Determine if an image exists within a larger image, and if so, find it, using Python

I will propose an answer that works fast and perfectly if you are looking for exact match both in size and in image values.

The idea is to calculate a brute force search of the wanted h x w template in a larger H x W image. The bruteforce approach would consist in looking at all the possible h x w windows over the image and check for pixel by pixel correspondence within the template. This however is very computationally expensive, but it can be accelerated.

im = np.atleast_3d(im)
H, W, D = im.shape[:3]
h, w = tpl.shape[:2]

By using the smart integral images one can calculate really fast the sum inside of a h x w window starting at every pixel. An integral image is a summed area table (cumulative summed array), that can be calculated with numpy really fast as:

sat = im.cumsum(1).cumsum(0)

and it has really nice properties, such as the calculation of the sum of all the values within a window with only 4 arithmetic operations:

Thus, by calculating the sum of the template and matching it with the sum of h x w windows over the integral image, it is easy to find a list of “possible windows” where sum of inside values is the same as the sum of the values in the template (a quick approximation).

iA, iB, iC, iD = sat[:-h, :-w], sat[:-h, w:], sat[h:, :-w], sat[h:, w:]
lookup = iD - iB - iC + iA

The above is a numpy vectorization of the operation of shown in the image for all the possible h x w rectangles over the image (thus, really quick).

This will reduce a lot the number of possible windows (to 2 in one of my tests). The last step, would be to check for exact matches with the template:

posible_match = np.where(np.logical_and.reduce([lookup[..., i] == tplsum[i] for i in range(D)]))
for y, x in zip(*posible_match):
    if np.all(im[y+1:y+h+1, x+1:x+w+1] == tpl):
        return (y+1, x+1)

Note that here y and x coordinates correspond to the A point in the image, which is the previous row and column to the template.

Putting all together:

def find_image(im, tpl):
    im = np.atleast_3d(im)
    tpl = np.atleast_3d(tpl)
    H, W, D = im.shape[:3]
    h, w = tpl.shape[:2]

    # Integral image and template sum per channel
    sat = im.cumsum(1).cumsum(0)
    tplsum = np.array([tpl[:, :, i].sum() for i in range(D)])

    # Calculate lookup table for all the possible windows
    iA, iB, iC, iD = sat[:-h, :-w], sat[:-h, w:], sat[h:, :-w], sat[h:, w:] 
    lookup = iD - iB - iC + iA
    # Possible matches
    possible_match = np.where(np.logical_and.reduce([lookup[..., i] == tplsum[i] for i in range(D)]))

    # Find exact match
    for y, x in zip(*possible_match):
        if np.all(im[y+1:y+h+1, x+1:x+w+1] == tpl):
            return (y+1, x+1)

    raise Exception("Image not found")

It works with both grayscale and color images and runs in 7ms for a 303x384 color image with a 50x50 template.

A practical example:

>>> from skimage import data
>>> im = gray2rgb(data.coins())
>>> tpl = im[170:220, 75:130].copy()

>>> y, x = find_image(im, tpl)
>>> y, x
(170, 75)

And to ilustrate the result:

Left original image, right the template. And here the exact match:

>>> fig, ax = plt.subplots()
>>> imshow(im)
>>> rect = Rectangle((x, y), tpl.shape[1], tpl.shape[0], edgecolor="r", facecolor="none")
>>> ax.add_patch(rect)

And last, just an example of the possible_matches for the test:

The sum over the two windows in the image is the same, but the last step of the function filters the one that doesn’t exactly match the template.