OpenCV - Intersection between two binary images

You can use cvAnd or cv::bitwise_and on the two images. The resulting image will be white only where both the input images are white.

EDIT: Here are the results of applying cv::bitwise_and, cv::bitwise_or and cv::bitwise_xor on binary images:

These are the two source images:

Here is the result of applying cv::bitwise_and:

Here is the result of applying cv::bitwise_or:

Here is the result of applying cv::bitwise_xor:

Here's how to do this in python (with the images above):

import cv2

img1 = cv2.imread('black_top_right_triangle.png',0)
img2 = cv2.imread('black_bottom_right_triangle.png',0)

img_bwa = cv2.bitwise_and(img1,img2)
img_bwo = cv2.bitwise_or(img1,img2)
img_bwx = cv2.bitwise_xor(img1,img2)

cv2.imshow("Bitwise AND of Image 1 and 2", img_bwa)
cv2.imshow("Bitwise OR of Image 1 and 2", img_bwo)
cv2.imshow("Bitwise XOR of Image 1 and 2", img_bwx)
cv2.waitKey(0)
cv2.destroyAllWindows()

If you need to install OpenCV for Python, save time by following these directions (installation has historically been quite a pain).