#%%
# The KL divergence score, quantifies how much one probability distribution differs from another probability distribution:
# $$D_{KL}(p||q) = H(p, q) - H(p)$$
# where entropy $H(p) = -\sum_i p_i \log_2(p_i)$, the average information in bit,
# and cross entropy $H(p, q) = - \sum_i p_i \log_2(q_i)$ is the average message length in bit.
#%%
import numpy as np
import matplotlib.pyplot as plt
from PIL import Image
#%%
def img2array(imgPath):
'''Load image as numpy array'''
image = Image.open(imgPath)
image = image.convert("L")
return np.array(image)
def pixelhistogram(gray_array):
'''Get the pixel histogram for a graycale image'''
histogram, bin_edges = np.histogram(gray_array, bins=256, range=(0, 256))
return histogram, bin_edges
def relativeerror(img, ref_img):
'''Calculate relative error'''
N = img.shape[0] * img.shape[1]
error = np.sum(np.abs(img - ref_img))/(np.max(ref_img) - np.min(ref_img))/ N
return error
def entropy(p_x):
'''Calculate the entropy of a distribution p(x)'''
e_sum = 0
for p in p_x:
e = p * np.log2(p) if p != 0 else 0
e_sum += e
return -e_sum
def crossentropy(p_x, q_x):
'''Calculate the cross entropy between distributions p(x), q(x)'''
e_sum = 0
for p, q in zip(p_x, q_x):
if p == 0:
e = 0
elif p != 0:
if q == 0:
q = 1E-12
e = p*np.log2(q)
e_sum += e
return -e_sum
def relativeentropy(p_x, q_x):
'''Calculate the relative entropy (or KL divergence) between between distributions p(x), q(x)'''
return crossentropy(p_x, q_x) - entropy(p_x)
# %%
def main():
# Load image
raw_img_path = './image0.png'
gen_img_path = './image1.png'
imgs = [img2array(path) for path in [raw_img_path, gen_img_path]]
# Show images
for i, img in enumerate(imgs):
plt.subplot(1, len(imgs), i+1)
plt.imshow(img, cmap='grey', vmin=0, vmax=255)
plt.show()
# Get the pixel distribution
hists=[]
p_xs=[]
bins=[]
fig, axs = plt.subplots(1, len(imgs), figsize=(15, 5))
for i, ax in enumerate(axs):
histogram, bin_edges = pixelhistogram(imgs[i])
p_x = histogram / (imgs[i].shape[0] * imgs[i].shape[1])
# Store the distribution
hists.append(histogram)
bins.append(bin_edges)
p_xs.append(p_x)
# Plot
ax.bar(bin_edges[:-1], p_x, width=1, align='edge', color='gray')
ax.set_title(f"Fig. {i+1} Distribution")
ax.set_xlabel("Pixel Value x")
ax.set_ylabel("Probability p(x)")
plt.tight_layout()
plt.show()
# Compare the KL divergence
p_x = p_xs[0] # Real Image Distribution
q_x = p_xs[1] # Genergated Image Distribution
KL_00 = relativeentropy(p_x, p_x) # Use the same distribution the KL divergece should be 0
KL_01 = relativeentropy(p_x, q_x) #
print('KL(img0, img0), KL(img0, img1)', KL_00, KL_01)
# If the number is close to 0, means the two images are basicly the same.
# KL divergence measures the inefficiency caused by the approximation (generated image).
# https://stats.stackexchange.com/questions/111445/analysis-of-kullback-leibler-divergence
# %%
main()
# %%