In modern image editing tools, such as Photoshop, color dodging of an image A with a mask B is implemented as the following ternary statement acting on every pixel index, called idx:

((B[idx] == 255) ? B[idx] : min(255, ((A[idx] << 8) / (255-B[idx]))))

This essentially divides the value of an A[idx] image pixel by the inverse of the B[idx] mask pixel value, while making sure that the resulting pixel value will be in the range of [0, 255] and that we do not divide by zero.

We could translate this into the following naïve Python function, which accepts two OpenCV matrices (image and mask) and returns the blended image:

def dodgeNaive(image, mask):
    # determine the shape of the input image
    width,height = image.shape[:2]

    # prepare output argument with same size as image
    blend = np.zeros((width,height), np.uint8)

    for col in xrange(width):
        for row in xrange(height):

            # shift image pixel value by 8 bits
            # divide by the inverse of the mask
            tmp = (image[c,r] << 8) / (255.-mask)

            # make sure resulting value stays within bounds
            if tmp > 255:
                tmp = 255
            blend[c,r] = tmp
    return blend

As you might have guessed, although this code might be functionally correct, it will undoubtedly be horrendously slow. Firstly, the function uses for loops, which are almost always a bad idea in Python. Secondly, NumPy arrays (the underlying format of OpenCV images in Python) are optimized for array calculations, so accessing and modifying each image[c,r] pixel separately will be really slow.

Instead, we should realize that the <<8 operation is the same as multiplying the pixel value with the number 2^8=256, and that pixel-wise division can be achieved with the cv2.divide function. Thus, an improved version of our dodge function could look like this:

import cv2

def dodgeV2(image, mask):
    return cv2.divide(image, 255-mask, scale=256)

We have reduced the dodge function to a single line! The dodgeV2 function produces the same result as dodgeNaive but is orders of magnitude faster. In addition, cv2.divide automatically takes care of division by zero, making the result 0 where 255-mask is zero.

Now, it is straightforward to implement an analogous burning function, which divides the inverted image by the inverted mask and inverts the result:

import cv2

def burnV2(image, mask):
    return 255 – cv2.divide(255-image, 255-mask, scale=256)

With these tricks in our bag, we are now ready to take a look at the entire procedure. The final code will be in its own class in the filters module. After we have converted a color image to grayscale, we aim to blend this image with its blurred negative:

The resulting image looks like this:

Did you notice that our code can be optimized further?

A Gaussian blur is basically a convolution with a Gaussian function. One of the beauties of convolutions is their associative property. This means that it does not matter whether we first invert the image and then blur it, or first blur the image and then invert it.

"Then what matters?" you might ask. Well, if we start with a blurred image and pass its inverse to the dodgeV2 function, then within that function, the image will get inverted again (the 255-mask part), essentially yielding the original image. If we get rid of these redundant operations, an optimized render method would look like this:

def render(img_rgb):
    img_gray = cv2.cvtColor(img_rgb, cv2.COLOR_BGR2GRAY)
    img_blur = cv2.GaussianBlur(img_gray, (21,21), 0, 0)
    img_blend = cv2.divide(img_gray, img_blur, scale=256)
    return img_blend

For kicks and giggles, we want to lightly blend our transformed image (img_blend) with a background image (self.canvas) that makes it look as if we drew the image on a canvas:

if self.canvas is not None:
    img_blend = cv2.multiply(img_blend, self.canvas, scale=1./256)
return cv2.cvtColor(img_blend, cv2.COLOR_GRAY2BGR)

And we're done! The final output looks like what is shown here: