They are optical flow implementations by Lucas-Kanade and Horn–Schunck respectively. You will see three different methods to implement optical flow by LK and HS. The file old_HS is a method using oritnal HS idea (with iteration),see paper: https://dspace.mit.edu/handle/1721.1/6337 The file New_HS which dosen't use iterations but compute u,v directly. Two HS implementations have same theories.

By the way,perhaps,there are some small bugs, when u wanna use them, please check. If you have any problem about this code, please feel free to contact me. Thanks.