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

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GURAY SONUGUR on 5 Feb 2020
Edited: Matt J on 5 Feb 2020
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?

Accepted Answer

Matt J
Matt J on 5 Feb 2020
Edited: Matt J on 5 Feb 2020
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.

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