Fuzzy regression method

Student Name: xxx

Image Quality Assessment using Non-Linear Regression MethodTitle:

Synopsis

Diverse picture ready applications, such as image/ video weight and picture entertainment rely heavily on the quality of a picture, more precisely, its quality concerning its perception by a human being. This is referred to as Subjective Image Quality Assessment (IQA). This is an indispensable component with regard to picture quality assessment as images determined to be high-quality through objective methods, have been shown to correlate badly with ratings from human viewers. However, the lack of uniformity resulting from human judgement poses a significant discrepancy in the reliability and accuracy of the assessment. There is therefore, there exists the need to develop models that accurately describe human perception. The approach of fuzzy regression methods using linear polynomials has been used to describe human perception, but possesses inherent shortfalls which limit its accuracy.

This research focuses on the use of non- linear polynomials in the fuzzy regression models. This process is designed to provide more accurate results compared to the unequivocal showing procedure, in cases where (a) the number of individuals (viewers) are inadequate; (b) assumptions using linear regression is not applicable; (c) data collected contains vague characteristics; (d) variety fuzziness gets achieved by human judgement, and (e) the event in question is ambiguous, [ CITATION Arn05 l 1033 ] and [ CITATION Eng09 l 1033 ]. The results collected aim to demonstrate that more fruitful data fitting and better hypothesis capacity can be achieved through fuzzy regression models.

: distortion, mean opinion score, confidence level, response timeKey words

Submission Letter

Acknowledgements

Nomenclature

Abbreviation

Average White Gaussian Noise

Gaussian Blur

Joint Photographic Experts Group

JPEG2000

Joint Photographic Experts Group (created in 2000)

Table of Contents

Synopsis ii

Submission Letter iii

Acknowledgements iv

Nomenclature v

1CHAPTER ONE

Introduction 1 1.1

Background Information 2 1.2

Problem Statement 4 1.3

5CHAPTER TWO

Review of Literature 5 2.

Subjective IQA model: 6 2.1

Statistical regression method 6 2.1.1

Fuzzy non- linear Regression Method 6 2.1.2

10CHAPTER THREE

Results and Discussion 10 3.

Database 10 3.1

Collected Results 13 3.2

Implementation 13 3.2.1

Subjective Analysis 13 3.2.2

30CHAPTER FOUR

Conclusion 30 4.

References 31 5.

CHAPTER ONE

    1. Introduction

Technological advancements have resulted in the invention of devices customized for capture, storage, compression, transmission and display of digital images, increasing the overall quality of the original image. The creation of prediction models that accurately represent image quality as perceived by humans is very challenging. As humans are considered to be the observers and consumers of virtually all digital images, subjective image quality assessment (IQA) is commonly used as a ground truth to develop computational image quality prediction models [ CITATION Eng09 l 1033 ]. However, it is impossible to incorporate subjective IQA into the design and optimization of image processing algorithms to achieve enhanced image quality.

There has been increasing interest, therefore, in correlating subjective IQA with quality assessment considered to be objective so as to predict or estimate perceived quality of the image. At the moment, there are no image quality prediction models that apply to a broad range of visual content and distortion types [ CITATION Eng09 l 1033 ].

    1. Background Information

The number of digital pictures uploaded to the internet has risen exponentially over the past few years. In 2013, 208,300 images were uploaded to Facebook every minute, and 27,800 images were uploaded to Instagram every minute [ CITATION Pop13 l 1033 ]. This influx of photos can be attributed to various digital and social trends such as ‘The Selfie Craze’, as well as new mobile applications to capture and upload pictures, which actively encourage the uploading of digital images. The raw visual information (original image) passes through a series of steps in an imaging pipeline, each of which affects the quality of the picture. There is, therefore, need to develop prediction algorithms to evaluate automatically image quality and determine the effect of each of these steps on image quality.

Traditionally, image quality was determined by use of fidelity metrics. However, fidelity metrics has been shown to, more often, not correlate well with human perceived quality, and thus are not popular. There has been considerable research to devise other image quality estimators with higher correlation with human-perceived quality [ CITATION Kee02 l 1033 ]. Such perceived quality determiners are usually devised and ascertained based on outcomes of psychophysical experiments [ CITATION SEM04 l 1033 ].

The ratings by the research population are averaged into one parameter; Mean Opinion Scores (MOS), that are mostly accepted as a baseline for the design of image and video quality estimators. These scores are instrumental in the training and validation of computational image quality prediction models. Visual stimuli rating, however, is a laborious undertaking given that the quality is to be judged across various visual contents or distortions, further worsened in case there is mixing of various distortions or such discrepancies exhibit complex patterns [ CITATION CTV08 l 1033 ]. This results in a significant discrepancy in the scores of quality between the volunteers of the experiment, compromising the reliability of the MOS based on significant deviation in opinion among the observers [ CITATION UEn11 l 1033 ].

Historically, models for predicting subjective IQA have been developed based on neural networks. However, neural networks lack transparency as they are the black box in nature and the training time required is much longer compared with statistical regression when the network size is large. Fuzzy modelling- based approaches have also been applied to develop models for IQA, but more explicit information can be found in statistical regression models that are in polynomial form. Hence, variable significances and interactions can be determined by the polynomial of the regression models.

Most of the time, people opt for statistical methods over fuzzy model base approaches or neural networks to generate an explicit model. Subjective image quality experiments are more inconsistent to changes over time because it involves human judgment, which may not perform accurately. The new image quality prediction model links objective IQA and subjective IQA. The main drawback with this method is it can function efficiently only within the range over which it is developed. Another constraint is that the experimental data should be normally distributed, which may not be possible every time. Another drawback is possibility of misconception due to the close relationship between subjective image quality measurements versus objective image quality metric [ CITATION Bob l 1033 ].

To solve the above issues, the fuzzy regression method is used. The advantage of fuzzy regression method is that it can model the fuzziness in the subjective opinion scores of people. This method can be applied even on incomplete or small sets of data. Fuzzy regression method is done in three individual cases by varying fuzziness, data size, and some participants with MOS data sets. From the results in [ CITATION Kit15 l 1033 ], the fuzzy regression method outperforms the traditional statistical method. However, this method uses linear polynomials. So this method only captures the linear relationship. In this project, we propose to use nonlinear polynomials in the fuzzy regression method.

    1. Problem Statement

In this digital age, many applications demand accurate picture quality assessment methods, for instance, biomedical image and communication, to facilitate their proper functioning. In this fast growing world, we need an appropriate algorithm that can evaluate the picture quality automatically and inconsistent manner so as not to compromise on speed and efficiency. Not only that, these algorithms must be in agreement with human judgments and perception. Several IQA methods that have been proposed in last decade to produce quality results, some of which have succeeded.

CHAPTER TWO

  1. Review of Literature

The only available methods for measuring the quality of an image are Subjective and Objective IQA. Certainly, a human’s being measurement of image quality, that is, subjective IQA gives the most accurate results. However, subjective evaluation is not a feasible endeavor for everyday application due to the high operation costs associated with a real- time processing system. Therefore, the main objective for IQA is to imitate the human perception and develop a computational algorithm that would measure the image quality using the same criteria as a human would [ CITATION Ulr12 l 1033 ].

Subjective image quality assessment has for a while now been taken as the basic truth for IQA. Since, this method is directly related to human judgment, it is a bit time- consuming and expensive as well, besides being impractical in real world applications. Furthermore, many other factors, including lighting conditions, image viewing distance, human’s vision ability and the observer’s mood, are to be considered. Hence, an appropriate method is needed; that can average human observing to evaluate image quality.

The primary objective of IQA is to develop a model that can estimate the quality of an image entirely and automatically for use in many applications in real time. Traditionally, statistical linear regression methods have been utilized in every field of engineering. The primary goal of the regression method is to express the changes of a dependent variable Y regarding the variation of the independent variable X.

fuzzy regression method

fuzzy regression method 1

However, this basic model do not accurately represent the data. Fuzzy regression functions were developed to come up with models that could more accurately describe the image quality. The general form for these models is;

fuzzy regression method 2

fuzzy regression method 3

fuzzy regression method 4

fuzzy regression method 5

[ CITATION Jin09 l 1033 ]. This is the main limitation of the fuzzy regression. The resultant fuzzy regression model, therefore, bears some resemblance to the statistically linear model.fuzzy regression method 7 , the fuzziness estimated by the regression is only linear to the value of fuzzy regression method 6The fuzzy components are assumed to be triangular fuzzy numbers [ CITATION Arn05 l 1033 ]. These models were deemed to be adequate. However, when the fuzzy polynomial only consists of the independent variables

. We may consider adding other terms later.fuzzy regression method 9 or lower terms to the equations, to achieve the characteristic of decreasing fuzziness with increasing x. in this early stage, we need to see the result of adding the term fuzzy regression method 8Nonetheless, this linear characteristic may not always be true particularly for image quality assessment. The fuzziness would decrease with increasing magnitude of x. Therefore, we may need to introduce the term

    1. Subjective IQA model:

      1. Statistical regression method

images.iAs per the statistical regression model developed in the paper[ CITATION Kit15 l 1033 ], the author defined equations for collected mean opinion score of N

fuzzy regression method 10

, M is normalized objective IQA matrix for the followingfuzzy regression method 12 withfuzzy regression method 11 and jWhere, the error term consider normally distributed with zero mean. M+1 coefficient is β

fuzzy regression method 13

There are two primary drawbacks associated with this method (Kim et. al, 1996). In conventional MOS, the fuzziness of human judgments can be addressed, whereas, in statistical regression method, it is not possible. To come up with an estimate, the following assumptions should be made;

  1. fuzzy regression method 14relationship should be continue over the data ray.fuzzy regression method 15and

  2. are normally distributed.fuzzy regression method 16Deviations of

  3. are normally distributed on regression.fuzzy regression method 17All

      1. Fuzzy non- linear Regression Method

to the fuzzy regression equation and observe the performance of the resulting non- linear method. Fuzzy non-linear regression can therefore be stated in a general equation as follows;fuzzy regression method 18Fuzzy regression method supersedes the statistical regression method in every aspect, such as a small error rate even with little data, with the most significant advantage being it considers the fuzziness of human judgment. Fuzzy non- linear regression models extend above fuzzy regression models by introducing non- linear polynomials. First, we plan to add the term

fuzzy regression method 19

fuzzy regression method 20

fuzzy regression method 21

can be calculated as;fuzzy regression method 27 respectively. Through basic fuzzy arithmetic, the center and spread values of fuzzy regression method 26 fuzzy coefficientfuzzy regression method 25 re the center and spread values of thefuzzy regression method 24 andfuzzy regression method 23 wherefuzzy regression method 22The fuzzy coefficients are set as constants in a symmetric and triangular format, represented as

fuzzy regression method 28

fuzzy regression method 29

. This, therefore, makes the above equation non- linear. According to [ CITATION Tan82 l 1033 ] and [ CITATION Wat88 l 1033 ], the centre and spread values can then get established by obtaining the solutions to the following analogous FnLR model;fuzzy regression method 31 term is introduced to reduce the fuzziness of the model with increasing values offuzzy regression method 30The

fuzzy regression method 32

The assumption here is that the method used to solve the FLR model can be applied to the FnLR model to come up with accurate results.

fuzzy regression method 33

fuzzy regression method 34

fuzzy regression method 35

fuzzy regression method 36

fuzzy regression method 37

.fuzzy regression method 41 interval of the fuzzy outputsfuzzy regression method 40 should be greater than or equal to the fuzzy regression method 39 of each crisp output fuzzy regression method 38The above equations aim to reduce the fuzziness of the system Δ within the constraints that the membership degree

as;fuzzy regression method 52 with respect to fuzzy regression method 51 , fuzzy regression method 50 can be deduced through the corresponding resultsfuzzy regression method 49 . It was proved that the optimal fuzzy coefficients and the related fuzzy outputs with respect to fuzzy regression method 48 and the corresponding fuzzy outputs denoted asfuzzy regression method 47 as fuzzy regression method 46 according to [ CITATION Mos93 l 1033 ]. The resulting optimal coefficients of the fuzzy model through the FnLR system can be denoted with the setting fuzzy regression method 45 ; fuzzy regression method 44 , denoted byfuzzy regression method 43 remain constant viz a viz the changes of the value offuzzy regression method 42As a solution to the above equations, the optimal centre values of

fuzzy regression method 53

fuzzy regression method 54

fuzzy regression method 55

fuzzy regression method 56

fuzzy regression method 57(Mat lab)

fuzzy regression method 58

fuzzy regression method 59

Forming the inequalities;

fuzzy regression method 60

fuzzy regression method 61

The lower and upper bonds are given by;

fuzzy regression method 62

fuzzy regression method 63

fuzzy regression method 64

fuzzy regression method 65

The general form of the equations is therefore, given as;

fuzzy regression method 66

fuzzy regression method 67

fuzzy regression method 68

CHAPTER THREE

  1. Results and Discussion

    1. Database

’ database. The database includes of 575 images, 4% of which are original images, having not undergone any degradation. All other images have experienced four different types of degradation, each divided into six quality levels of increasing magnitude, with the first level representing the mildest distortion while the sixth represents the most severe deterioration. The database contains the following degradations;Video Communications Laboratory @ FER ([email protected])Databases based on subjective IQA have an imperative role in developing and putting new image quality measures to test. There are several such databases used to establish the correlation with objective measures, but this study focuses on the ‘

  1. Average White Gaussian Noise (AWGN)

A sum of the original image and normally distributed pseudorandom numbers was used to calculate the AWGN degradation, at six different standard deviations for the degradation levels. This was done in Matlab.

  1. Gaussian Blur

pixels. Using the Irfanview software, six different sizes of Gaussian function were used to calculate blur degradation [CITATION Irf l 1033 ]. Without normalization, it can be expressed by; fuzzy regression method 69It is calculated as filtering of an image with Gaussian function with different size

fuzzy regression method 70

  1. JPEG2000

bits per pixel, using ‘kdu_compress’.[ CITATION htt l 1033 ]fuzzy regression method 72 and finallyfuzzy regression method 71This was performed so that the final size was

. The subjective experiment got accomplished based on a group of 188 volunteers between the ages of 20 – 30, who were non- experts. Each subject had to grade about 96 images, but with no prior knowledge of the degradation that the picture had experienced. Each image got rated between 16 and 36 times. The method of Single Stimulus (SS), which uses a numeric criterion with 100 grades, was employed in the experiment. The external factors for perception were controlled by providing artificial lighting and the monitors calibrated appropriately. fuzzy regression method 73Using Matlab, JPEG degradation was performed using six different qualities in the range

Experimental outcomes were collected, with mean ratings for each picture being obtained. The results from all observers on a single image are compared, and if the result from either of the observers differs significantly from the average, the result is discarded [ CITATION ITU02 l 1033 ]. In this test configuration, there was only one test condition. To make up for this, the single test configuration had one iteration and single window per mix of test conditions and linear alignment. It allowed for the second step to be discarded. There were 118 observers and 575 test images.

primary moment of the variable parameter Y. In this case described as;th is defined as the 4fuzzy regression method 74The results were checked using kurtosis β to determine whether their distribution was normal or not.

fuzzy regression method 75

The process can be mathematically expressed as;

fuzzy regression method 76

fuzzy regression method 77

fuzzy regression method 78

fuzzy regression method 79

For every observer, the values of P and Q got established and in case any value was greater than the number of tested images by 2% the observer got eliminated;

fuzzy regression method 80

fuzzy regression method 81

In this case, 2 observers were eliminated. Recommendation[ CITATION ITU02 l 1033 ] proposes 0.2% that would lead to 55 observers being discarded. For a 1% ratio, 17 volunteers would be eliminated but correlation results between OIQA and SIQA measures would subsequently be lower.

, using the equations;fuzzy regression method 82Results for every observer were later rescaled to the same full range of

fuzzy regression method 83

fuzzy regression method 84

fuzzy regression method 85

fuzzy regression method 86 image (including reference images)fuzzy regression method 88 viewer gave for thefuzzy regression method 87represents the grade that the

fuzzy regression method 89represents rescaled grades of the same viewer

fuzzy regression method 90 subjectfuzzy regression method 91represents all grades of

Average Mean Opinion Score (MOS) finally got determined for each of the distorted images as an arithmetic mean of all grades for each image.

    1. Collected Results

      1. Implementation

23 images were subjected to varying degrees of distortions and shown to a target population of 10 people. As with normal subjective assessments, the respondents were required to evaluate the clarity of the image presented before them, and give a mean opinion score (MOS) between 1 and 100. The time taken by the respondents to give their opinion score was recorded. The respondents were also required to state the confidence level at which they gave the mean opinion score.

The images subjected to the various distortions were shown to the respondents in order of the level of distortion, that is, IMG_1 is subjected to all 6 levels of a distortion and then shown to the respondent in order of increasing level, then IMG_2 follows, and so forth. After the last image at the last level of distortion has been shown to the respondent, the cycle is repeated with the images subjected to another type of distortion.

      1. Subjective Analysis

The results for each of the respondents with reference to the various distortions is as below;

        1. Original Images

The table below gives the results obtained when the 10 respondents were asked to evaluate the clarity (fuzziness) of 23 images. The results recorded for each respondent are recorded in the columns with respect to the image being examined.

Opinion Scores, Response Times and Confidence Levels of the Respondents when shown the Original ImagesTable 1:

fuzzy regression method 92

The opinion score given to an image by a single observer may be subject to a myriad of factors which could render the result inaccurate, or in the very least, abnormally different. Some of these underlying factors include lighting of the test area, quality perception of the respondent, content of the image, inherent personal bias, among others. In order to correct for this inaccuracy, the mean score is taken for the 10 respondents so that tendencies by either of them tend to even out in the final result, providing relatively more accurate data.

Taking the mean of the values of the results obtained from the respondents gives;

Average values for the Original ImagesTable 2:

fuzzy regression method 93

The results obtained above will act as the control values for the experiment, against which the varying degrees of distortion carried out in the images.

The images below show the mean opinion score for the 10 respondents interviewed, with the average confidence level for the scores given for each image, while also considering the response time

fuzzy regression method 94

Figure 1: Mean Opinion Score and Confidence Level for Original Images

The mean opinion scores recorded show that there is relatively high consistency in the quality of the original images, with IMG_14 getting the highest score of 100% and IMG_15 & IMG_22 getting the lowest score of 98%.

The original images do not exhibit uniform scores in terms of quality, with significant variations being observed. The fluctuation exhibited by the MOS values can be attributed to the factors determining the development of the original image. Some of these factors include, the camera used to take the image, the skill level of the individual who took the image, as well as, the techniques used to render the image. These factors also affect the confidence level of the observers as they might be unsure of what elements to look at to accurately determine the fuzziness of the image, given that the content in the images is varied across different fields. There is also an element of randomness as the images were not assigned to their numbers following any particular order, meaning that a bit of fluctuation is expected.

The human brain, and in extension, human perception relies quite heavily on comparison. This means that the score an observer will rate an image will be with respect to the score of the image seen immediately before. This means that if a fuzzy image follows a clearer one, it is likely that the fuzzy image will get lower scores than if the fuzzy image was shown before the clear one. This phenomena is exhibited by the scores given to the images IMG_14 and IMG_15.

Considering the mean opinion score and the confidence level curves, we can infer that image IMG_22 is the least clear image. It possesses the lowest score and all the respondents are 100% confident that the score they gave is the correct one.

fuzzy regression method 95

Figure 2: Average Response Time for Original Images

’ principle where the respondents give their scores faster as the test progresses. However, IMG_22 is the exception to this as the respondents took more time to analyze it. This may be due to the content or technique used to capture the image. The response time curve also supports the inference that IMG_22 is the least clear image, as the respondents took the maximum amount of time to analyze it before giving their opinion score.repetitionThe curve above shows that the respondents took less time to analyze subsequent images as they did the previous ones. This can be attributed to the ‘

        1. Average White Gaussian Noise (AWGN)

AWGN is a basic noise model that is used in IQA techniques to mimic the effect of various random processes that occur in nature, that affect human perception of image quality. The distortion is done on the original 23 images to varying levels and the images shown to respondents who give their opinion score.

The mean opinion scores for the various distortion levels are represented below;

fuzzy regression method 96

Figure 3: Effect of Varying Degrees of AWGN Distortion on Opinion Score

In general, the results exhibit a systematic drop in the mean opinion scores as the level of distortion increases. As the distortion level is increased, the clarity of the image is reduced, resulting in the low mean opinion score.

It can also be seen that despite the level of distortion, the pattern in the mean opinion score of the respective images is more or less similar. This means that the opinion of the respondents remains relatively unchanged at the various levels of distortion.

It can be inferred that the image IMG_10 is least affected and Image IMG_9, on the other hand, is most affected by the AWGN distortion. This is due to the crests and troughs that are exhibited in the curves at distortions 2 to 6.

fuzzy regression method 97

Figure 4: Effect of Varying Degrees of AWGN Distortion on Confidence Level

The confidence level of the respondents decreases with increasing levels of distortion. This means that as the fuzziness of the image increases, the respondents are less sure that their perception of the image is accurate, meaning that they are less confident in their opinion scores. The respondents exhibited the largest confidence level in the scores they gave for images IMG_06 and IMG_10.

The confidence level of the respondents is erratic for the first few images, but as the tests continue the respondents become more confident in their scores. The distortion correlation between the AWGN fuzziness and the confidence level was found to be 0.2199.

fuzzy regression method 98

Figure 5: Effect of Varying Degrees of AWGN Distortion on Response Time

The response time taken by the respondents to give their opinion score increases as the level of distortion increases. This means that the respondents take relatively more time to analyze distorted images, compared to the original images. This can be attributed to the fact that the respondents see the images in increasing levels of distortion, meaning they take more time to determine the score.

The distortion correlation between the fuzziness brought about by the AWGN distortion and the response time was determined to be 0.3184.

        1. Gaussian Blur (BLU)

Gaussian Blur is a widely used effect in graphics software, used to reduce the noise and detail in images. This smoothing effect is done using a Gaussian function.

The mean opinion scores for the various distortion levels are represented below;

fuzzy regression method 99

Figure 6: Effect of Varying Degrees of Gaussian Blur Distortion on Mean Opinion Score

In general, the results exhibit a systematic drop in the mean opinion scores as the level of distortion increases. As the distortion level is increased, the clarity of the image is reduced, resulting in the low mean opinion score.

It can also be seen that despite the level of distortion, the pattern in the mean opinion score of the respective images is more or less similar. This means that the opinion of the respondents remains relatively unchanged at the various levels of distortion.

It can be inferred that the image IMG_4 is least affected and image IMG_15 and IMG_22, on the other hand, is most affected by the Gaussian Blur distortion. This is due to the crests and troughs that are exhibited in the curves at distortions 2 to 6.

fuzzy regression method 100

Figure 7: Effect of Varying Degrees of Gaussian Blur Distortion on Confidence Level

The confidence level of the respondents decreases with increasing levels of distortion. This means that as the fuzziness of the image increases, the respondents are less sure that their perception of the image is accurate, meaning that they are less confident in their opinion scores. The respondents exhibited the largest confidence level in the scores they gave for image IMG_03, and least for image IMG_17.

The confidence level of the respondents is erratic for the first few images, but as the tests continue the respondents become more confident in their scores. However, the confidence level is more erratic than for the AWGN distortion, meaning that the respondents were less sure of the opinion scores for the Gaussian Blur distortion.

The distortion correlation between the Gaussian Blur fuzziness and the confidence level was found to be 0.6475.

fuzzy regression method 101

Figure 8: Effect of Varying Degrees of Gaussian Blur Distortion on Response Time

The response time taken by the respondents to give their opinion score increases as the level of distortion increases. This means that the respondents take relatively more time to analyze distorted images, compared to the original images. This can be attributed to the fact that the respondents see the images in increasing levels of distortion, meaning they take more time to determine the score.

The distortion correlation between the fuzziness brought about by the Gaussian Blur distortion and the response time was determined to be 0.5433.

        1. JPEG2000

JPEG2000 is a system used for image compression and coding. The mean opinion scores for the various distortion levels are represented below;

fuzzy regression method 102

Figure 9: Effect of Varying Degrees of JPEG2000 Distortion on Confidence Level

The confidence level of the respondents decreases with increasing levels of distortion. This means that as the fuzziness of the image increases, the respondents are less sure that their perception of the image is accurate, meaning that they are less confident in their opinion scores. The respondents exhibited the least confidence level in the scores they gave for image IMG_11, and image IMG_17 for the higher levels of distortion.

The confidence level of the respondents is erratic for the first few images, but as the tests continue the respondents become more confident in their scores. However, the confidence level is more erratic than for the AWGN distortion, meaning that the respondents were less sure of the opinion scores for the Gaussian Blur distortion.

The distortion correlation between the JPEG2000 fuzziness and the confidence level was found to be 0.9503.

fuzzy regression method 103

Figure 10: Effect of Varying Degrees of JPEG2000 Distortion on Mean Opinion Score

In general, the results exhibit a systematic drop in the mean opinion scores as the level of distortion increases. As the distortion level is increased, the clarity of the image is reduced, resulting in the low mean opinion score.

It can also be seen that despite the level of distortion, the pattern in the mean opinion score of the respective images is more or less similar. This means that the opinion of the respondents remains relatively unchanged at the various levels of distortion.

It can be inferred that the image IMG_07 is least affected and image IMG_09, on the other hand, is most affected by the JPEG2000 distortion. This is due to the crests and troughs that are exhibited in the curves at the distortions on levels 2 to 6.

fuzzy regression method 104

Figure 11: Effect of Varying Degrees of JPEG2000 Distortion on Response Time

The response time taken by the respondents to give their opinion score increases as the level of distortion increases. This means that the respondents take relatively more time to analyze distorted images, compared to the original images. This can be attributed to the fact that the respondents see the images in increasing levels of distortion, meaning they take more time to determine the score.

The distortion correlation between the fuzziness brought about by the JPEG2000 distortion and the response time was determined to be 0.9050.

        1. JPEG

In digital photography, JPEG is a commonly used method of lossy compression for digital images. The image below shows the mean opinion scores for the various distortion levels are represented below;

fuzzy regression method 105

Figure 12: Effect of Various Levels of JPEG Distortion on Mean Opinion Scores

In general, the results exhibit a systematic drop in the mean opinion scores as the level of distortion increases. As the distortion level is increased, the clarity of the image is reduced, resulting in the low mean opinion score.

It can also be seen that despite the level of distortion, the pattern in the mean opinion score of the respective images is more or less similar. This means that the opinion of the respondents remains relatively unchanged at the various levels of distortion.

It can be inferred that the image IMG_15 is most affected by the JPEG distortion. This is due to the crests and troughs that are exhibited in the curves at the distortions on levels 2 to 6.

fuzzy regression method 106

Figure 13: Effect of Varying Degrees of JPEG2000 Distortion on Confidence Level

The confidence level of the respondents decreases with increasing levels of distortion. This means that as the fuzziness of the image increases, the respondents are less sure that their perception of the image is accurate, meaning that they are less confident in their opinion scores. The respondents exhibited the least confidence level in the scores they gave for image IMG_11, and image IMG_17 for the higher levels of distortion.

The confidence level of the respondents is erratic for the first few images, but as the tests continue the respondents become more confident in their scores. However, the confidence level is more erratic than for the AWGN distortion, meaning that the respondents were less sure of the opinion scores for the Gaussian Blur distortion.

The distortion correlation between the JPEG fuzziness and the confidence level was found to be 0.5957.

fuzzy regression method 107

Figure 14: Effect of Varying Degrees of JPEG Distortion on Response Time

The response time taken by the respondents to give their opinion score increases as the level of distortion increases. This means that the respondents take relatively more time to analyze distorted images, compared to the original images. This can be attributed to the fact that the respondents see the images in increasing levels of distortion, meaning they take more time to determine the score.

The distortion correlation between the fuzziness brought about by the JPEG distortion and the response time was determined to be 0.6011.

CHAPTER FOUR

  1. Conclusion

The following observations have been made from the results collected and analyzed;

  1. The level of distortion of an image determines the opinion score that the respondent is most likely to give during an assessment, with higher levels of distortion exhibiting less favourable mean opinion scores. This applies for all the types of distortions analyzed in this experiment.

  2. The time it takes for a respondent to score an image (response time) increases as the level of distortion on the image increases. This also applies for all the types of distortions analyzed in the experiment.

  3. Different types of distortions exhibit better correlation in terms of the confidence levels and response times of the participants, with the JPEG2000 and AWGN distortions showing the highest and lowest correlations respectively.

  4. The confidence levels and response times shared a relatively similar correlation with the specific type of distortion that the image was subjected to, exhibiting very little variation in the values calculated

Therefore, the fuzziness of an image is dependent on the type and level of distortion it was subjected to. Different types of distortions exhibit different correlations with regard to the confidence levels and response times of the respondents.

  1. References

. Stockholm, Sweden: Royal Institute of Technology, n.d.Subjective vs Objective Image QualityBoberg, Anders E.

. 2008. pp. 73 — 76.Proceedings of IEEE Southwest Symposium on Image Analysis and InterpretationC.T. Vu, E.C. Larson, D.M. Chandler. «Visual Fixation Patterns when Judging Image Quality: Effects of distortion type, amount and subject experience.»

(2009): 525 — 547.Image Commun. 24 (7)Engelke U., Kusuma T.M., Zepernick H., Caldera M. «Reduced- Reference Metric Design for Objective Perceptual Quality Assessment in Wireless Imaging.»

. n.d.Irfanview softwarehttp://www.irfanview.com/.

. n.d.JPEG2000 coderhttp://www.kakadusoftware.com.

(January 2002).International Telecommunication Union/ ITU Radiocommunication Sector«Methodology for the Subjective Asessment of the Quality of Television Pictures.» ITU-R BT.500- 11.

(2009): 2505 — 2523.Fuzzy Sets and Systems 160Jingli Lu, Ruili Wang. «An Enhanced Fuzzy Linear Regression Model with more Flexible Spreads.»

Keelan, B. W. «Handbook of Image Quality: Characterization and Prediction.» 2002.

(2015): 102 — 110.Engineering Applications of Artificial Intelligence 45Kit Yan Chan, Ulrich Engelke. «Fuzzy Regression for Perceptual Image Quality Assessment.»

(1993): 303 — 327.Fuzzy Sets Syst. 58 (3)Moskowitz H., Kim K.J. «On assessing the H Value in Fuzzy LInear Regression.»

. 30 October 2015.〉http://www.popphoto.com/news/2013/05/how-manyphotos-are-uploaded-to-internet-every-minute〈 27 May 2013. How Many Phots are Uploaded to the Internet Every Minute?PopPhoto.

Lawrence Erlbaum Associates, 2004.Designing Experiments and Analyzing Data: A Model Comparison Perspective, 2nd Ed.S.E. Maxwell, H.D. Delaney.

. University Park, Pennsylvania, USA: Pennsylvania State University, 2005.Fuzzy Regression ModelsShapiro, Arnold F.

(1982): 903 — 907.IEEE Trans. Syst. Man Cybern. 12 (6)Tanaka H., Uejima S., Asai K. «Linear Regression Analysis with Fuzzy Model.»

. 2011. 183 — 188.Proceedings of International Workshop on Quality of Multimedia ExperienceU. Engelke, Y. Pitrey, P. Le Callet. «Towards an Inter- observer Analysis Framework for Multimedia Quality Assessment.»

(2012): 935 — 947.Signal Processing: Image Communcation 27 Ulrich Engelke, Anthony Maeder, Hans- Jurgen Zepernick. «Human Observer Confidence in Image Quality Assessment.»

(1988): 275 — 289.Fuzzy Sets Syst. 27 (3)Watada J., Tanaka H. «Possibilistic Linear Systems and their Application to the Linear Regression Model.»