Derivative of affine transformation

Aug 2008
Hi there,

I've got a problem, which need to solve the derivative of affine transformation.

For example, a 2D affine transform is:

\(\displaystyle A_T(f_{x,y})=\left( \begin{array}{ccc}
a_{11} & a_{12} & a_{13} \\
a_{21} & a_{22} & a_{23} \\
0 & 0 & 1 \end{array} \right)
\left( \begin{array}{c}
x \\
y \\
1 \end{array} \right)=
\left( \begin{array}{c}
x^' \\
y^' \\
1 \end{array} \right)\)

Here we got \(\displaystyle a_{ij}\), which are 6 affine parameters. Then if we want to get the partial derivative of each parameter \(\displaystyle a_{ij}\), which is:

\(\displaystyle \frac{\partial A_T}{\partial a}\)

May I ask how to solve the equation above please? Thanks. (Rofl)