SSIM是一种衡量两幅图片相似度的指标。
出处来自于2004年的一篇TIP,
标题为:Image Quality Assessment: From Error Visibility to Structural Similarity
地址为:https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1284395
理论
详细推导见:https://blog.csdn.net/weixin_41923961/article/details/84795832
应用方法:
实际应用中,SSIM(x,y)通过作以(x,y)为中心的窗口,获得局部(x,y)点的局部均值,求取Ux矩阵,Uy矩阵;
sigmax平方通过 “方差等于平方的期望减去期望的平方,平方的均值减去均值的平方”求得
sigmaxy 通过“协方差,乘积的均值减去均值的乘积”求得
tensorflow代码
#%%
import tensorflow as tf
import numpy as np
import torch
#%%
#模仿matlab的fspecial函数,创建滤波算子(计算SSIM用)
def _tf_fspecial_gauss(size, sigma, channels=1):
"""Function to mimic the 'fspecial' gaussian MATLAB function
"""
x_data, y_data = np.mgrid[-size//2 + 1:size//2 + 1, -size//2 + 1:size//2 + 1]
x_data = np.expand_dims(x_data, axis=-1)
x_data = np.expand_dims(x_data, axis=-1)
y_data = np.expand_dims(y_data, axis=-1)
y_data = np.expand_dims(y_data, axis=-1)
x = tf.constant(x_data, dtype=tf.float32)
y = tf.constant(y_data, dtype=tf.float32)
g = tf.exp(-((x**2 + y**2)/(2.0*sigma**2)))
window = g / tf.reduce_sum(g)
return tf.tile(window, (1,1,channels,channels))
#计算ssim
def tf_ssim(img1, img2, cs_map=False, mean_metric=True, filter_size=11, filter_sigma=1.5):
_, height, width, ch = img1.get_shape().as_list()
size = min(filter_size, height, width)
sigma = size * filter_sigma / filter_size if filter_size else 0
window = _tf_fspecial_gauss(size, sigma, ch) # window shape [size, size]
K1 = 0.01
K2 = 0.03
L = 1 # depth of image (255 in case the image has a differnt scale)
C1 = (K1*L)**2
C2 = (K2*L)**2
#求取滑块内均值Ux Uy,均方值Ux_sq
padded_img1 = tf.pad(img1, [[0, 0], [size//2, size//2], [size//2, size//2], [0, 0]], mode="CONSTANT") #img1 上下左右补零
padded_img2 = tf.pad(img2, [[0, 0], [size//2, size//2], [size//2, size//2], [0, 0]], mode="CONSTANT") #img2 上下左右补零
mu1 = tf.nn.conv2d(padded_img1, window, strides=[1,1,1,1], padding='VALID') #利用滑动窗口,求取窗口内图像的的加权平均
mu2 = tf.nn.conv2d(padded_img2, window, strides=[1,1,1,1], padding='VALID')
mu1_sq = mu1*mu1 #img(x,y) Ux*Ux 均方
mu2_sq = mu2*mu2 #img(x,y) Uy*Uy
mu1_mu2 = mu1*mu2 #img(x,y) Ux*Uy
#求取方差,方差等于平方的期望减去期望的平方,平方的均值减去均值的平方
paddedimg11 = padded_img1*padded_img1
paddedimg22 = padded_img2*padded_img2
paddedimg12 = padded_img1*padded_img2
sigma1_sq = tf.nn.conv2d(paddedimg11, window, strides=[1,1,1,1],padding='VALID') - mu1_sq #sigma1方差
sigma2_sq = tf.nn.conv2d(paddedimg22, window, strides=[1,1,1,1],padding='VALID') - mu2_sq #sigma2方差
sigma12 = tf.nn.conv2d(paddedimg12, window, strides=[1,1,1,1],padding='VALID') - mu1_mu2 #sigma12协方差,乘积的均值减去均值的乘积
ssim_value = tf.clip_by_value(((2*mu1_mu2 + C1)*(2*sigma12 + C2))/((mu1_sq + mu2_sq + C1)*(sigma1_sq + sigma2_sq + C2)), 0, 1)
if cs_map: #只考虑contrast对比度,structure结构,不考虑light亮度
cs_map_value = tf.clip_by_value((2*sigma12 + C2)/(sigma1_sq + sigma2_sq + C2), 0, 1) #对比度结构map
value = (ssim_value, cs_map_value)
else:
value = ssim_value
if mean_metric: #求取矩阵的均值,否则返回ssim矩阵
value = tf.reduce_mean(value)
return value
img1 = np.arange(10000,dtype=np.float32).reshape([1,100,100,1])
img2 = np.arange(10000,dtype=np.float32).reshape([1,100,100,1])-2
with tf.Session() as sess:
value = tf_ssim(tf.constant(img1),tf.constant(img2))
print(sess.run(value))
输出结果:
0.9999688