mirror of
https://github.com/wassname/scikit-image.git
synced 2026-06-27 18:25:32 +08:00
Kyle Jackson
234 lines
7.7 KiB
Python
234 lines
7.7 KiB
Python
from __future__ import division
|
|
|
|
__all__ = ['compare_ssim',
|
|
'structural_similarity']
|
|
|
|
import numpy as np
|
|
from scipy.ndimage import uniform_filter, gaussian_filter
|
|
|
|
from ..util.dtype import dtype_range
|
|
from ..util.arraypad import crop
|
|
from .._shared.utils import deprecated
|
|
|
|
|
|
def compare_ssim(X, Y, win_size=None, gradient=False,
|
|
dynamic_range=None, multichannel=False,
|
|
gaussian_weights=False, full=False, **kwargs):
|
|
"""Compute the mean structural similarity index between two images.
|
|
|
|
Parameters
|
|
----------
|
|
X, Y : ndarray
|
|
Image. Any dimensionality.
|
|
win_size : int or None
|
|
The side-length of the sliding window used in comparison. Must be an
|
|
odd value. If `gaussian_weights` is True, this is ignored and the
|
|
window size will depend on `sigma`.
|
|
gradient : bool
|
|
If True, also return the gradient.
|
|
dynamic_range : int
|
|
The dynamic range of the input image (distance between minimum and
|
|
maximum possible values). By default, this is estimated from the image
|
|
data-type.
|
|
multichannel : int or None
|
|
If True, treat the last dimension of the array as channels. Similarity
|
|
calculations are done independently for each channel then averaged.
|
|
gaussian_weights : bool
|
|
If True, each patch has its mean and variance spatially weighted by a
|
|
normalized Gaussian kernel of width sigma=1.5.
|
|
full : bool
|
|
If True, return the full structural similarity image instead of the
|
|
mean value
|
|
|
|
Other Parameters
|
|
----------------
|
|
use_sample_covariance : bool
|
|
if True, normalize covariances by N-1 rather than, N where N is the
|
|
number of pixels within the sliding window.
|
|
K1 : float
|
|
algorithm parameter, K1 (small constant, see [1]_)
|
|
K2 : float
|
|
algorithm parameter, K2 (small constant, see [1]_)
|
|
sigma : float
|
|
sigma for the Gaussian when `gaussian_weights` is True.
|
|
|
|
Returns
|
|
-------
|
|
mssim : float
|
|
The mean structural similarity over the image.
|
|
grad : ndarray
|
|
The gradient of the structural similarity index between X and Y [2]_.
|
|
This is only returned if `gradient` is set to True.
|
|
S : ndarray
|
|
The full SSIM image. This is only returned if `full` is set to True.
|
|
|
|
Notes
|
|
-----
|
|
To match the implementation of Wang et. al. [1]_, set `gaussian_weights`
|
|
to True, `sigma` to 1.5, and `use_sample_covariance` to False.
|
|
|
|
References
|
|
----------
|
|
.. [1] Wang, Z., Bovik, A. C., Sheikh, H. R., & Simoncelli, E. P.
|
|
(2004). Image quality assessment: From error visibility to
|
|
structural similarity. IEEE Transactions on Image Processing,
|
|
13, 600-612.
|
|
https://ece.uwaterloo.ca/~z70wang/publications/ssim.pdf
|
|
|
|
.. [2] Avanaki, A. N. (2009). Exact global histogram specification
|
|
optimized for structural similarity. Optical Review, 16, 613-621.
|
|
http://arxiv.org/abs/0901.0065
|
|
|
|
"""
|
|
if not X.dtype == Y.dtype:
|
|
raise ValueError('Input images must have the same dtype.')
|
|
|
|
if not X.shape == Y.shape:
|
|
raise ValueError('Input images must have the same dimensions.')
|
|
|
|
if multichannel:
|
|
# loop over channels
|
|
args = dict(win_size=win_size,
|
|
gradient=gradient,
|
|
dynamic_range=dynamic_range,
|
|
multichannel=False,
|
|
gaussian_weights=gaussian_weights,
|
|
full=full)
|
|
args.update(kwargs)
|
|
nch = X.shape[-1]
|
|
mssim = np.empty(nch)
|
|
if gradient:
|
|
G = np.empty(X.shape)
|
|
if full:
|
|
S = np.empty(X.shape)
|
|
for ch in range(nch):
|
|
ch_result = compare_ssim(X[..., ch], Y[..., ch], **args)
|
|
if gradient and full:
|
|
mssim[..., ch], G[..., ch], S[..., ch] = ch_result
|
|
elif gradient:
|
|
mssim[..., ch], G[..., ch] = ch_result
|
|
elif full:
|
|
mssim[..., ch], S[..., ch] = ch_result
|
|
else:
|
|
mssim[..., ch] = ch_result
|
|
mssim = mssim.mean()
|
|
if gradient and full:
|
|
return mssim, G, S
|
|
elif gradient:
|
|
return mssim, G
|
|
elif full:
|
|
return mssim, S
|
|
else:
|
|
return mssim
|
|
|
|
K1 = kwargs.pop('K1', 0.01)
|
|
K2 = kwargs.pop('K2', 0.03)
|
|
sigma = kwargs.pop('sigma', 1.5)
|
|
if K1 < 0:
|
|
raise ValueError("K1 must be positive")
|
|
if K2 < 0:
|
|
raise ValueError("K2 must be positive")
|
|
if sigma < 0:
|
|
raise ValueError("sigma must be positive")
|
|
use_sample_covariance = kwargs.pop('use_sample_covariance', True)
|
|
|
|
if win_size is None:
|
|
if gaussian_weights:
|
|
win_size = 11 # 11 to match Wang et. al. 2004
|
|
else:
|
|
win_size = 7 # backwards compatibility
|
|
|
|
if np.any((np.asarray(X.shape) - win_size) < 0):
|
|
raise ValueError(
|
|
"win_size exceeds image extent. If the input is a multichannel "
|
|
"(color) image, set multichannel=True.")
|
|
|
|
if not (win_size % 2 == 1):
|
|
raise ValueError('Window size must be odd.')
|
|
|
|
if dynamic_range is None:
|
|
dmin, dmax = dtype_range[X.dtype.type]
|
|
dynamic_range = dmax - dmin
|
|
|
|
ndim = X.ndim
|
|
|
|
if gaussian_weights:
|
|
# sigma = 1.5 to approximately match filter in Wang et. al. 2004
|
|
# this ends up giving a 13-tap rather than 11-tap Gaussian
|
|
filter_func = gaussian_filter
|
|
filter_args = {'sigma': sigma}
|
|
|
|
else:
|
|
filter_func = uniform_filter
|
|
filter_args = {'size': win_size}
|
|
|
|
# ndimage filters need floating point data
|
|
X = X.astype(np.float64)
|
|
Y = Y.astype(np.float64)
|
|
|
|
NP = win_size ** ndim
|
|
|
|
# filter has already normalized by NP
|
|
if use_sample_covariance:
|
|
cov_norm = NP / (NP - 1) # sample covariance
|
|
else:
|
|
cov_norm = 1.0 # population covariance to match Wang et. al. 2004
|
|
|
|
# compute (weighted) means
|
|
ux = filter_func(X, **filter_args)
|
|
uy = filter_func(Y, **filter_args)
|
|
|
|
# compute (weighted) variances and covariances
|
|
uxx = filter_func(X * X, **filter_args)
|
|
uyy = filter_func(Y * Y, **filter_args)
|
|
uxy = filter_func(X * Y, **filter_args)
|
|
vx = cov_norm * (uxx - ux * ux)
|
|
vy = cov_norm * (uyy - uy * uy)
|
|
vxy = cov_norm * (uxy - ux * uy)
|
|
|
|
R = dynamic_range
|
|
C1 = (K1 * R) ** 2
|
|
C2 = (K2 * R) ** 2
|
|
|
|
A1, A2, B1, B2 = ((2 * ux * uy + C1,
|
|
2 * vxy + C2,
|
|
ux ** 2 + uy ** 2 + C1,
|
|
vx + vy + C2))
|
|
D = B1 * B2
|
|
S = (A1 * A2) / D
|
|
|
|
# to avoid edge effects will ignore filter radius strip around edges
|
|
pad = (win_size - 1) // 2
|
|
|
|
# compute (weighted) mean of ssim
|
|
mssim = crop(S, pad).mean()
|
|
|
|
if gradient:
|
|
# The following is Eqs. 7-8 of Avanaki 2009.
|
|
grad = filter_func(A1 / D, **filter_args) * X
|
|
grad += filter_func(-S / B2, **filter_args) * Y
|
|
grad += filter_func((ux * (A2 - A1) - uy * (B2 - B1) * S) / D,
|
|
**filter_args)
|
|
grad *= (2 / X.size)
|
|
|
|
if full:
|
|
return mssim, grad, S
|
|
else:
|
|
return mssim, grad
|
|
else:
|
|
if full:
|
|
return mssim, S
|
|
else:
|
|
return mssim
|
|
|
|
|
|
@deprecated('compare_ssim')
|
|
def structural_similarity(X, Y, win_size=None, gradient=False,
|
|
dynamic_range=None, multichannel=False,
|
|
gaussian_weights=False, full=False, **kwargs):
|
|
"""""" + compare_ssim.__doc__
|
|
return compare_ssim(X, Y, win_size=win_size, gradient=gradient,
|
|
dynamic_range=dynamic_range,
|
|
multichannel=multichannel,
|
|
gaussian_weights=gaussian_weights, full=full, **kwargs)
|