XOR-ing and Summing Two Black and White Images

Question

Starting with two images im1 and im2 created with the PIL module, we have the corresponding black and white images,

bw_im1 = im1.convert('1')      

and

bw_im2 = im2.convert('1')    

Each pixel of bw_im2 and bw_im2 is either 0 or 256.

Suppose both bw_im2 and bw_im2 have the same size.

How do you XOR all the corresponding entries and then sum them up?

My Work

I wrote the following stub / proof of concept Python program, but worried that using the code (unpacking/translating over) would be complicated. There might be a more direct and efficient way to process the pixels in the two images.

import numpy as np

M = np.zeros((2, 3))
M[0,2] = 255
M[1,0] = 255
M[1,1] = 255    
print(M)

N = np.zeros((2, 3))
N = np.zeros((2, 3))
N[0,2] = 255
N[1,1] = 255  
N[1,2] = 255
print(N)

list_M = list(M)
list_N = list(N)
xor_signal = 0
for row in range(0, len(list_M)):
    for col in range(0,len(list_M[row])):
        xor_signal = xor_signal + int(bool(list_M[row][col]) !=  bool(list_N[row][col]))

print(xor_signal)

OUTPUT

[[  0.   0. 255.]
 [255. 255.   0.]]
[[  0.   0. 255.]
 [  0. 255. 255.]]
2

Answer 1

You can use PIL's ImageChops like this:

#!/usr/local/bin/python3
import numpy as np
from PIL import Image, ImageChops

# Open images
im1 = Image.open("im1.png")
im2 = Image.open("im2.png")

result = ImageChops.logical_xor(im1,im2)
result.save('result.png')

So, if you start with these two:

The result will be:

Of course, if you are a physicist, you can write that like this ;-)

#!/usr/local/bin/python3
from PIL import Image, ImageChops 
ImageChops.logical_xor(Image.open("im1.png"), Image.open("im2.png")).save('result.png')

---

Or you can use Numpy's XOR like this:

#!/usr/local/bin/python3
import numpy as np
from PIL import Image

# Open images
im1 = Image.open("im1.png")
im2 = Image.open("im2.png")

# Make into Numpy arrays
im1np = np.array(im1)*255
im2np = np.array(im2)*255

# XOR with Numpy
result = np.bitwise_xor(im1np, im2np).astype(np.uint8)

# Convert back to PIL image and save
Image.fromarray(result).save('result.png')

You can sum the pixels by adding this at the end:

print('Sum: {}'.format(np.sum(result)))

---

Or you can not bother writing any Python and just type the following ImageMagick command into your Terminal:

magick im1.png im2.png -evaluate-sequence xor result.png

If you are using v6, or older, use the following instead:

convert im1.png im2.png -evaluate-sequence xor result.png