Implement the photometric stereo technique described in the lecture. Your program should have two parts:

$$Read in the images and corresponding light source directions, and estimate the surface normals and albedo map.

$$Reconstruct the depth map from the surface with the implementation of the Horn integration technique given below in $`$horn$\_$integrate$`$ function. Note that you will typically want to run the $`$horn$\_$integrate$`$ function with $10000-100000$ iterations, meaning it will take a while.