OPTICAL FLOW

You will compute the optical flow between frames $$frame$\_0037.$png$$ and $$frame$\_0038.$png$$:

Read the images. Convert them to gray scale. Scale the values to be in the range $[0,1],$ by dividing the gray scale values by $255.$

Write a function $[$u$,$ v$]=$ optical$\_$flow$($I$1,$I$2,$window$\_$size,eig$\_$thr$)$ that implements Lucas$-$Kanade optical flow algorithm. The input will be a pair of images and the output will be an optical flow field $($u$,$ v$).$

Here, u and v are the components of the optical flow. window$\_$size is the length of the side of the window you will use for optical flow computation. eig$\_$thr is the threshold such that if it is larger than the smallest value of $,$ then the optical flow at that position will not be estimated $($set to be equal to $(0,0).)$

Run the code for window$\_$size $=5,7,9.$ Plot the resulting vector field of the optical flow algorithm on top of the first image for each window$\_$size. You can set eig$\_$thr to $0\mathrm{.}01.$

Comment on your observations.

If you code with MATLAB, you can use the following functions:

The matlab command imgradientxy will compute Ix and Iy of an image:

$[$Ix Iy$]=$ imgradientxy$($I$)$;

For computing weighted aggregates, you can use:

H $=$ fspecial$(\text{'}$gaussian$\text{'},[55],$sigma$)$;

Iout $=$ imfilter$($Iin$,$H$,$'same'$)$;

Use the function quiver to plot the vector field $($u$,$v$).$