SSIM(结构相似性)-数学公式及python实现

本文主要是介绍SSIM(结构相似性)-数学公式及python实现，希望对大家解决编程问题提供一定的参考价值，需要的开发者们随着小编来一起学习吧！

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

与PSNR一样，SSIM也经常用作图像质量的评价。

---

先了解SSIM的输入
SSIM的输入就是两张图像，我们要得到其相似性的两张图像。其中一张是未经压缩的无失真图像(即ground truth)，另一张就是你恢复出的图像。所以，SSIM可以作为super-resolution质量的指标。
假设我们输入的两张图像分别是x和y，那么

式1是SSIM的数学定义，其中：

总结：

1. SSIM具有对称性，即SSIM(x,y)=SSIM(y,x)
2. SSIM是一个0到1之间的数，越大表示输出图像和无失真图像的差距越小，即图像质量越好。当两幅图像一模一样时，SSIM=1；

---

如PSNR一样，SSIM这种常用计算函数也被tensorflow收编了，我们只需在tf中调用ssim就可以了：

tf.image.ssim(x, y, 255)

源代码如下：

def ssim(img1, img2, max_val):"""Computes SSIM index between img1 and img2.This function is based on the standard SSIM implementation from:Wang, Z., Bovik, A. C., Sheikh, H. R., & Simoncelli, E. P. (2004). Imagequality assessment: from error visibility to structural similarity. IEEEtransactions on image processing.Note: The true SSIM is only defined on grayscale.  This function does notperform any colorspace transform.  (If input is already YUV, then it willcompute YUV SSIM average.)Details:- 11x11 Gaussian filter of width 1.5 is used.- k1 = 0.01, k2 = 0.03 as in the original paper.The image sizes must be at least 11x11 because of the filter size.Example:# Read images from file.im1 = tf.decode_png('path/to/im1.png')im2 = tf.decode_png('path/to/im2.png')# Compute SSIM over tf.uint8 Tensors.ssim1 = tf.image.ssim(im1, im2, max_val=255)# Compute SSIM over tf.float32 Tensors.im1 = tf.image.convert_image_dtype(im1, tf.float32)im2 = tf.image.convert_image_dtype(im2, tf.float32)ssim2 = tf.image.ssim(im1, im2, max_val=1.0)# ssim1 and ssim2 both have type tf.float32 and are almost equal.img1: First image batch.img2: Second image batch.max_val: The dynamic range of the images (i.e., the difference between themaximum the and minimum allowed values).Returns:A tensor containing an SSIM value for each image in batch.  Returned SSIMvalues are in range (-1, 1], when pixel values are non-negative. Returnsa tensor with shape: broadcast(img1.shape[:-3], img2.shape[:-3])."""_, _, checks = _verify_compatible_image_shapes(img1, img2)with ops.control_dependencies(checks):img1 = array_ops.identity(img1)# Need to convert the images to float32.  Scale max_val accordingly so that# SSIM is computed correctly.max_val = math_ops.cast(max_val, img1.dtype)max_val = convert_image_dtype(max_val, dtypes.float32)img1 = convert_image_dtype(img1, dtypes.float32)img2 = convert_image_dtype(img2, dtypes.float32)ssim_per_channel, _ = _ssim_per_channel(img1, img2, max_val)# Compute average over color channels.return math_ops.reduce_mean(ssim_per_channel, [-1])

---

参考：https://en.wikipedia.org/wiki/Structural_similarity

这篇关于SSIM(结构相似性)-数学公式及python实现的文章就介绍到这儿，希望我们推荐的文章对编程师们有所帮助！

---