Covariance between the individual channels of an image

To what extent do the pixel values within pairs of channels in this image vary together?

Busan night scene import numpy as np from PIL import Image from sklearn.preprocessing import MinMaxScaler def mean(x): return sum(x) / len(x) def cov(x, y): mean_x, mean_y = mean(x), mean(y) return sum([(xi - mean_x) * (yi - mean_y) for xi, yi in zip(x, y)]) / (len(x) - 1) mms = MinMaxScaler(feature_range=(-1, 1)) im ='busan_night_scene.jpg') imnp = np.array(im) channels = [mms.fit_transform(imnp[:,:,i]).ravel() for i in range(3)] channel_names = ['red', 'green', 'blue'] combinations = [(0, 1), (1, 2), (2, 0)] for ch1, ch2 in combinations: covariance = cov(channels[ch1], channels[ch2]) print('Covariance between %s and %s channel: %.5f (also with numpy? %s)' % ( channel_names[ch1], channel_names[ch2], covariance, np.allclose(np.cov(channels[ch1], channels[ch2])[0][1], covariance) )) """ Covariance between red and green channel: 0.20282 (also with numpy? True) Covariance between green and blue channel: 0.09542 (also with numpy? True) Covariance between blue and red channel: 0.04822 (also with numpy? True) """

There is almost no pronounced relationship (0.04822) between the blue and red channels and a slightly positive one (0.20282) between the red and the green channels in this image.