KLT Tracking: Assume that the image in problem $2(I^0)$ comes from a video sequence and yields an

initial feature detection at the center pixel: $(x,y)=(4,4).$ Use the KLT tracking algorithm to

determine the feature location in the "next" frame given as:

$J^0=\left[\begin{array}{ccccccc}0& 5& 10& 10& 10& 10& 10\\ 0& 5& 10& 10& 10& 10& 10\\ 1& 5& 10& 20& 21& 20& 20\\ 0& 5& 10& 20& 39& 40& 40\\ 1& 5& 10& 20& 39& 200& 199\\ 1& 5& 10& 20& 40& 197& 197\\ 1& 5& 10& 20& 40& 200& 200\end{array}\right]$

a$)$ Using an integration window of $33$ pixels and no image pyramid $($i$.$e$.,$ only original images: $I^0$

and $J^0),$ compute the estimated location of the tracked feature

b$)$ Using an integration window of $33$ pixels and an image pyramid of depth $2($i$.$e$.,$ original images

and down$-$sampled image by factor of $2).$ The down$-$sampled images are provided below for

convenience.

$I^1=\left[\begin{array}{cccc}20& 20& 20& 20\\ 20& 200& 200& 200\\ 20& 200& 200& 200\\ 20& 200& 200& 200\end{array}\right],J^1=\left[\begin{array}{cccc}5& 10& 10& 10\\ 5& 20& 40& 40\\ 5& 20& 197& 197\\ 5& 20& 200& 200\end{array}\right]$