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Quality is a very important parameter for all objects and their functionalities. For authentic quality evaluation ground truth is required. But in practice, it is very difficult to find the ground truth. Usually, image quality is being assessed by MSE means Mean Square Error and PSNR means Peak Signal to Noise Ratio. In contrast to MSE and PSNR, recently, SSIM (Structured Similarity Indexing Method) is proposed which compares the structural measure between obtained and original images. This paper is mainly stressed on SSIM and compares the finding with MSE and PSNR. To measure the image quality we have done a simulation work by adding noise to bench-marked original images and then calculated MSE, PSNR and SSIM of the corresponding image. We have found the superiority of the SSIM in comparison to MSE and PSNR.

Keywords: Image quality, computer simulation, Salt & Pepper noise, Gaussian noise.

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Image Quality (often Image Quality Assessment, IQA).It is also considered as a characteristics property of an image. Degradation of perceived images is also measured by image quality assessment.This degradation is calculated compared to an ideal image.
Image quality can be technically described as they can be objectively determined in terms of deviations from the ideal models. Subjective perception of an image is also related to image quality, as an example: A photograph of a human look 1, 2.
Examples are how colors are represented in a black-and-white image, as well as in color images, or that the reduction of image quality from noise depends on how the noise correlates with the information the viewer seeks in the image rather than its overall strength.
Subjective measures of quality also relate to the fact that, the camera’s deviation from the ideal models of image formation is undesirable.
There are several techniques and metrics that can be used for image quality measurement. They can be classified depending on the availability of a reference image or features from a reference image 3.
Full-reference (FR) methods – FR metrics try to assess the quality of a test image by comparing it with a reference image that is assumed to have perfect quality, e.g. the original of an image versus a JPEG-compressed version of the image.

Reduced-reference (RR) methods – RR metrics assess the quality of a test and reference image based on a comparison of features extracted from both images.

No-reference (NR) methods – NR metrics try to assess the quality of a test image without any reference to the original one.
Image quality metrics can also be classified in terms of measuring only one specific type of degradation (e.g., blurring, blocking, or ringing), or taking into account all possible signal distortions, that is, multiple kinds of artifacts.
A full-reference image quality assessment technique SSIM (Structural Similarity) index method on an image calculates the mean SSIM value compared to the MSE and PSNR value is focused on this paper.
The mean squared error (MSE) is the most widely used and also the simplest full reference metric which is calculated by the squared intensity differences of distorted and reference image pixels and averaging them with the peak signal-to-noise ratio (PSNR) of the related quantity.
Image quality assessment metrics such as MSE, PSNR are mostly applicable as they are simple to calculate, clear in physical meanings, and also convenient to implement in mathematically in the optimization context. But they are sometimes very mismatched to perceive visual quality. In that case we have taken into account the most widely used and effective method structured similarity method which gives us the minimum mean value between the two experimental images where the mean squared error is very high and the PSNR value is rather countable comparing to MSE.
We will calculate the SSIM, MSE and PSNR value between the two images (original and a recovered image) and calculate the minimum error rate between these values.

II. Objectives of Quality Assessment of Images

Image quality assessment technique is used to measure the degradation of the recovered image (noise free image) to improve the quality of digital images. Practically there are two kinds of evaluation: subjective and objective 4. Subjective evaluation is not convenient, time-consuming and also expensive to implement. Afterwards the objective image quality metrics are developed through lots of efforts. The most commonly used objective image quality measures are MSE, PSNR, and SSIM. In this paper we focus on full reference objective quality metric.

III. Quality Assessment Techniques

There are so many image quality techniques largely used to evaluate and assess the quality of images such as MSE – Mean Square Error, UIQI-Universal Image Quality Index, PSNR – Peak Signal to Noise Ratio, SSIM – Structured Similarity Index Method, HVS – Human Vision System, FSIM- Feature Similarity Index Method etc. In this paper we have worked on SSIM, MSE and PSNR methods. Now we will discuss about this three techniques details.

IV. Mean Squared Error (MSE)

The MSE is a measure of the quality of an estimator—it is always non-negative, and values closer to zero are better.
The MSE is the second moment (about the origin) of the error, and thus incorporates both the variance of the estimator and its bias. For an unbiased estimator, the MSE is the variance of the estimator. Like the variance, MSE has the same units of measurement as the square of the quantity being estimated. In an analogy to standard deviation, taking the square root of MSE yields the root-mean-square error or root-mean-square deviation (RMSE or RMSD), which has the same units as the quantity being estimated; for an unbiased estimator, the RMSE is the square root of the variance, known as the standard deviation.

Mean squared error (MSE) or mean squared deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures the average of the squares of the errors or deviations—that is, the difference between the estimator and what is estimated. MSE is a risk function, corresponding to the expected value of the squared error loss or quadratic loss. 4

The MSE (mean Squared Error) between two images such as g(x,y) and g ?(x,y) is:
eMSE = 1/(M N) ?_(n=0)^M??_(m=1)^N??g ?(n,m)-g(n,m)?2
Mean squared error strongly depends on the intensity scaling of image, a disadvantage of mse. MSE of 100.0 for an 8-bit image (with pixel values in the range 0-255) looks odd; but a MSE of 100.0 for a 10-bit image (pixel values in 0, 1023) is barely noticeable.

V. Peak Signal to Noise Ratio (PSNR)

Peak signal-to-noise ratio, often abbreviated PSNR, is an engineering term for the ratio between the maximum possible power of a signal and the power of corrupting noise that affects the fidelity of its representation. Because many signals have a very wide dynamic range, PSNR is usually expressed in terms of the logarithmic decibel scale.

PSNR is most commonly used to measure the quality of reconstruction of lossy compression codecs (e.g., for image compression). The signal in this case is the original data, and the noise is the error introduced by compression. When comparing compression codecs, PSNR is an approximation to human perception of reconstruction quality. One has to be extremely careful with the range of validity of this metric as it is only conclusively valid when used to compare results from the same type code and content 5.
In lossy image and video compression,the psnr value varies between 30 and 50 dB and the bit depth is 8 bits, where the higher is the better. Again for the 16-bit data the PSNR value varies between 60 and 80 dB 6, 7. In wireless transmission quality loss are considered to be accepted ranges 20 dB to 25 dB 8, 9.

(PSNR) is expressed as
PSNR=10log10 (peakval2/MSE)

VI. Structural Similarity Index Method (SSIM)

SSIM is a perception-based model that considers image degradation as perceived change in structural information, while also incorporating important perceptual phenomena, including both luminance masking and contrast masking terms. Structural information is the idea that the pixels have strong inter-dependencies especially when they are spatially close. These dependencies carry important information about the structure of the objects in the visual scene. Luminance masking is a phenomenon whereby image distortions tend to be less visible in bright regions, while contrast masking is a phenomenon whereby distortions become less visible where there is significant activity or “texture” in the image.

The structural similarity (SSIM) index is a method that can predict the perceived quality of digital images and videos.
It is used for measuring the similarity between two images. It is a full reference metric which can also be said the prediction of image quality based on a distortion-free image as reference.

Multi-Scale SSIM
A more advanced form of SSIM, called Multi scale SSIM (MS-SSIM)2 is conducted over multiple scales through a process of multiple stages of sub-sampling, reminiscent of multi scale processing in the early vision system. It has been shown to perform equally well or better than SSIM on different subjective image and video databases 10, 11, 12.
Three-component SSIM
Three-component SSIM (3-SSIM) is a form of SSIM that takes into account the fact that the human eye can see differences more precisely on textured or edge regions than on smooth regions.9 The resulting metric is calculated as a weighted average of SSIM for three categories of regions: edges, textures, and smooth regions. The proposed weighting is 0.5 for edges, 0.25 for the textured and smooth regions. The authors mention that a 1/0/0 weighting (ignoring anything but edge distortions) leads to results that are closer to subjective ratings. This suggests that edge regions play a dominant role in image quality perception 13.

Structural Dissimilarity
Structural dissimilarity (DSSIM) is a distance metric derived from SSIM (though the triangle inequality is not necessarily satisfied).
DSSIM(x,y) = (1-SSIM(x,y))/2

The Structural Similarity (SSIM) Index quality assessment metric is based on the computation of three terms, namely the luminance, contrast and the structural term. The overall index is a multiplicative combination of these three terms. 12
SSIM (x, y) = l (x, y) ?? c (x, y) ?? s (x, y) ?
Where, l = luminance,
c= contrast,
s= structure and ?, ? and ? are positive constants 14.
L (x, y) = (2µxµy+C1) / (µx2+µy2+C1)
C (x,y) = ( 2?x ?y + C2 ) / ( ?x2+ ?y2+C2 )
S (x,y) =( ?xy + C3 ) / ( ?x ?y + C3 )
Where ?x, ?y, ?x,?y and ?xy are the local means, standard deviations, and cross-covariance for images x, y. If
? = ? = ? = 1 (the default for Exponents), and C3 = C2/2 (default selection of C3) the index simplifies to:

SSIM (x, y) = ((2µxµy+C1) (2?xy + C2)) / ((µx2+µy2+C1) (?x2+ ?y2+C2))

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