mutual info for discrete variables (in this example, 2 images)

mutual_info.py

import numpy as np
from scipy.misc import imread
from itertools import product


# https://www.mathworks.com/matlabcentral/fileexchange/36538-very-fast-mutual-information-betweentwo-images?focused=3869473&tab=function
def mutual_info(X, Y, levels=256):
    # example inputs are images, but it shouldn't matter
    X = X.astype("float32")
    Y = Y.astype("float32")
    tsz = len(X.ravel())
    X_norm = X - X.min() + 1
    Y_norm = Y - Y.min() + 1

    matAB = np.zeros((tsz, 2))
    matAB[:, 0] = X_norm.ravel()
    matAB[:, 1] = Y_norm.ravel()

    # joint histogram, match matlab
    h, x_edges, y_edges = np.histogram2d(matAB[:, 0] + 1, matAB[:, 1] + 1, bins=levels)
    h = np.concatenate((0. * h[:, 0][:, None], h), axis=1)
    h = np.concatenate((0. * h[0, :][None, :], h), axis=0)
    hn = h / np.sum(h.ravel())
    y_marg = np.sum(hn, axis=0)
    x_marg = np.sum(hn, axis=1)

    Hy = -np.sum(y_marg * np.log2(y_marg + (y_marg == 0))) # Entropy of Y
    Hx = -np.sum(x_marg * np.log2(x_marg + (x_marg == 0))) # Entropy of X

    arg_xy2 = hn * (np.log2(hn + (hn == 0)))
    h_xy = np.sum(-arg_xy2.ravel()) # joint entropy
    M = Hx + Hy - h_xy # mutual information
    return M


aa = imread("first_image.png", flatten=False, mode=None)
bb = imread("second_image.png", flatten=False, mode=None)

mi = mutual_info(aa, bb)
from IPython import embed; embed(); raise ValueError()