One way to reduce the false contour artefacts in thresholding (binary quantization) is to add uniformly distributed white noise to the input image prior to quantization. Specifically, to each input pixel of the grayscale image, f(x, y), we add an independent uniform [-128,128] random number, and then the thresholding is done. This technique is called half-toning. The following code block shows an implementation:

im = Image.open('../images/swans.jpg').convert('L')
im = Image.fromarray(np.clip(im + np.random.randint(-128, 128, (im.height, im.width)), 0, 255).astype(np.uint8))
pylab.figure(figsize=(12,18))
pylab.subplot(221), plot_image(im, 'original image (with noise)')
th = [0, 50, 100, 150, 200]
for i in range(2, 5):
    im1 = im.point(lambda x: x > th[i])
    pylab.subplot(2,2,i), plot_image(im1, 'binary image with threshold=' + str(th[i]))
pylab.show()

Notice that even though the resulting binary images are somewhat noisy, the false contouring has been dramatically reduced, and with enough blurring (for example, when looking at them from a distance), they give us the impression of having several gray-levels: