Corner$\_1)$ In the given image in $($Edge$\_1),$ three pixels are marked with bold. Two of the pixels is on the corner and on the edge while the other is on a plain region. For only these three pixels $($on the corner, on the edge and on plain$),$ solve below problems individually:

a$)$ By using central difference outputs $($in Edge$\_1-($a$)),$ find values in Harris corner detector's matrix $M$ for desired locations $($i$.$e$.$ corner, edge, plain$)$ where $M=\left[\begin{array}{cc}{I}_x^2**H& I_x{I}_y**H\\ I_x{I}_y**H& I_y^2**H\end{array}\right]$ and $I_x$ is $x-$derivative, $I_y$ is y$-$derivative

and $H$ is $33$ box filter, i$.$e$.H=\frac{1}{9}\left[\begin{array}{ccc}1& 1& 1\\ 1& 1& 1\\ 1& 1& 1\end{array}\right].$

b$)$ Using the matrix in $($a$),$ compute Eigen values ${}_1$ and ${}_2.$

c$)$ Using Eigen values in $($b$),$ compute Harris corner detector's R value. $($Choose $k=0\mathrm{.}04)$

i$)$ Solve $($a$),($b$),($c$)$ for the pixel on the corner.

ii$)$ Solve $($a$),($b$),($c$)$ for the pixel on the edge.

iii$)$ Solve $($a$),($b$),($c$)$ for the pixel on the plain.