|Date:||2017-04-05 (last modified), 2008-10-08 (created)|
A basic particle filter tracking algorithm, using a uniformly distributed step as motion model, and the initial target colour as determinant feature for the weighting function. This requires an approximately uniformly coloured object, which moves at a speed no larger than stepsize per frame.
This implementation assumes that the video stream is a sequence of numpy arrays, an iterator pointing to such a sequence or a generator generating one. The particle filter itself is a generator to allow for operating on real-time video streams.
#!python from numpy import * from numpy.random import * def resample(weights): n = len(weights) indices =  C = [0.] + [sum(weights[:i+1]) for i in range(n)] u0, j = random(), 0 for u in [(u0+i)/n for i in range(n)]: while u > C[j]: j+=1 indices.append(j-1) return indices def particlefilter(sequence, pos, stepsize, n): seq = iter(sequence) x = ones((n, 2), int) * pos # Initial position f0 = seq.next()[tuple(pos)] * ones(n) # Target colour model yield pos, x, ones(n)/n # Return expected position, particles and weights for im in seq: np.add(x, uniform(-stepsize, stepsize, x.shape), out=x, casting="unsafe") # Particle motion model: uniform step x = x.clip(zeros(2), array(im.shape)-1).astype(int) # Clip out-of-bounds particles f = im[tuple(x.T)] # Measure particle colours w = 1./(1. + (f0-f)**2) # Weight~ inverse quadratic colour distance w /= sum(w) # Normalize w yield sum(x.T*w, axis=1), x, w # Return expected position, particles and weights if 1./sum(w**2) < n/2.: # If particle cloud degenerate: x = x[resample(w),:] # Resample particles according to weights
The following code shows the tracker operating on a test sequence featuring a moving square against a uniform background.
#!python if __name__ == "__main__": from pylab import * from itertools import izip import time from IPython import display ion() seq = [ im for im in zeros((20,240,320), int)] # Create an image sequence of 20 frames long x0 = array([120, 160]) # Add a square with starting position x0 moving along trajectory xs xs = vstack((arange(20)*3, arange(20)*2)).T + x0 for t, x in enumerate(xs): xslice = slice(x-8, x+8) yslice = slice(x-8, x+8) seq[t][xslice, yslice] = 255 for im, p in izip(seq, particlefilter(seq, x0, 8, 100)): # Track the square through the sequence pos, xs, ws = p position_overlay = zeros_like(im) position_overlay[np.array(pos).astype(int)] = 1 particle_overlay = zeros_like(im) particle_overlay[tuple(xs.T)] = 1 draw() time.sleep(0.3) clf() # Causes flickering, but without the spy plots aren't overwritten imshow(im,cmap=cm.gray) # Plot the image spy(position_overlay, marker='.', color='b') # Plot the expected position spy(particle_overlay, marker=',', color='r') # Plot the particles display.clear_output(wait=True) display.display(show())
Section author: Unknown, BAlexRobinson, Kevin George