SSIM(结构相似性)-数学公式及python实现

「爱情、让人受尽委屈。」 2023-01-08 12:29 175阅读 0赞

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][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。

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**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  
![20210120110340979.png][]

![20210120110404658.png][]

式1是SSIM的数学定义，其中：

![20210120110428446.png][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3NoeWpoeXAxMQ_size_16_color_FFFFFF_t_70][]  
**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；

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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). Image
      quality assessment: from error visibility to structural similarity. IEEE
      transactions on image processing.
    
      Note: The true SSIM is only defined on grayscale.  This function does not
      perform any colorspace transform.  (If input is already YUV, then it will
      compute 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 the
          maximum the and minimum allowed values).
    
      Returns:
        A tensor containing an SSIM value for each image in batch.  Returned SSIM
        values are in range (-1, 1], when pixel values are non-negative. Returns
        a 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])

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参考：[https://en.wikipedia.org/wiki/Structural\_similarity][https_en.wikipedia.org_wiki_Structural_similarity]

[https_ieeexplore.ieee.org_stamp_stamp.jsp_tp_arnumber_1284395]: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1284395
[PSNR]: https://blog.csdn.net/leviopku/article/details/84586446
[20210120110340979.png]: /images/20221119/d7c551f5d8a3498287d8e842d5a9d1a6.png
[20210120110404658.png]: /images/20221119/9f1fc801f95c4715b5b368bfd9e7278d.png
[20210120110428446.png]: /images/20221119/4ade3f219650427f98d33ee445175da5.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3NoeWpoeXAxMQ_size_16_color_FFFFFF_t_70]: /images/20221119/59d1c18d3ba644bfb6b240e59e5ba17d.png
[https_en.wikipedia.org_wiki_Structural_similarity]: https://en.wikipedia.org/wiki/Structural_similarity