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ssim.py
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#!/usr/bin/env python
"""Module providing functionality to implement Structural Similarity Image
Quality Assessment. Based on original paper by Z. Whang
"Image Quality Assessment: From Error Visibility to Structural Similarity" IEEE
Transactions on Image Processing Vol. 13. No. 4. April 2004.
"""
import sys
import numpy
from scipy import signal
from scipy import ndimage
def gaussian2(size, sigma):
"""Returns a normalized circularly symmetric 2D gauss kernel array
f(x,y) = A.e^{-(x^2/2*sigma^2 + y^2/2*sigma^2)} where
A = 1/(2*pi*sigma^2)
as define by Wolfram Mathworld
http://mathworld.wolfram.com/GaussianFunction.html
"""
A = 1 / (2.0 * numpy.pi * sigma ** 2)
x, y = numpy.mgrid[-size // 2 + 1:size // 2 + 1, -size // 2 + 1:size // 2 + 1]
g = A * numpy.exp(-((x ** 2 / (2.0 * sigma ** 2)) + (y ** 2 / (2.0 * sigma ** 2))))
return g
def fspecial_gauss(size, sigma):
"""Function to mimic the 'fspecial' gaussian MATLAB function
"""
x, y = numpy.mgrid[-size // 2 + 1:size // 2 + 1, -size // 2 + 1:size // 2 + 1]
g = numpy.exp(-((x ** 2 + y ** 2) / (2.0 * sigma ** 2)))
return g / g.sum()
def ssim(img1, img2, cs_map=False):
"""Return the Structural Similarity Map corresponding to input images img1
and img2 (images are assumed to be uint8)
This function attempts to mimic precisely the functionality of ssim.m a
MATLAB provided by the author's of SSIM
https://ece.uwaterloo.ca/~z70wang/research/ssim/ssim_index.m
"""
img1 = img1.astype(numpy.float64)
img2 = img2.astype(numpy.float64)
size = 11
sigma = 1.5
window = fspecial_gauss(size, sigma)
K1 = 0.01
K2 = 0.03
L = 255 # bitdepth of image
C1 = (K1 * L) ** 2
C2 = (K2 * L) ** 2
mu1 = signal.fftconvolve(window, img1, mode='valid')
mu2 = signal.fftconvolve(window, img2, mode='valid')
mu1_sq = mu1 * mu1
mu2_sq = mu2 * mu2
mu1_mu2 = mu1 * mu2
sigma1_sq = signal.fftconvolve(window, img1 * img1, mode='valid') - mu1_sq
sigma2_sq = signal.fftconvolve(window, img2 * img2, mode='valid') - mu2_sq
sigma12 = signal.fftconvolve(window, img1 * img2, mode='valid') - mu1_mu2
if cs_map:
return (((2 * mu1_mu2 + C1) * (2 * sigma12 + C2)) / ((mu1_sq + mu2_sq + C1) *
(sigma1_sq + sigma2_sq + C2)),
(2.0 * sigma12 + C2) / (sigma1_sq + sigma2_sq + C2))
else:
return ((2 * mu1_mu2 + C1) * (2 * sigma12 + C2)) / ((mu1_sq + mu2_sq + C1) *
(sigma1_sq + sigma2_sq + C2))
def msssim(img1, img2):
"""This function implements Multi-Scale Structural Similarity (MSSSIM) Image
Quality Assessment according to Z. Wang's "Multi-scale structural similarity
for image quality assessment" Invited Paper, IEEE Asilomar Conference on
Signals, Systems and Computers, Nov. 2003
Author's MATLAB implementation:-
http://www.cns.nyu.edu/~lcv/ssim/msssim.zip
"""
level = 5
weight = numpy.array([0.0448, 0.2856, 0.3001, 0.2363, 0.1333])
downsample_filter = numpy.ones((2, 2)) / 4.0
im1 = img1.astype(numpy.float64)
im2 = img2.astype(numpy.float64)
mssim = numpy.array([])
mcs = numpy.array([])
for l in range(level):
ssim_map, cs_map = ssim(im1, im2, cs_map=True)
mssim = numpy.append(mssim, ssim_map.mean())
mcs = numpy.append(mcs, cs_map.mean())
filtered_im1 = ndimage.filters.convolve(im1, downsample_filter,
mode='reflect')
filtered_im2 = ndimage.filters.convolve(im2, downsample_filter,
mode='reflect')
im1 = filtered_im1[::2, ::2]
im2 = filtered_im2[::2, ::2]
return (numpy.prod(mcs[0:level - 1] ** weight[0:level - 1]) *
(mssim[level - 1] ** weight[level - 1]))