined as follows.

Which one is true? I can not calculate tx and ty values in combined tform matrices.

Can anyone help me?

Answer 1

The second form is the one expected by maketform. The only difference between the two conventions is that with the first, the transformation matrix transforms a column-vector by left-hand matrix multiplication, while with the second form, points are represented as row vectors and are transformed by right-hand matrix multiplication.