# Prospects of Structural Similarity Index for Medical Image Analysis
## 2 Historical Review and Basic Principles of SSIM  
Quantifying an image objectively to acquire quality statistics is a crucial task in an image processing procedure because it can provide the feature and property information of the image; thus, several attempts at developing a computer-based observer have been conducted by researchers. Nevertheless, creating a reliable algorithm for measuring an image is challenging and is concerned with the HVS because humans are the end-users of the images. For example, in terms of video communication, a perfect IQM can be deployed as a benchmark for measuring other IQMs when assessing a particular task. We can select the best IQM algorithm based on performance [33; 35; 50; 51]. Moreover, in the field of medical image analysis, with the assistance of computer vision, clinicians can improve their confidence when diagnosing patients. This becomes more vital if the task is related to human disease diagnosis [52; 53; 54; 55; 56]. Two traditional quality metrics, MSE and PSNR, are widely used to evaluate images because they are able to provide a physical meaning and are relatively simple in terms of their calculation. However, such quality measures are frequently inconsistent with the HVS because they can provide the same value of quality for two completely different distorted images, even when one image is more perceivable than another [6; 7]. The performances of common IQAs were shown by [PERSON] and [PERSON] [9] in 1995, inspiring [PERSON] and [PERSON] [14] to develop a novel universal IQM to overcome the MSE and PSNR incompatibility in 2002. At the time, MSE and SNR, along with their differentiations considered, were incompatible with HVS, particularly when employing a specific condition directed at an image with a particular level of degradation. This first attempt in developing a new universal quality index can be utilized not only in a two-dimensional image processing system but also in other areas, such as speech and pattern recognitions relative to a one-dimensional analysis, because the new universal quality metric offers comparisons between two signals. These two signals refer to one signal as a reference and the other acting as the original signal with implemented noise. Using these two signals, we can calculate the signal quality quantitatively. Therefore, their study was recognized as a full-reference (FR) [57] IQA when considering that the model of the image distortion is influenced by three aspects, i.e., correlation loss, luminance distortion, and contrast distortion. A description of the developed novel universal quality index is as follows:  
\[Q=\frac{4\sigma_{xy}\overline{xy}}{\left(\sigma_{x}^{2}+\sigma_{y}^{2}\right)+ \left(\overline{x}^{2}+\overline{y}^{2}\right)}\, \tag{1}\]  
where \(x=\{x_{i}|i=1,\,2,\,3,\,\dots,\,N\}\) is the original image, and \(y=\{y_{i}|i=1,\,2,\,3,\,\dots,\,N\}\) denotes the image under test, with \(\overline{x}=\
icefrac{{1}}{{N}}\sum_{i=1}^{N}x_{i}\) and \(\overline{y}=\
icefrac{{1}}{{N}}\sum_{i=1}^{N}y_{i}\) as the average grayscale level (luminance) for the original and test images, respectively. In addition, \(\sigma_{\overline{x}}^{2}=\
icefrac{{1}}{{N}}-\
icefrac{{1}}{{\sum_{i=1}^{N }}}\left(x_{i}-\overline{x}\right)^{2}\) and \(\sigma_{y}^{2}=\
icefrac{{1}}{{N}}-\
icefrac{{1}}{{\sum_{i=1}^{N}}}\left(y_{i }-\overline{y}\right)^{2}\) are squares of the standard deviation for the original and test images, and \(\sigma_{xy}=\
icefrac{{1}}{{N}}-\
icefrac{{1}}{{\sum_{i=1}^{N}}}\left(x_{i}- \overline{x}\right)\left(y_{i}-\overline{y}\right)\) refers to the covariance between the original and test images. Moreover, the quality score \(Q\) is within the range of \(-1\) to \(1\); however, in most cases, \(Q\) is from \(0\) to \(1\) with \(0\) representinga non-similarity and 1 demonstrating a perfect match between the reference and noised images.