Optical Flow, Lucas Kanade in Python

Following is the Lucas Kanade optical flow algorithm in Python. We used it successfully on two png images, as well as through OpenCV to follow a point in successive frames. More details are at Github.

import numpy as np
import scipy.signal as si
from PIL import Image

def gauss_kern():
   h1 = 15
   h2 = 15
   x, y = np.mgrid[0:h2, 0:h1]
   x = x-h2/2
   y = y-h1/2
   sigma = 1.5
   g = np.exp( -( x**2 + y**2 ) / (2*sigma**2) );
   return g / g.sum()

def deriv(im1, im2):
   g = gauss_kern()
   Img_smooth = si.convolve(im1,g,mode='same')
   fx,fy=np.gradient(Img_smooth)  
   ft = si.convolve2d(im1, 0.25 * np.ones((2,2))) + \
       si.convolve2d(im2, -0.25 * np.ones((2,2)))
                 
   fx = fx[0:fx.shape[0]-1, 0:fx.shape[1]-1]  
   fy = fy[0:fy.shape[0]-1, 0:fy.shape[1]-1];
   ft = ft[0:ft.shape[0]-1, 0:ft.shape[1]-1];
   return fx, fy, ft

import matplotlib.pyplot as plt
import numpy as np
import scipy.signal as si
from PIL import Image
import deriv
import numpy.linalg as lin

def lk(im1, im2, i, j, window_size) :
   fx, fy, ft = deriv.deriv(im1, im2)
   halfWindow = np.floor(window_size/2)
   curFx = fx[i-halfWindow-1:i+halfWindow,
              j-halfWindow-1:j+halfWindow]
   curFy = fy[i-halfWindow-1:i+halfWindow,
              j-halfWindow-1:j+halfWindow]
   curFt = ft[i-halfWindow-1:i+halfWindow,
              j-halfWindow-1:j+halfWindow]
   curFx = curFx.T
   curFy = curFy.T
   curFt = curFt.T

   curFx = curFx.flatten(order='F')
   curFy = curFy.flatten(order='F')
   curFt = -curFt.flatten(order='F')
 
   A = np.vstack((curFx, curFy)).T
   U = np.dot(np.dot(lin.pinv(np.dot(A.T,A)),A.T),curFt)
   return U[0], U[1]