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. |
Source
import numpy as np
import matplotlib.pyplot as plt
from skimage import data, img_as_float
from skimage.measure import compare_ssim as ssim
img = img_as_float(data.camera())
rows, cols = img.shape
noise = np.ones_like(img) * 0.2 * (img.max() - img.min())
noise[np.random.random(size=noise.shape) > 0.5] *= -1
def mse(x, y):
return np.linalg.norm(x - y)
img_noise = img + noise
img_const = img + abs(noise)
fig, (ax0, ax1, ax2) = plt.subplots(nrows=1, ncols=3, figsize=(16, 6),
sharex=True, sharey=True,
subplot_kw={'adjustable': 'box-forced'})
plt.tight_layout()
mse_none = mse(img, img)
ssim_none = ssim(img, img, dynamic_range=img.max() - img.min())
mse_noise = mse(img, img_noise)
ssim_noise = ssim(img, img_noise,
dynamic_range=img_const.max() - img_const.min())
mse_const = mse(img, img_const)
ssim_const = ssim(img, img_const,
dynamic_range=img_noise.max() - img_noise.min())
label = 'MSE: %2.f, SSIM: %.2f'
ax0.imshow(img, cmap=plt.cm.gray, vmin=0, vmax=1)
ax0.set_xlabel(label % (mse_none, ssim_none))
ax0.set_title('Original image')
ax0.axes.get_yaxis().set_visible(False)
ax1.imshow(img_noise, cmap=plt.cm.gray, vmin=0, vmax=1)
ax1.set_xlabel(label % (mse_noise, ssim_noise))
ax1.set_title('Image with noise')
ax1.axes.get_yaxis().set_visible(False)
ax2.imshow(img_const, cmap=plt.cm.gray, vmin=0, vmax=1)
ax2.set_xlabel(label % (mse_const, ssim_const))
ax2.set_title('Image plus constant')
ax2.axes.get_yaxis().set_visible(False)
plt.show()
Python source code: download
(generated using skimage 0.12.3)
IPython Notebook: download
(generated using skimage 0.12.3)