$3.$ Affine Motion $(4$ points$)$ Suppose that displacement of each pixel satisfies an affine model in Equation $5.[$x$+$uy$+$v$]=[$A$11$A$21$A$12$A$22][$xy$]+[$b$1$b$2]$ Then as for optical flow estimation, we only need to estimate the parameters for the affine model. We let each pixel contribute equally to the parameter estimation. That is to say: $1)$ all the pixels are involved in the estimation; $2)$ the weight for each pixel equals to $1.$ Question $3\mathrm{.}1$: Please derive a closed$-$form solution for estimating the parameters. $($Recall the derivation of the linear models for estimating the displacement of each pixel.$)$ Question $3\mathrm{.}2$: Given two images I$1$ and I$2$ in Figure $1,$ please use your derivation to estimate the parameters of their affine model. $($Give the equation and the numeric values of the parameters.$)$