Grayscale by matrix-Reinventor of Python image processing-

A story about image processing and grayscale conversion only by matrix calculation without relying on the image processing library. Also possible with Pythonista

** Click here for basics **

What is a "reinventor"?

Instead of relying on Open CV or Pillow, I will actually write various image processing using numpy and matplotlib. It's a combination that can also be used with the iOS app Pythonista.

import numpy as np
import matplotlib.pyplot as plt

In addition, the following functions are convenient for displaying images. (For details, Basics)

def img_show(img : np.ndarray, cmap = 'gray', vmin = 0, vmax = 255, interpolation = 'none') -> None:
    '''np.Display an image with array as an argument.'''
    
    #Set dtype to uint8
    img = np.clip(img,,vmin,vmax).astype(np.uint8)
    
    #Display image
    plt.imshow(img, cmap = cmap, vmin = vmin, vmax = vmax, interpolation = interpolation)
    plt.show()
    plt.close()

Grayscale

Grayscale is a method of calculating the black and white value Y from the RGB values assigned to each pixel. Here, various grayscale methods that were not dealt with in Basics ) Also try. See the link for a detailed explanation. They are treated in the same order.

The image used is'tiger.jpeg'

img = plt.imread('tiger.jpeg')
R, G, B = img[...,0], img[...,1], img[...,2]

A function for comparing and arranging color and black and white is defined here.

def align_show(img_gray):
    #img_gray to N*M*Convert to 3
    img_pseudogray = np.einsum('ij,k->ijk',img_gray,[1,1,1])

    #Display side by side
    img_show(np.concatenate((img,img_pseudogray), axis = 1))

Median method

$ \ rm Y = \ frac {\ max (R, G, B) + \ min (R, G, B)} {2} $. It is a method. In short, the average of the maximum and minimum values. In the actual calculation, the order of calculation is partially changed from the above formula to avoid overflow.

img_mid_v = np.max(img, axis = 2)/2 +np.min(img, axis = 2)/2
img_show(img,img_mid_v)

There is no problem at first glance, but the button (?) In the middle of the maze is hard to see.

Weighted average method by NTSC coefficient

$ \ rm Y = (0.298912 R + 0.586611 G + 0.114478 B) $. These coefficients are the result of taking into account the effect of each RGB on the human eye (psychological weighting).

img_ntsc = (0.298912 * R + 0.586611 * G + 0.114478 * B)
align_show(img_ntsc)

Goodness

Weighted average and correction by HDTV coefficient

$ \ rm Y = ((0.222015 R) ^ X + (0.706655 G) ^ X + (0.071330 B) ^ X) ^ {1 / X} $. This also incorporates psychological weighting.

X = 2.2
img_hdtv = ((0.222015*R)**X + (0.706655*G)**X + (0.071330*B)**X)**(1/X)
align_show(img_hdtv)

It's so different that I can't tell the difference from the NTSC method.

Simple averaging method

This is a method of averaging $ \ rm Y = \ frac {R + G + B} {3} $. Probably the most intuitive way. It may be said that it is the NTSC method before taking the weighted average.

img_mean = np.mean(img)
align_show(img_mean)

G channel method

How to extract only the G channel $ \ rm Y = G $. It seems to be the fastest.

img_g_channel = G
align_show(img_g_channel)

I wonder if the red part is a little too dark ...

Median method

How to retrieve the median $ \ rm Y = median (R, G, B) $. I feel that the idea is similar to the median method.

img_median = np.median(img, axis = 2)
align_show(img_median)

As with the median method, the green is too dark.

Summary