def mean_squared_error(image0, image1):
"""
Compute the mean-squared error between two images.
Parameters
----------
image0, image1 : ndarray
Images. Any dimensionality, must have same shape.
Returns
-------
mse : float
The mean-squared error (MSE) metric.
Notes
-----
.. versionchanged:: 0.16
This function was renamed from ``skimage.measure.compare_mse`` to
``skimage.metrics.mean_squared_error``.
"""
check_shape_equality(image0, image1)
image0, image1 = _as_floats(image0, image1)
diff = image0 - image1
return cp.mean(diff * diff, dtype=cp.float64)
def peak_signal_noise_ratio(image_true, image_test, *, data_range=None):
check_shape_equality(image_true, image_test)
if data_range is None:
if image_true.dtype != image_test.dtype:
warn(
"Inputs have mismatched dtype. Setting data_range based on "
"im_true.",
stacklevel=2)
dmin, dmax = dtype_range[image_true.dtype.type]
true_min, true_max = np.min(image_true), np.max(image_true)
if true_max > dmax or true_min < dmin:
raise ValueError(
"im_true has intensity values outside the range expected for "
"its data type. Please manually specify the data_range")
if true_min >= 0:
# most common case (255 for uint8, 1 for float)
data_range = dmax
else:
data_range = dmax - dmin
image_true, image_test = _as_floats(image_true, image_test)
err = mean_squared_error(image_true, image_test)
return 10 * np.log10((data_range**2) / err)
def normalized_root_mse(image_true, image_test, *, normalization="euclidean"):
"""
Compute the normalized root mean-squared error (NRMSE) between two
images.
Parameters
----------
image_true : ndarray
Ground-truth image, same shape as im_test.
image_test : ndarray
Test image.
normalization : {'euclidean', 'min-max', 'mean'}, optional
Controls the normalization method to use in the denominator of the
NRMSE. There is no standard method of normalization across the
literature [1]_. The methods available here are as follows:
- 'euclidean' : normalize by the averaged Euclidean norm of
``im_true``::
NRMSE = RMSE * sqrt(N) / || im_true ||
where || . || denotes the Frobenius norm and ``N = im_true.size``.
This result is equivalent to::
NRMSE = || im_true - im_test || / || im_true ||.
- 'min-max' : normalize by the intensity range of ``im_true``.
- 'mean' : normalize by the mean of ``im_true``
Returns
-------
nrmse : float
The NRMSE metric.
Notes
-----
.. versionchanged:: 0.16
This function was renamed from ``skimage.measure.compare_nrmse`` to
``skimage.metrics.normalized_root_mse``.
References
----------
.. [1] https://en.wikipedia.org/wiki/Root-mean-square_deviation
"""
check_shape_equality(image_true, image_test)
image_true, image_test = _as_floats(image_true, image_test)
# Ensure that both 'Euclidean' and 'euclidean' match
normalization = normalization.lower()
if normalization == "euclidean":
denom = cp.sqrt(cp.mean((image_true * image_true), dtype=cp.float64))
elif normalization == "min-max":
denom = image_true.max() - image_true.min()
elif normalization == "mean":
denom = image_true.mean()
else:
raise ValueError("Unsupported norm_type")
return cp.sqrt(mean_squared_error(image_true, image_test)) / denom
def peak_signal_noise_ratio(image_true, image_test, *, data_range=None):
"""
Compute the peak signal to noise ratio (PSNR) for an image.
Parameters
----------
image_true : ndarray
Ground-truth image, same shape as im_test.
image_test : ndarray
Test image.
data_range : int, optional
The data range of the input image (distance between minimum and
maximum possible values). By default, this is estimated from the image
data-type.
Returns
-------
psnr : float
The PSNR metric.
Notes
-----
.. versionchanged:: 0.16
This function was renamed from ``skimage.measure.compare_psnr`` to
``skimage.metrics.peak_signal_noise_ratio``.
References
----------
.. [1] https://en.wikipedia.org/wiki/Peak_signal-to-noise_ratio
"""
check_shape_equality(image_true, image_test)
if data_range is None:
if image_true.dtype != image_test.dtype:
warn(
"Inputs have mismatched dtype. Setting data_range based on "
"im_true.",
stacklevel=2,
)
dmin, dmax = dtype_range[image_true.dtype.type]
true_min, true_max = cp.min(image_true), cp.max(image_true)
if true_max > dmax or true_min < dmin:
raise ValueError(
"im_true has intensity values outside the range expected for "
"its data type. Please manually specify the data_range")
if true_min >= 0:
# most common case (255 for uint8, 1 for float)
data_range = dmax
else:
data_range = dmax - dmin
image_true, image_test = _as_floats(image_true, image_test)
err = mean_squared_error(image_true, image_test)
return 10 * cp.log10((data_range * data_range) / err)
def normalized_root_mse(image_true, image_test, *, normalization='euclidean'):
check_shape_equality(image_true, image_test)
image_true, image_test = _as_floats(image_true, image_test)
# Ensure that both 'Euclidean' and 'euclidean' match
normalization = normalization.lower()
if normalization == 'euclidean':
denom = np.sqrt(np.mean((image_true * image_true), dtype=np.float64))
elif normalization == 'min-max':
denom = image_true.max() - image_true.min()
elif normalization == 'mean':
denom = image_true.mean()
else:
raise ValueError("Unsupported norm_type")
return np.sqrt(mean_squared_error(image_true, image_test)) / denom
def multiscale_structural_similarity(im1, im2,*,win_size=None, data_range=None, multichannel=False, gaussian_weights=False):
check_shape_equality(im1, im2)
weights = np.array([0.0448, 0.2856, 0.3001, 0.2363, 0.1333])
levels = weights.size
downsample_filter = np.ones((2, 2, 1)) / 4.0
mssim = np.array([])
mcs = np.array([])
for _ in range(levels):
ssim, cs = structural_similarity(im1, im2, win_size=win_size,data_range=data_range,multichannel=multichannel, gaussian_weights=gaussian_weights)
mssim = np.append(mssim, ssim)
mcs = np.append(mcs, cs)
filtered = [convolve(im, downsample_filter, mode='reflect') for im in [im1, im2]]
im1, im2 = [x[::2, ::2, :] for x in filtered]
return (np.prod(mcs[0:levels-1] ** weights[0:levels-1]) * (mssim[levels-1] ** weights[levels-1]))
def mean_squared_error(image0, image1):
check_shape_equality(image0, image1)
image0, image1 = _as_floats(image0, image1)
return np.mean((image0 - image1)**2, dtype=np.float64)
def structural_similarity(im1,
im2,
*,
win_size=None,
gradient=False,
data_range=None,
multichannel=False,
gaussian_weights=False,
full=False,
**kwargs):
"""
Compute the mean structural similarity index between two images.
Parameters
----------
im1, im2 : ndarray
Images. Any dimensionality with same shape.
win_size : int or None, optional
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, optional
If True, also return the gradient with respect to im2.
data_range : float, optional
The data range of the input image (distance between minimum and
maximum possible values). By default, this is estimated from the image
data-type.
multichannel : bool, optional
If True, treat the last dimension of the array as channels. Similarity
calculations are done independently for each channel then averaged.
gaussian_weights : bool, optional
If True, each patch has its mean and variance spatially weighted by a
normalized Gaussian kernel of width sigma=1.5.
full : bool, optional
If True, also return the full structural similarity image.
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
Standard deviation for the Gaussian when `gaussian_weights` is True.
Returns
-------
mssim : float
The mean structural similarity index over the image.
grad : ndarray
The gradient of the structural similarity between im1 and im2 [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.
.. versionchanged:: 0.16
This function was renamed from ``skimage.measure.compare_ssim`` to
``skimage.metrics.structural_similarity``.
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,
:DOI:`10.1109/TIP.2003.819861`
.. [2] Avanaki, A. N. (2009). Exact global histogram specification
optimized for structural similarity. Optical Review, 16, 613-621.
:arxiv:`0901.0065`
:DOI:`10.1007/s10043-009-0119-z`
"""
check_shape_equality(im1, im2)
print('hi')
if multichannel:
print('multichannel')
# loop over channels
args = dict(win_size=win_size,
gradient=gradient,
data_range=data_range,
multichannel=False,
gaussian_weights=gaussian_weights,
full=full)
args.update(kwargs)
nch = im1.shape[-1]
mssim = np.empty(nch)
if gradient:
G = np.empty(im1.shape)
if full:
S = np.empty(im1.shape)
for ch in range(nch):
ch_result = structural_similarity(im1[..., ch], im2[..., 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 gaussian_weights:
# Set to give an 11-tap filter with the default sigma of 1.5 to match
# Wang et. al. 2004.
truncate = 3.5
if win_size is None:
if gaussian_weights:
# set win_size used by crop to match the filter size
r = int(truncate * sigma + 0.5) # radius as in ndimage
win_size = 2 * r + 1
else:
win_size = 7 # backwards compatibility
if np.any((np.asarray(im1.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 data_range is None:
if im1.dtype != im2.dtype:
warn(
"Inputs have mismatched dtype. Setting data_range based on "
"im1.dtype.",
stacklevel=2)
dmin, dmax = dtype_range[im1.dtype.type]
data_range = dmax - dmin
ndim = im1.ndim
if gaussian_weights:
filter_func = gaussian_filter
filter_args = {'sigma': sigma, 'truncate': truncate}
else:
filter_func = uniform_filter
filter_args = {'size': win_size}
# ndimage filters need floating point data
im1 = im1.astype(np.float64)
im2 = im2.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(im1, **filter_args)
uy = filter_func(im2, **filter_args)
print(ux.shape, uy.shape)
# compute (weighted) variances and covariances
uxx = filter_func(im1 * im1, **filter_args)
uyy = filter_func(im2 * im2, **filter_args)
uxy = filter_func(im1 * im2, **filter_args)
print(uxx.shape, uyy.shape, uxy.shape)
vx = cov_norm * (uxx - ux * ux)
vy = cov_norm * (uyy - uy * uy)
vxy = cov_norm * (uxy - ux * uy)
print(vx.shape, vy.shape, vxy.shape)
R = data_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
print(S.shape)
# to avoid edge effects will ignore filter radius strip around edges
pad = (win_size - 1) // 2
print(S.shape)
# compute (weighted) mean of ssim
mssim = crop(S, pad).mean()
print(mssim)
if gradient:
print('hi')
# The following is Eqs. 7-8 of Avanaki 2009.
grad = filter_func(A1 / D, **filter_args) * im1
grad += filter_func(-S / B2, **filter_args) * im2
grad += filter_func((ux * (A2 - A1) - uy * (B2 - B1) * S) / D,
**filter_args)
grad *= (2 / im1.size)
if full:
return mssim, grad, S
else:
return mssim, grad
else:
print('hi')
if full:
print('hi')
return mssim, S
else:
print('hi2')
print(mssim)
return mssim
if true_max > dmax or true_min < dmin:
raise ValueError(
"im_true has intensity values outside the range expected for "
"its data type. Please manually specify the data_range")
if true_min >= 0:
# most common case (255 for uint8, 1 for float)
data_range = dmax
else:
data_range = dmax - dmin
image_true, image_test = _as_floats(image_true, image_test)
err = mean_squared_error(image_true, image_test)
return 10 * np.log10((data_range ** 2) / err)
def mean_squared_error(image0, image1):
"""
Compute the mean-squared error between two images.
Parameters
----------
image0, image1 : ndarray
Images. Any dimensionality, must have same shape.
Returns
-------
mse : float
The mean-squared error (MSE) metric.
check_shape_equality(image0, image1)
image0, image1 = _as_floats(image0, image1)
return np.mean(ne.evaluate("(image0 - image1) ** 2"), dtype=np.float64)