def _SSIMForMultiScale(img1, img2, max_val=255, filter_size=11, filter_sigma=1.5, k1=0.01, k2=0.03):
img1 = img1.astype(np.float64)
img2 = img2.astype(np.float64)
_, height, width, _ = img1.shape
size = min(filter_size, height, width)
sigma = size * filter_sigma / filter_size if filter_size else 0
if filter_size:
window = np.reshape(_FSpecialGauss(size, sigma), (1, size, size, 1))
mu1 = signal.fftconvolve(img1, window, mode='valid')
mu2 = signal.fftconvolve(img2, window, mode='valid')
sigma11 = signal.fftconvolve(img1 * img1, window, mode='valid')
sigma22 = signal.fftconvolve(img2 * img2, window, mode='valid')
sigma12 = signal.fftconvolve(img1 * img2, window, mode='valid')
else:
mu1, mu2 = img1, img2
sigma11 = img1 * img1
sigma22 = img2 * img2
sigma12 = img1 * img2
mu11 = mu1 * mu1
mu22 = mu2 * mu2
mu12 = mu1 * mu2
sigma11 -= mu11
sigma22 -= mu22
sigma12 -= mu12
c1 = (k1 * max_val) ** 2
c2 = (k2 * max_val) ** 2
v1 = 2.0 * sigma12 + c2
v2 = sigma11 + sigma22 + c2
ssim = np.mean((((2.0 * mu12 + c1) * v1) / ((mu11 + mu22 + c1) * v2)))
cs = np.mean(v1 / v2)
return ssim, cs
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