# Prospects of Structural Similarity Index for Medical Image Analysis
## 3 Current Improvement in SSIM
### Other SSIM Types  
Since SSIM has emerged by bringing about a new IQM model to quantify the images, it has had the potential to substitute for the MSE or PSNR, and thus, to the best of our knowledge, there are more than 20 different types of SSIM that have been developed to solve the issues of the original SSIM or according to the main objective of a specific task. In addition, SSIM IQA can be modified by combining the information content weighting with an MS-SSIM [72]. This paper merely reviews the popular SSIMs suitable for the goal of this paper. Subsequently, this subsection provides a brief description of the improved SSIM developed from 2015-2020. By splitting the images into two regions according to their inter-patch and intra-patch, a novel SSIM scheme was introduced [73]. The two-component indices complement each other. The first index has a goal to inspect the inter-patch feature by examining the disparities on the center patch and the spatial neighborhoods. By contrast, the second component makes an effort to evaluate the intra-patch feature by measuring the similarity in the curvature and gradient. To obtain a single similarity score, an integration approach  
Figure 11: ISSIM-S procedures to quantify the image quality (adapted from [17]). Figure 12: MS-ISSIM-S procedures to quantify the image quality (adapted from [71]). \(L\) is low-pass filtering, and \(2\downarrow\) denotes downsampling by 2.  
is executed. If the quality of the image is low, the assigned weight is higher for the first component. The SSIM can be expanded to examine not only the image but also the other scopes, such as three-dimensional (3D) video displays [74]. The prime major is focused on the availability of a source image or reference image, and thus SSIM is called FR IQM. In [74], the authors proposed using the SSIM as a perceptual IQA to measure the 3D video visual quality by combining it with a joint bit, which they called the SSIM-based joint bit allocation approach. This scheme promises an enhanced 3D video visual quality. Surprisingly, in 2018, [PERSON] et al. offered an upgraded SSIM version by providing a no-reference SSIM (NSSIM) [75]. They improved the SSIM from an FR to no-reference (NR) IQA. This scheme offers a solution in a practical environment because the original image is not always available, and even distorted images are widely accessible. Using the re-blur theory by utilizing Gaussian blur, NSSIM may extract the features of the images and then use them to obtain the information related to the blurriness. In addition, the blurriness can define a novel model of NSSIM and can be written as  
\[b(\mathbf{x},\mathbf{y})=\frac{2d_{x}d_{y}+C_{4}}{d_{x}^{2}+d_{y}^{2}+C_{4}}\, \tag{35}\]  
where \(d_{x}\) and \(d_{y}\) are the distorted image and its re-blurred image, respectively. In addition, \(C_{4}\) is a small constant to avoid instability when \(d_{x}^{2}+d_{y}^{2}\) is close to zero. A new metric of SSIM is formulated as  
\[SSIM_{r}(\mathbf{x},\mathbf{y})=[l(\mathbf{x},\mathbf{y})]^{\alpha}\cdot[c(\mathbf{x},\mathbf{y})]^{ \beta}\cdot[s(\mathbf{x},\mathbf{y})]^{\gamma}\cdot[b(\mathbf{x},\mathbf{y})]^{\lambda}, \tag{36}\]  
with \(\lambda\) as the exponent coefficient for \(b(\mathbf{x},\mathbf{y})\). As with the original SSIM, this new metric applies a sliding window to measure the local similarity, and thus the mean score is  
\[MSSIM_{r}(\mathbf{X},\mathbf{Y})=\frac{1}{M}\sum_{j=1}^{M}SSIM_{r}\Big{(}\mathbf{x}_{j}, \mathbf{y}_{j}\Big{)}. \tag{37}\]  
Finally, the NSSIM can be determined as  
\[NSSIM(\mathbf{x},\mathbf{y})=1-MSSIM_{r}(\mathbf{X},\mathbf{Y}). \tag{38}\]  
Another type of SSIM is the contrast sensitivity function SSIM (CSF + SSIM) [76]. This CSF + SSIM combines the non-linear characteristics of the luminance perception with the contrast sensitivity characteristics from the HVS for a contrast-distorted image evaluation.