def ergas(GT, P, r=4, ws=8):
"""calculates erreur relative globale adimensionnelle de synthese (ergas).
:param GT: first (original) input image.
:param P: second (deformed) input image.
:param r: ratio of high resolution to low resolution (default=4).
:param ws: sliding window size (default = 8).
:returns: float -- ergas value.
"""
GT, P = _initial_check(GT, P)
rmse_map = None
nb = 1
_, rmse_map = rmse_sw(GT, P, ws)
means_map = uniform_filter(GT, ws) / ws**2
# Avoid division by zero
idx = means_map == 0
means_map[idx] = 1
rmse_map[idx] = 0
ergasroot = np.sqrt(np.sum(((rmse_map**2) / (means_map**2)), axis=2) / nb)
ergas_map = 100 * r * ergasroot
s = int(np.round(ws / 2))
return np.mean(ergas_map[s:-s, s:-s])
def mse(GT, P):
"""Calculates mean squared error (mse).
:param GT: first (original) input image
:paran P: second (deformed) input image
:returns: float -- mse value
"""
GT, P = _initial_check(GT, P)
return np.mean((GT.astype(np.float64) - P.astype(np.float64))**2)
def rmse(GT, P):
"""Calculates root mean squared error (rmse).
:param GT: first (original) input image
:paran P: second (deformed) input image
:returns: float -- rmse value
"""
GT, P = _initial_check(GT, P)
return np.sqrt(mse(Gt, P))
def uqi(GT, P, ws=8):
"""calculates universal image quality index (uqi).
:param GT: first (original) input image.
:param P: second (deformed) input image.
:param ws: sliding window size (default = 8).
:returns: float -- uqi value.
"""
GT, P = _initial_check(GT, P)
return np.mean(
[_uqi_single(GT[:, :, i], P[:, :, i], ws) for i in range(GT.shape[2])])
def msssim(GT,
P,
weights=[0.0448, 0.2856, 0.3001, 0.2363, 0.1333],
ws=11,
K1=0.01,
K2=0.03,
MAX=None):
"""calculates multi-scale structural similarity index (ms-ssim).
:param GT: first (original) input image.
:param P: second (deformed) input image.
:param weights: weights for each scale (default = [0.0448, 0.2856, 0.3001, 0.2363, 0.1333]).
:param ws: sliding window size (default = 11).
:param K1: First constant for SSIM (default = 0.01).
:param K2: Second constant for SSIM (default = 0.03).
:param MAX: Maximum value of datarange (if None, MAX is calculated using image dtype).
:returns: float -- ms-ssim value.
"""
if MAX is None:
MAX = np.iinfo(GT.dtype).max
GT, P = _initial_check(GT, P)
scales = len(weights)
fltr_specs = dict(fltr=Filter.GAUSSIAN, sigma=1.5, ws=11)
if isinstance(weights, list):
weights = np.array(weights)
mssim = []
mcs = []
for _ in range(scales):
_ssim, _cs = ssim(GT,
P,
ws=ws,
K1=K1,
K2=K2,
MAX=MAX,
fltr_specs=fltr_specs)
mssim.append(_ssim)
mcs.append(_cs)
filtered = [uniform_filter(im, 2) for im in [GT, P]]
GT, P = [x[::2, ::2, :] for x in filtered]
mssim = np.array(mssim, dtype=np.float64)
mcs = np.array(mcs, dtype=np.float64)
return np.prod(_power_complex(mcs[:scales - 1],
weights[:scales - 1])) * _power_complex(
mssim[scales - 1], weights[scales - 1])
def vifp(GT, P, sigma_nsq=2):
"""calculates Pixel Based Visual Information Fidelity (vif-p).
:param GT: first (original) input image.
:param P: second (deformed) input image.
:param sigma_nsq: variance of the visual noise (default = 2)
:returns: float -- vif-p value.
"""
GT, P = _initial_check(GT, P)
# GT,P = GT[:,:,np.newaxis],P[:,:,np.newaxis]
return np.mean([
_vifp_single(GT[:, :, i], P[:, :, i], sigma_nsq)
for i in range(GT.shape[2])
])
def scc(GT, P, win=[[-1, -1, -1], [-1, 8, -1], [-1, -1, -1]], ws=8):
"""calculates spatial correlation coefficient (scc).
:param GT: first (original) input image.
:param P: second (deformed) input image.
:param fltr: high pass filter for spatial processing (default=[[-1,-1,-1],[-1,8,-1],[-1,-1,-1]]).
:param ws: sliding window size (default = 8).
:returns: float -- scc value.
"""
GT, P = _initial_check(GT, P)
coefs = np.zeros(GT.shape)
for i in range(GT.shape[2]):
coefs[:, :, i] = _scc_single(GT[:, :, i], P[:, :, i], win, ws)
return np.mean(coefs)
def psnr(GT, P, MAX=None):
"""Calculates peak signal-to-noise ratio (psnr)
:param GT: frist (orginal) input image.
:param P: second (deformed) input image.
:param MAX: maximum value of datarange (if None, MAX is calculated using image dtype)
return: float -- psnr value in dB.
"""
if MAX is None:
MAX = np.iinfo(GT.dtype).max
GT, P = _initial_check(GT, P)
mse_value = mse(GT, P)
if mse_value == 0:
return np.inf
return 10 * np.log10(MAX**2 / mse_value)
def rmse_sw(GT, P, ws=8):
"""calculates root mean squared error (rmse) using sliding window.
:param GT: first (original) input image.
:param P: second (deformed) input image.
:param ws: sliding window size (default = 8).
:returns: tuple -- rmse value,rmse map.
"""
GT, P = _initial_check(GT, P)
rmse_map = np.zeros(GT.shape)
vals = np.zeros(GT.shape[2])
for i in range(GT.shape[2]):
vals[i], rmse_map[:, :, i] = _rmse_sw_single(GT[:, :, i], P[:, :, i],
ws)
return np.mean(vals), rmse_map
def rase(GT, P, ws=8):
"""calculates relative average spectral error (rase).
:param GT: first (original) input image.
:param P: second (deformed) input image.
:param ws: sliding window size (default = 8).
:returns: float -- rase value.
"""
GT, P = _initial_check(GT, P)
_, rmse_map = rmse_sw(GT, P, ws)
GT_means = uniform_filter(GT, ws) / ws**2
N = GT.shape[2]
M = np.sum(GT_means, axis=2) / N
rase_map = (100. / M) * np.sqrt(np.sum(rmse_map**2, axis=2) / N)
s = int(np.round(ws / 2))
return np.mean(rase_map[s:-s, s:-s])
def sam(GT, P):
"""calculates spectral angle mapper (sam).
:param GT: first (original) input image.
:param P: second (deformed) input image.
:returns: float -- sam value.
"""
GT, P = _initial_check(GT, P)
GT = GT.reshape((GT.shape[0] * GT.shape[1], GT.shape[2]))
P = P.reshape((P.shape[0] * P.shape[1], P.shape[2]))
N = GT.shape[1]
sam_angles = np.zeros(N)
for i in range(GT.shape[1]):
val = np.clip(
np.dot(GT[:, i], P[:, i]) /
(np.linalg.norm(GT[:, i]) * np.linalg.norm(P[:, i])), -1, 1)
sam_angles[i] = np.arccos(val)
return np.mean(sam_angles)
def ssim(GT,
P,
ws=11,
K1=0.03,
K2=0.03,
MAX=None,
fltr_specs=None,
mode='valid'):
"""Calculates structural similarity index (ssim).
:param GT: first (original) input image
:param P: second (deformed) input image
:param ws: sliding window size (default = 11)
:param K1: first constant for SSIM (default = 0.01)
:param K2: second constant for SSIM (default = 0.03)
:param MAX: Maximum value of datarange (if None, MAX is calculated using image dtype).
:returns: tuple -- ssim value, cs value.
"""
if MAX is None:
MAX = np.iinfo(GT.dtype).max
GT, P = _initial_check(GT, P)
if fltr_specs is None:
fltr_specs = dict(fltr=Filter.UNIFORM, ws=ws)
C1 = (K1 * MAX)**2
C2 = (K2 * MAX)**2
ssims = []
css = []
for i in range(GT.shape[2]):
ssim, cs = _ssim_single(GT[:, :, i], P[:, :, i], ws, C1, C2,
fltr_specs, mode)
ssims.append(ssim)
css.append(cs)
return np.mean(ssims), np.mean(css)