Affine Transformation
It is not necessarily affine. An affine matrix in homogeneous coordinates has a form like:

$$\begin{bmatrix} a_{11} &amp; a_{12} &amp; a_{13} \\ a_{21} &amp; a_{22} &amp; a_{23} \\ 0 &amp; 0 &amp; 1 \end{bmatrix}$$

(assuming you use a column vector convention). Here, the upper-left 2&times;2 submatrix is the linear part, and $(a_{13}, a_{23})$ is the translation vector of the affine transform.

If the lower row of the matrix has some values other than $[0, 0, 1]$, then it is in general a projective transform, not an affine one.