Structural similarity index

When comparing images, the mean squared error (MSE)–while simple to implement–is not highly indicative of perceived similarity. Structural similarity aims to address this shortcoming by taking texture into account [1], [2].

The example shows two modifications of the input image, each with the same MSE, but with very different mean structural similarity indices.

[1]

Zhou Wang; Bovik, A.C.; ,”Mean squared error: Love it or leave it? A new look at Signal Fidelity Measures,” Signal Processing Magazine, IEEE, vol. 26, no. 1, pp. 98-117, Jan. 2009.

[2]

Z. Wang, A. C. Bovik, H. R. Sheikh and E. P. Simoncelli, “Image quality assessment: From error visibility to structural similarity,” IEEE Transactions on Image Processing, vol. 13, no. 4, pp. 600-612, Apr. 2004.

import numpy as np
import matplotlib.pyplot as plt

from skimage import data, img_as_float
from skimage.metrics import structural_similarity as ssim
from skimage.metrics import mean_squared_error


img = img_as_float(data.camera())
rows, cols = img.shape

noise = np.ones_like(img) * 0.2 * (img.max() - img.min())
rng = np.random.default_rng()
noise[rng.random(size=noise.shape) > 0.5] *= -1

img_noise = img + noise
img_const = img + abs(noise)

fig, axes = plt.subplots(nrows=1, ncols=3, figsize=(10, 4),
                         sharex=True, sharey=True)
ax = axes.ravel()

mse_none = mean_squared_error(img, img)
ssim_none = ssim(img, img, data_range=img.max() - img.min())

mse_noise = mean_squared_error(img, img_noise)
ssim_noise = ssim(img, img_noise,
                  data_range=img_noise.max() - img_noise.min())

mse_const = mean_squared_error(img, img_const)
ssim_const = ssim(img, img_const,
                  data_range=img_const.max() - img_const.min())

ax[0].imshow(img, cmap=plt.cm.gray, vmin=0, vmax=1)
ax[0].set_xlabel(f'MSE: {mse_none:.2f}, SSIM: {ssim_none:.2f}')
ax[0].set_title('Original image')

ax[1].imshow(img_noise, cmap=plt.cm.gray, vmin=0, vmax=1)
ax[1].set_xlabel(f'MSE: {mse_noise:.2f}, SSIM: {ssim_noise:.2f}')
ax[1].set_title('Image with noise')

ax[2].imshow(img_const, cmap=plt.cm.gray, vmin=0, vmax=1)
ax[2].set_xlabel(f'MSE: {mse_const:.2f}, SSIM: {ssim_const:.2f}')
ax[2].set_title('Image plus constant')

plt.tight_layout()
plt.show()