【超分辨率】基于结构相似性的图像质量评价SSIM及其python实现

在超分辨率问题中，一直存在着两个经典的图像质量评价算法。其中一个是PSNR(峰值性噪比)，还一个便是SSIM（结构相似性评价）。由于最近有用到SSIM，自己写了个python代码版本的SSIM放在文章最后。

SSIM算法简单介绍

其中ux、uy分别表示图像X和Y的均值，σX、σY分别表示图像X和Y的方差，σXY表示图像X和Y的协方差，即

C1、C2、C3为常数，为了避免分母为0的情况，通常取C1=(K1*L)^2, C2=(K2*L)^2, C3=C2/2, 一般地K1=0.01, K2=0.03, L=255. 则

SSIM取值范围[0,1]，值越大，表示图像失真越小.

在实际应用中，可以利用滑动窗将图像分块，令分块总数为N，考虑到窗口形状对分块的影响，采用高斯加权计算每一窗口的均值、方差以及协方差，然后计算对应块的结构相似度SSIM，最后将平均值作为两图像的结构相似性度量，即平均结构相似性MSSIM：

上述这些描述转载于：
https://www.cnblogs.com/vincent2012/archive/2012/10/13/2723152.html

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SSIM算法python实现

import numpy as np
from PIL import Image 
from scipy.signal import convolve2d

def matlab_style_gauss2D(shape=(3,3),sigma=0.5):
    """
    2D gaussian mask - should give the same result as MATLAB's
    fspecial('gaussian',[shape],[sigma])
    """
    m,n = [(ss-1.)/2. for ss in shape]
    y,x = np.ogrid[-m:m+1,-n:n+1]
    h = np.exp( -(x*x + y*y) / (2.*sigma*sigma) )
    h[ h < np.finfo(h.dtype).eps*h.max() ] = 0
    sumh = h.sum()
    if sumh != 0:
        h /= sumh
    return h

def filter2(x, kernel, mode='same'):
    return convolve2d(x, np.rot90(kernel, 2), mode=mode)

def compute_ssim(im1, im2, k1=0.01, k2=0.03, win_size=11, L=255):

    if not im1.shape == im2.shape:
        raise ValueError("Input Imagees must have the same dimensions")
    if len(im1.shape) > 2:
        raise ValueError("Please input the images with 1 channel")

    M, N = im1.shape
    C1 = (k1*L)**2
    C2 = (k2*L)**2
    window = matlab_style_gauss2D(shape=(win_size,win_size), sigma=1.5)
    window = window/np.sum(np.sum(window))

    if im1.dtype == np.uint8:
        im1 = np.double(im1)
    if im2.dtype == np.uint8:
        im2 = np.double(im2)

    mu1 = filter2(im1, window, 'valid')
    mu2 = filter2(im2, window, 'valid')
    mu1_sq = mu1 * mu1
    mu2_sq = mu2 * mu2
    mu1_mu2 = mu1 * mu2
    sigma1_sq = filter2(im1*im1, window, 'valid') - mu1_sq
    sigma2_sq = filter2(im2*im2, window, 'valid') - mu2_sq
    sigmal2 = filter2(im1*im2, window, 'valid') - mu1_mu2

    ssim_map = ((2*mu1_mu2+C1) * (2*sigmal2+C2)) / ((mu1_sq+mu2_sq+C1) * (sigma1_sq+sigma2_sq+C2))

    return np.mean(np.mean(ssim_map))


if __name__ == "__main__":
    im1 = Image.open("1.png")
    im2 = Image.open("2.png")

    print(compute_ssim(np.array(im1),np.array(im2)))