Let's use the PIL Image module's convert() function for color quantization, with the P mode and the color argument as the maximum number of possible colors. We'll also use the SciPy stats module's signaltonoise() function to find the Signal-to-Noise Ratio (SNR) of an image (parrot.jpg), which is defined as the mean divided by the standard deviation of the image array:

im = Image.open('../images/parrot.jpg')
pylab.figure(figsize=(20,30))
num_colors_list = [1 << n for n in range(8,0,-1)]
snr_list = []
i = 1
for num_colors in num_colors_list:
    im1 = im.convert('P', palette=Image.ADAPTIVE, colors=num_colors)
    pylab.subplot(4,2,i), pylab.imshow(im1), pylab.axis('off')
    snr_list.append(signaltonoise(im1, axis=None))
    pylab.title('Image with # colors = ' + str(num_colors) + ' SNR = ' +
    str(np.round(snr_list[i-1],3)), size=20)
    i += 1
pylab.subplots_adjust(wspace=0.2, hspace=0)
pylab.show()

This shows how the image quality decreases with color-quantization, as the number of bits to store a pixel reduces:

Frame two is as follows:

We'll now plot the impact of color-quantization on the SNR of the image, which is typically a measure for image quality—the higher the SNR, the better the quality:

pylab.plot(num_colors_list, snr_list, 'r.-')
pylab.xlabel('# colors in the image')
pylab.ylabel('SNR')
pylab.title('Change in SNR w.r.t. # colors')
pylab.xscale('log', basex=2)
pylab.gca().invert_xaxis()
pylab.show()

As can be seen, although the color-quantization reduces image size (since the number of bits/pixel gets reduced), it also makes the quality of the image poorer, measured by the SNR: