# Prospects of Structural Similarity Index for Medical Image Analysis
## 3 Current Improvement in SSIM
### Improved SSIM with Sharpness Comparison  
In 2016, [PERSON] and [PERSON] developed an improved version of SSIM, called improved SSIM with the sharpness comparison (ISSIM-S) [17]. The idea behind this improvement is to anticipate the shortcomings of SSIM in overestimating when quantifying blurred images but underestimating when measuring the images with a spatial translation; however, the spatial translated images are more visible from a human perspective than the blurred images. ISSIM-S uses the spatial domain with an improved assessment comparison in terms of sharpness. Although the focus of ISSIM-S is to accommodate the feasible IQA in measuring the images contaminating the rotation, translation, and scaling, ISSIM-S shows promising results in the assessment of images through several acquisitions, such as histogram equalization, mean luminance shifting, median filtering, impulsive noise, JPEG compression, and mean filtering. The main shortcomings of SSIM are in the structural comparison, as in Equation (6). When the calculated SSIM does not include a structural comparison and only consists of the luminance and contrast, as in Equations (4) and (5), respectively, the similarity score of the spatial translation is not predicted to be low and has a consistent measurement with respect to HVS. However, if the three components of the SSIM are integrated into the SSIM calculation, the measure index evaluates the blurred image with a high SSIM value. By contrast, a slight vertical translated image has a low SSIM score, whereas the blurred image is noisier than the translated image. Figure 10 shows a demonstration of using the \"Lena\" image to present the original, spatial translated, and JPEG compressed images with a green line in the vertical center of the images. As compared, the JPEG compression image is less perceptible than the image with the spatial translation, as shown in Figure 10b,c when they are compared with the reference image, as shown in Figure 10a. According to the original article on ISSIM-S, the evaluation of the images shown in Figure 10 offers an overestimation of the SSIM score for Figure 10c; however, there is an underestimation of Figure 10b. Under normal circumstances, Figure 10b is more perceptible  
Figure 10: Demonstration using “Lena” to present the comparison among (**a**) original, (**b**) vertical translation, and (**c**) JPEG compressed images with a green line indicating the image’s vertical center (adapted from [17]). than Figure 10c. This small SSIM score is obtained because of the drawback in the structural comparison. Therefore, to fix this disadvantage, ISSIM-S defines a new structure factor to be  
\[\widetilde{s}(\mathbf{x},\mathbf{y})=\frac{\left(2\sigma_{x-}\sigma_{y-}+C_{2}\right) \left(2\sigma_{x+}\sigma_{y+}+C_{2}\right)}{\left(\sigma_{x-}^{2}+\sigma_{y-}^ {2}+C_{2}\right)\left(\sigma_{x+}^{2}+\sigma_{y+}^{2}+C_{2}\right)}\, \tag{28}\]  
where \(\sigma_{x-}\) denotes a standard deviation for image \(\mathbf{x}\) smaller than \(\mu_{x}\), whereas \(\sigma_{x+}\) is the standard deviation for image \(\mathbf{x}\) larger than \(\mu_{x}\). In addition, \(\sigma_{y-}\) denotes a standard deviation for image \(\mathbf{y}\) smaller than \(\mu_{y}\), and meanwhile, \(\sigma_{y+}\) is the standard deviation for image \(\mathbf{y}\) larger than \(\mu_{y}\). The definition of \(\widetilde{s}(\mathbf{x},\mathbf{y})\) is the correlation of the standard deviation when having positive or negative scores because \(\sigma_{x-}\) and \(\sigma_{x+}\) (or \(\sigma_{y-}\) and \(\sigma_{y+}\)) can correspond to the object structure by fractioning into brighter and darker regions locally. Nevertheless, by improving only \(s(\mathbf{x},\mathbf{y})\) into \(\widetilde{s}(\mathbf{x},\mathbf{y})\), the presence of an overestimation even exists in the JPEG compressed image. Therefore, a new comparison is necessary to be added, namely a sharpness comparison \(h(\mathbf{x},\mathbf{y})\). With the added \(h(\mathbf{x},\mathbf{y})\), ISSIM-S has confidence in the improvement by two novel upgraded parameters.