3. ImageOps equalize

See: https://pillow.readthedocs.io/en/stable/reference/ImageOps.html#PIL.ImageOps.equalize

3.1. Equalize

Use the ImageOps.equalize(image, mask=None) method to equalize the image histogram to return an image with a uniform distribution of grayscale values in the output image.
mask - only the pixels selected by the mask are included in the analysis.
Only L and RGB images can be used.

3.2. Equalize RGB

The code below produces an RGB PNG with no transparency.
from PIL import Image, ImageOps

with Image.open("test_images/cliffs.jpg") as im:
    im1 = ImageOps.equalize(im)
    im1.save("imageOps/equalize.png")
../_images/compare_equalize.png

3.3. Equalize RGBA

The code below produces an RGBA PNG with transparency added back using black colours being transparent.
from PIL import Image, ImageOps

with Image.open("test_images/shapes.png") as im:
    im1 = im.convert(mode='RGB')
    im1 = ImageOps.equalize(im1)
    im1.save("imageOps/equalize_rgb.png")

    im1 = im1.convert(mode='RGBA')

    datas = im1.getdata()
    newData = []
    for pixel in datas:
        if pixel[0] == 0 and pixel[1] == 0 and pixel[2] == 0: # finding black colour by its RGB value
            # storing a transparent value when we find a black colour
            newData.append((0, 0, 0, 0))
        else:
            newData.append(pixel) # other colours remain unchanged

    im1.putdata(newData)
    im1.save("imageOps/equalize_rgba.png")
../_images/compare_equalize_rgba.png