Histogram matching is an image processing task where an image is altered in such a way that its histogram matches the histogram of another reference (template) image's histogram. The algorithm is described as follows:

1. Compute the cumulative histogram for each image.
2. For any given pixel value, x_i, in the input image, find the corresponding pixel value, x_j, in the output image by matching the input image's histogram with the template image's histogram (G(x_i)=H(x_j), as shown in the following diagram.
3. Replace pixel x_i in the input with x_j as shown in the following diagram:

In this recipe, we will implement histogram matching for colored images on our own.

As usual, let's start by importing the required libraries:

from skimage.exposure import cumulative_distribution
from skimage.color import rgb2gray
import matplotlib.pylab as plt
import numpy as np

Perform the following steps to implement histogram matching:

1. Let's implement the histogram-matching algorithm with the hist_matching() function, which accepts the original and the template image's cdf along with the original image:
   

def hist_matching(c, c_t, im):
 b = np.interp(c, c_t, np.arange(256))
             # find closest matches to b_t
 pix_repl = {i:b[i] for i in range(256)} 
             # dictionary to replace the pixels
 mp = np.arange(0,256)
 for (k, v) in pix_repl.items():
  mp[k] = v
 s = im.shape
 im = np.reshape(mp[im.ravel()], im.shape)
 im = np.reshape(im, s)
 return im

2. Compute cdf of an image with the following function:

def cdf(im):
 c, b = cumulative_distribution(im)
 for i in range(b[0]):
  c = np.insert(c, 0, 0)
 for i in range(b[-1]+1, 256):
  c = np.append(c, 1)
 return c

3. Finally, read the input and template images, compute their cdfs, and create the output image with the hist_matching() function. Plot the input, template, and output images by running the following code:

im = imread('images/goddess.png').astype(np.uint8)
im_t = imread('images/leaves.png')

im1 = np.zeros(im.shape).astype(np.uint8)
for i in range(3):
 c = cdf(im[...,i])
 c_t = cdf(im_t[...,i])
 im1[...,i] = hist_matching(c, c_t, im[...,i])

plt.figure(figsize=(20,17))
plt.subplots_adjust(left=0, top=0.95, right=1, bottom=0, \
                    wspace=0.05, hspace=0.05)
plt.subplot(221), plt.imshow(im), plt.axis('off'), \
                    plt.title('Input Image', size=25)
plt.subplot(222), plt.imshow(im_t), plt.axis('off'), \
                    plt.title('Template Image', size=25)
plt.subplot(223), plt.imshow(im1[...,:3]), plt.axis('off'), \
                    plt.title('Output Image', size=25)
plt.show()

The cumulative_distribution() function from the scikit-image.exposure module was used to compute the cdf of an image.

Since we needed all the pixel values starting from 0 to 255, we used np.insert() with an appropriate cdf value (0 for all the smaller pixel values and 1 for higher pixel values not present).

For each of the color channels, cdf was computed separately for the input and the template images using the cdf() function, and then the hist_matching() function was invoked with these values along with the input image to construct the corresponding color channel in the output image.

The following diagram shows the output image generated for these given input and template images:

You can use histogram matching to change an image taken in daylight to a night-vision image using an appropriate template image. The next example shows a similar fun application of histogram matching:

For more information, refer to the following links:

• https://scikit-image.org/docs/dev/api/skimage.exposure.html#skimage.exposure.cumulative_distribution
• https://www.youtube.com/watch?v=4VLMlL90tLE
• The Histogram matching section (Chapter 4) from the book Hands-on Image Processing with Python