https://doi.org/10.31449/inf.v46i6.3953 Informatica 46 (2022) 53–65 53 Color Distortion and Edge Feature for Perceptual Quality Assessment Ahmed Zeggari 1 , Zianou Ahmed Seghir 2 , Mounir Hemam 2 , Fella Hachouf 3 and Meriem Djezzar 4, 5 E-mail : ahmed.zeggari@univ-tebessa.dz, zianou_ahmed_seghir@yahoo.fr, hemam.mounir@univ-khenchela.dz, hachouf.fella@gmail.com, meriem.djezzar@univ-khenchela.dz 1 Math & Computer Sciences Dept. University of Tebessa, Tebessa. Algeria 2 Khenchela University, ICOSI Laboratory, BP 1252 El Houria, 40004 Khenchela, Algeria 3 Automatic and Robotic Laboratory, Mentouri Constantine University, Algeria 4 University of Abbes Laghrour, Khenchela, Algeria 5 LIRE Laboratory, Constantine 2 - Abdelhamid Mehri -University, Constantine, Algeria Keywords: gradient similarity, color distortion, Ruderman operator, distorted pixel measure Received: January 30, 2022 The color distortion effect has an important impact on the perceived quality, which is ignored in previous related works. Unified with the color distortion outcome and edge similarity, a new full- reference image quality assessment was proposed named the gradient similarity-based distorted pixel and deformed color measure (GDCM). The components RGB of the color image are converted into image coded in YIQ color space. Then, Ruderman operators and the gradient images are calculated from the Y component. I and Q elements are used to identify the color distortion. Finally, the previous results are combined to compute the ultimate measure. Experimental results on databases illustrate that the GDCM performs very well. Povzetek: Prispevek predstavlja novo tehniko za oceno kakovosti slike, ki temelji na barvnem popačenju in značilnostih robov. 1 Introduction The image quality is reduced by different kinds of degradations. So, its quality needs to be assessed. Using the automatic image quality assessment (IQA) measures instead of the subjective one, is the purpose of the research in this area. As mentioned in the previous sentence, there are two ways to measure the image quality: the subjective methods are the first one, where the human observer is the ultimate judge of image quality. In the other hand, objective methods seek to assess the image quality by using machine. These objective IQA methods of identifying reliable quality are of three types, namely: full-reference (FR) measure, no- reference measure (NR) and reduced-reference (RR) measure. The perfection version of image is used to compare the distorted one in FR method [41-44]. NR [39-40] do not need a reference image and has only access to image test, its quality is evaluated without knowing the ideal version. RR methods assess the quality of test image using some features of reference image and the entire test one. In this work, FR IQA method is introduced. Several researchers have already established an understanding of the human visual system (HVS) [25] in order to apply it for image quality. The most important ambition of an objective IQA measure, is to produce a method that imitates the HVS, then, the quality of a perceived image is instinctively evaluated. To reach this goal, it is significant to compare the measure performance with the subjective assessment. In the literature, it has been proved that the most important role of human eyes is to pick the contour or structure information from vision field. Hence, HVS is totally suitable for this goal. The issue of developing an objective assessment measure is the principle reason of this research work. This later can abolish the expensive study of the subjective assessment, where the scores values generated from it are more closer to human judgment. For an important use, a new method based on distorted pixel and deformed color (GDCM), which is useful for practical applications, such as compression and quality improvement, is developed to assess the image quality. Experiments are carried out using sets of reference images with its deformed versions from TID2008 database [15], CSIQ database [16]; and LIVE database [14], TID2013 database [17]. Some existing models are involved in the comparison of the proposed method such as SSIM [9, 27], PSNR [9]; VSNR [9, 24], MS-SSIM [9, 1]; IFC [9, 22], NQM [9, 26]; VIF [9,23], DCTex [4]; Fsim [7], MAD [11]; GSM [10], GSDM [8]; and GVRO (the gradient similarity and visual region of interest based Ruderman operator measure and the distance transform (DT) [5]) [20], DTSSIMC (color distortion and gradient similarity combined with structure, luminance and contrast comparison method) [21]. The rest of the paper is organized as follows. In section 2, some algorithms of the image quality 54 Informatica 46 (2022) 53–65 A. Zeggari et al. measurement are presented. GDCM is presented in section 3. Results are reported in Section 4. Section 5 is conclusions and future works. 2 Related works The most used measures are MSE and PSNR. These later are failed in the measurement of visual quality as perceived by the human visual system (HVS). Therefore, numerous attempts have been made to design IQA measures inspired from the human visual system (HVS). These types of metrics highlight the importance of the sensitivity of the HVS to different visual signals, for instance contrast, frequency content, luminance and the interaction between different signal components. The two examples are the noise quality measure (NQM) [26] and the visual signal-to-noise ratio (VSNR) [24]. In the few past years Z. Wang et al. proposed a new metric named Structural Similarity Index (SSIM) [27] based on the measurement of structure distortion. In SSIM three components are calculated; the structure, contrast and luminance are its fundamental elements. Although its successful in IQA, SSIM struggle in the evaluation of the noisy and blurry images [2]. Several works are introduced in the literature [2, 3] trying to improve this latter by combining new features with the original one (SSIM). The first improvement is presented in [2] called GSSIM (Gradient Similarity). Sobel operator is used to achieve the edge information due to its simplicity and efficiency. This later is utilized in determination of edge information where the contrast comparison and structure comparison in [27] are replaced by the gradient-based contrast comparison and structure comparison respectively. This measure is very remarkable in employing edge information with SSIM [27], but it cannot be suitable for color distortion quality evaluation. The multi-scale structural similarity (MS-SSIM) index [1] has resulted in much better performance than its single-scale counterpart. In [22, 23] information theory is presented for the judgment of image fidelity and two methods are proposed for the assessment of full- reference image quality. The information fidelity criterion (IFC) [22] quantifies the information shared between the reference image and the distorted images, while the visual information fidelity model (VIF) [23], which is a extension of the information fidelity metric (IFC), employed the reference image as well to calculate the relative fidelity of the information. IFC and VIF were derived from a statistical model for natural scenes, a model for image distortions, while VIF is inspired from a model of the human visual system. All of them are able to evaluate the quality of an image. MS-SSIM and SSIM share a common error when combining a single quality from a local quality map, all positions are considered of equal importance. In VIF, images are subdivided into separate sub-bands and these sub-bands may have different weights in the pooling step; however, within each sub-band, each position is always given the same value. The most apparent distortion algorithm (MAD) [11] uses two techniques. Thus, local luminance and a contrast masking check out high quality images. Changes Table 1: Summary of the Related works. Ref Year Pearson linear correlation coefficient (CC) DATABASES MICT [30] (2000) LIVE JPEG/ JPEG2000 [14] (2003) LIVE [14] (2004) IVC [29] (2005) LIVE [14] (2005) A57 [31] (2007) toyama [28] (2008) CSIQ [16] (2009) TID2008 [15] (2009) WIQ [32] (2010) TID2013 [17] (2013) NQM [26] 2000 / / / / / / / / / / / MS-SSIM [1] 2003 / 0.969 / / / / / / / / / SSIM [27] 2004 / / 0.967 / / / / / / / / IFC [22] 2005 / / / / 0.929 / / / / / / VIF [23] 2006 / / / / 0.950 / / / / / / VSNR [24] 2007 / / / / 0.889 / / / / / / MAD [11] 2010 / / / / 0.968 / 0.895 0.950 0.831 / / Fsim [7] 2011 0.908 / / 0.938 0.960 0.925 / 0.912 0.874 / / DCTex [4] 2011 / / / used used used used used used / / GSM [10] 2012 / / / 0.923 0.952 0.904 0.925 0.914 0.858 / / GSDM [8] 2015 / / / 0.925 0.961 0.903 / 0.955 0.879 0.87 / DTSSIMC [21] 2018 / / / / 0.953 0.932 / 0.947 0.887 / 0.889 GVRO [20] 2021 / / / 0.940 0.961 0.933 0.903 0.914 0.877 0.867 / Color distortion and edge feature for perceptual quality assessment Informatica 46 (2022) 53–65 55 in the local dimensions of spatial-frequency components are used for low-quality images. In [4], DCTex metric is proposed with consideration of the texture masking effect and contrast sensitivity function. The metric is able to detect image distortion that is common in real-world applications. Another measure [7] that uses the phase congruency [6] is proposed to enrich IQA literature. Even it gives good results, it took more time to make an assessment. The pixel-wise gradient magnitude similarity deviation (GSM) [10] explores the image gradient feature to record image local structures. GSM computes the similarity among the gradients of reference and distorted images, and then calculates a few more detail. The gradient similarity and distorted pixel measures (GSDM) are utilized for IQA in [8]. Following modifications of the reference and the distorted pictures with distorted pixel measure and gradient mask, the gradient similarity and distorted pixel measures map among the reference and the distorted images are calculated using a simple function. The distance transform, color distortion and gradient similarity combined with structure, luminance and contrast comparison method (DTSSIMC) [21] is proposed to deal with SSIM to process color pictures by adding the color distortion idea and DT [5]. The pictures were first turned to gradient images. The gradient pictures are then used to compute the traditional SSIM components. Following that, DT images are computed. The color distortion is finally established. Even, DTSSIMC employs color distortions, it took more time to predict image quality score. A novel FR IQA method called gradient similarity and visual region of interest based Ruderman [12] operator measure (GVRO) is suggested [20]. As a result, the proposed scheme increases the effectiveness of IQA measures by using edge information as well as regions of interest and the Ruderman measure. Five imaging components are calculated based on the image characteristic. Firstly, the reference and test pictures are converted using the Ruderman operator, yielding Ruderman images. Secondly, the visual region of interest is calculated using local entropy. Then, Canny and suggested gradient are utilized to obtain gradient pictures from reference and test pictures, as well as, gradient maps are created using prior images. Lastly, the proposed approach is derived from all of the measurements. On the other hand, because structural information cannot represent color changes between the reference picture and the distorted image, the above IQA approaches cannot appropriately evaluate image color distortion. Furthermore, color images are increasingly being employed in our daily lives and, in addition, color information carries significant signals for visual perception. Color information should thus be considered in order to increase the accuracy of IQA approaches. This work developed the color similarity (CS) method by proposing an enhancement of gradient similarity based distorted pixel measure (GSDM) [8] with the incorporation of color distortion component inside it. It is mentioned even the gradient operator extract the edge from image, and then it is used in IQA as the previous work [33-38], one found that the gradient operator cannot differentiate color distortion in image. To avoid these issues, the transformation of color image to another image coded YIQ color space [13] is investigated. Consequently, the gradient similarity based distorted pixel and deformed color measure (GDCM) is emerged. To summary all related works used in this paper, the table 1 is established. The accuracy of these works is introduced by using the pearson linear correlation coefficient (CC), where the values close to value one or minus one are suitable for the best CC. Only the values of CC of database used in the related work are mentioned. Some values of CC are not introduced, the word "used" is utilized to show that this database is explored by this work but the CC is not computed, for instance, DCTex [4] work. The details on the formula of CC and databases are explained in the result section. Figure 1: The proposed IQA measure framework. 56 Informatica 46 (2022) 53–65 A. Zeggari et al. 3 The gradient similarity based distorted pixel and deformed color measure In this stage, IQA is reduced to full-reference. It is known that HVS extracts the edge or structure from vision field. A new measure based on edge information is proposed taking into account this recent concept. Moreover, the pixel distortion is computed using Ruderman operator [12]. The color distortion is computed in this later to improve the former one [8]. The deformed and reference images are noted as Dis (R, C) and Ref(R, C) respectively. All of them have R × C pixels. The proposed method structure is set as follows for this purpose: ▪ Compute edge information utilizing gradient similarity. ▪ Determine distorted pixels using Ruderman operator. ▪ Find color distortion. ▪ Determine spatial pooling approach for proposed measure. A simple flowchart depicting computation of the proposed measure is shown in Figure 1. The following variables and abbreviations used in the proposed method and the rest of manuscript are defined as: Ref: reference image. Dis: deformed image. R × C: image size. CFI_map: color similarity map of hue (I). CFQ_map: color similarity map of saturation (Q) channel information. 𝐷𝑅𝑒𝑓 : distorted reference. 𝐷𝐷𝑖𝑠 : deformed distorted image Y: brightness. 𝜇 (𝑘 , 𝑙 ) : local mean within the 3×3 block surrounding position (𝑘 , 𝑙 ). 𝜎 (𝑘 , 𝑙 ) : standard deviation of 𝑌 (𝑘 , 𝑙 ) within the block. 𝐷𝑀 _𝑚𝑎𝑝 : distorted map. G 1 : gradients magnitude of reference image. G 2 : gradients magnitude of deformed image. 𝐺 _𝑚𝑎𝑝 : Gradient map. GDC_map: deformed color measure map. GSDM: gradient similarity and distorted pixel measures. ROCC: Spearman’s rank order correlation coefficient. SSIM: structural similarity index measure. TID: Tampere image database. CSIQ: Categorical Subjective Image Quality. PSNR: peak signal-to-noise ratio. CC: Pearson’s linear correlation coefficient. MS-SSIM: multi-scale structural similarity index measure. NR: no-reference image quality assessment. RR: reduced-reference image quality assessment. FR: full-reference image quality assessment. IQA: image quality assessment. MOS: mean opinion score. ROCC: Kendall’s rank order correlation coefficient. HVS : human visual system. GVRO: gradient similarity and visual region of interest based Ruderman operator measure. DT :the distance transform. DTSSIMC: color distortion and gradient similarity combined with structure, luminance and contrast comparison method . NQM: noise quality measure. VSNR: visual signal-to-noise ratio. IFC : information fidelity criterion. VIF : visual information fidelity model. MAD: most apparent distortion algorithm. GSM: The pixel-wise gradient magnitude similarity deviation. CS :Solor Similarity. GDCM: Gradient Similarity based distorted pixel and deformed Color Measure. DMOS P: predicted Difference Mean Opinion Score. RMSE: Root mean square prediction error. KROCC: Kendall rank-order correlation coefficient. 3.1 Color distortion measure The edge information delivered by the gradient operator cannot show the distortion in color images. So, some particular measurements are used to deal with information delivered by color. The exchange between RGB to YIQ color space [13] is given as follows: [ 𝑌 𝐼 𝑄 ] = [ 0.299 0.587 0.144 0.596 −0.275 −0.321 0.212 −0.528 0.311 ] [ 𝑅 𝐺 𝐵 ] (1) The chromatic channels of reference (Ref) and distorted (Dis) images are: I 1 (I 2), and Q 1 (Q 2), they measured with the equation (1). In addition, Y 1 and Y 2 are the gray images of Ref and Dis respectively. They will be used in computing the others metrics. The chromatic features of I and Q are employed to calculate CFI_map and CFQ_map, the similarity is defined as follows: 𝑪𝑭𝑰 _𝒎𝒂𝒑 = 𝟐 𝑰 𝟏 . 𝑰 𝟐 + 𝑻 𝟑 𝑰 𝟏 𝟐 + 𝑰 𝟐 𝟐 + 𝑻 𝟑 (2) 𝑪𝑭𝑸 _𝒎𝒂𝒑 = 𝟐 𝑸 𝟏 . 𝑸 𝟐 + 𝑻 𝟑 𝑸 𝟏 𝟐 + 𝑸 𝟐 𝟐 + 𝑻 𝟑 where T 3=(T 2 . 255) 2 , T 2 << 1. 3.2 Ruderman operator The dissimilarity between the test and reference images is calculated by Ruderman operator [12]. The formulas that calculate the distorted reference (𝐷𝑅𝑒𝑓 ) image is given by: 𝑫𝑹𝒆𝒇 ̂ (𝒌 , 𝒍 ) = 𝒀 𝟏 (𝒌 , 𝒍 ) − 𝝁 (𝒌 , 𝒍 ) 𝝈 (𝒌 , 𝒍 ) + 𝟏 (3) Where, k ∈ 1, 2 … R, l ∈1, 2 … C are spatial indices Color distortion and edge feature for perceptual quality assessment Informatica 46 (2022) 53–65 57 𝝁 (𝒌 , 𝒍 ) = 𝟏 (𝟐𝐈𝐈 + 𝟏 )(𝟐𝐉𝐉 + 𝟏 ) ∑ ∑ 𝒀 𝟏 (𝒌 + 𝒊𝒊 , 𝒍 + 𝒋𝒋 ) 𝑱𝑱 𝒋𝒋 =−𝑱𝑱 𝑰𝑰 𝒊𝒊 =−𝑰𝑰 (4) 𝝈 (𝒌 , 𝒍 ) = 𝟏 (𝟐𝐈𝐈 + 𝟏 )(𝟐𝐉𝐉 + 𝟏 ) √ ∑ ∑ [𝒀 𝟏 (𝒌 + 𝒊 , 𝒍 + 𝒋 ) − 𝝁 (𝒌 , 𝒍 )] 𝟐 𝑱𝑱 𝒋𝒋 =−𝑱𝑱 𝑰𝑰 𝒊𝒊 =−𝑰𝑰 (5) In the previous formulas the local mean 𝜇 (𝑘 , 𝑙 ) is computed within 3×3 block. Also, the standard deviation 𝜎 (𝑘 , 𝑙 ) of 𝑌 1 (𝑘 , 𝑙 ) is measured with the same size of block. II and JJ values are fixed to 1. The deformed distorted image, which calculated with the same previous formulas, is named 𝐷𝐷𝑖𝑠 . Combining 𝐷𝑅𝑒𝑓 and 𝐷𝐷𝐼𝑆 the distorted map (𝐷𝑀 _𝑚𝑎𝑝 ) is emerged and is expressed in the following formula 𝐷𝑀 _𝑚𝑎𝑝 = 2𝐷𝑅𝑒𝑓 . 𝐷𝐷 𝑖𝑠 + 𝑇 1 𝐷𝑅𝑒𝑓 2 + 𝐷𝐷 𝑖𝑠 2 + 𝑇 1 (6) where T 1=(T 2 . 255) 2 , T 2 << 1. 3.3 Edge similarity detection The gradient process enables identify the highest change in the intensity or color in an image. The image's edges always seem to have a high gradient value. When there is a smooth area of the image, the gradient value is reduced. In the discrete domain, the gradient amplitude could generally computed using certain operators and estimate the derivative of the picture function using the difference between neighboring pixels. The alteration of each pixel in the picture is generally examined in the conventional image gradient method, and the first or second derivative of nearby edges is utilized to determine the gradient operator in the original image. For convolution computations, tiny region patterns are often employed. Edge image has important rule in vision field. This important information is produced from image using more edges detection. The gradient is employed in the proposed measure to compute this information. A new operator is proposed to generate this later. It is a pair of 3×3 convolution kernels, and it identifies the horizontal and vertical boundaries in images. It is introduced in the following formula: Gx Gy Mask ( 27.5 0 −27.5 34 0 −34 27.5 0 −27.5 ) 1 ( 27.5 34 27.5 0 0 0 −27.5 −34 −27.5 ) Gradient magnitude is given by equation (7) |𝐺 | = √𝐺𝑥 2 + 𝐺𝑦 2 (7) Gradients magnitude for reference (𝒀 𝟏 ) and deformed (𝒀 𝟐 ) images are calculated using the previous equation. G 1 and G 2 are the gradients magnitude of reference and deformed images respectively. Afterwards, the Gradient map (𝐺 _𝑚𝑎𝑝 ) is defined as 𝐺 _𝑚𝑎𝑝 = 2𝐺 1 . 𝐺 2 + 𝑇 1 𝐺 1 2 + 𝐺 2 2 + 𝑇 1 (8) 3.4 Combined measures In this stage all previous computed measures are combined to form the gradient similarity based distorted pixel and deformed color measure map (GDC_map). Then, GDCM is computed from GDC_map as its standard deviation, it is represented by the following equations. 𝑮𝑫𝑪 _𝒎𝒂𝒑 = 𝑫𝑴 _𝒎𝒂𝒑 . 𝑮 _𝒎𝒂𝒑 . 𝑪𝑭𝑰 _𝒎𝒂𝒑 . 𝑪𝑭𝑸 _𝒎𝒂𝒑 (9) 𝑮𝑫𝑪𝑴 = √ 𝟏 𝐑 . 𝐂 ∑ ∑(𝑮𝑫𝑪 − 𝑮𝑫𝑪 _𝒎𝒂𝒑 (𝒑 , 𝒒 )) 𝟐 𝐑 𝐪 =𝟏 𝐂 𝐩 =𝟏 (10) Where 𝑮𝑫𝑪 = 𝟏 𝐑 . 𝐂 ∑ ∑ 𝑮𝑫𝑪 _𝒎𝒂𝒑 (𝒑 , 𝒒 ) 𝐑 𝐪 =𝟏 𝐂 𝐩 =𝟏 (11) Figure 2 shows a flowchart of High-level overview of the proposed method demonstrating the suggested measure's calculation. 4 Experimental results and analysis This section contains the outcomes of our experiments. Section 4.1 first introduces the benchmark IQA datasets that were employed. Section 4.2 then discusses the assessment measures and procedure used. Section 4.3 concludes with a comparison of proposed method to the state-of-the-art. Figure 3: Reference images in databases TID2008 and TID2013. 58 Informatica 46 (2022) 53–65 A. Zeggari et al. 4.1 Databases The proposed method has been tested on many databases. The live database [14], TID2008 database [15], CISQ database [16] and TID2013 database [17] are used in these tests. In terms of the number of reference images, the number of distorted pictures, the number of quality distortion categories, the number of human observers, and the image format, these four databases are highly varied. The Tampere Image Database (TID2008) [15] is intended for evaluation of full-reference image visual quality assessment metrics. TID2008 allows estimating how a given metric corresponds to mean human perception. The TID2008 contains 25 reference images (see figure 3) and 1700 distorted images (25 reference images × 17 types of distortions × 4 levels of distortions). Reference images are obtained by cropping from Kodak Lossless True Color Image Suite. All images are saved in database in Bitmap format without any compression. File names are organized in such a manner that they indicate a number of the reference image, then a number of distortion's type, and, finally, a number of distortion's level: "iXX_YY_Z.bmp". The MOS was obtained from the results of 838 experiments carried out by observers from three countries: Finland, Italy, and Ukraine (251 experiments have been carried out in Finland, 150 in Italy, and 437 in Ukraine). Totally, the 838 observers have performed 256428 comparisons of visual quality of distorted images or 512856 evaluations of relative visual quality in image pairs. Higher value of MOS (0 - minimal, 9 - maximal, MSE of each score is 0.019) corresponds to higher visual quality of the image. Color space transforming Figure 2: High-level overview of the proposed method. Reference image Test image Y 1 I 1 Q 1 Y 2 I 2 Q 2 G 1 G 2 𝐺 _𝑚𝑎𝑝 𝐷𝑅𝑒𝑓 𝐷𝐷 𝑖𝑠 𝐷𝑀 _𝑚𝑎𝑝 𝑪𝑭𝑰 _𝒎𝒂𝒑 𝑪𝑭𝑸 _𝒎𝒂𝒑 𝑮𝑫𝑪 _𝒎𝒂𝒑 Color space transforming Color distortion and edge feature for perceptual quality assessment Informatica 46 (2022) 53–65 59 The Tampere Image Database (TID2013) [17] is the largest image quality database available in the public domain, both in terms of test images and number of subjects. TID2013 is an extension of TID2008. TID2013 is intended for evaluation of full-reference image visual quality assessment metrics. TID2013 allows estimating how a given metric corresponds to mean human perception. The TID2013 contains 25 reference images (see figure 3) and 3000 distorted images (25 reference images x 24 types of distortions x 5 levels of distortions). Reference images are obtained by cropping from Kodak Lossless True Color Image Suite. The Categorical Subjective Image Quality (CSIQ) is an image database [16]. It comprises 30 original images (see figure 4) from which degraded images are generated using six types of degradations at four to five levels. The degradations used in CSIQ are: JPEG, JPEG2000, global contrast decrements, additive pink Gaussian noise, additive white Gaussian noise, and Gaussian blurring. CSIQ consists of 866 degraded images being the result of the deformation of the original images by the different types of previous degradations. CSIQ images are subjectively evaluated based on linear displacement of the images. Four liquid crystal display (LCD) screens at 1920×1200 resolution were calibrated following RGB color space and placed side by side with equal viewing distance to the viewer. Observers were instructed to keep the viewing distance stable at approximately 80 cm. All degraded versions of an original image were viewed simultaneously through the screen. Each observer placed these images in the screen, in which the horizontal distance between two images reflects the perceived quality of these images. An image placed close to the others means that: the observer thinks that their quality is not much different. On the other hand, placing a distant image to the left of the others means that the viewer thinks the old image is much worse in quality comparing to the last image. As a final step, image ratings are realigned. In this experiment, 35 observers participated. Observers include male and female with normal visual acuity or correct to normal. The ages of the observers range from 21 to 35. In general, the image database contains 5000 subjective estimates that are reported in the form of DMOS (Difference Mean Opinion Score). The LIVE database [14] consists of 779 distorted images generated from 29 reference images (see figure 5). This later was constructed from twenty nine high resolution color images that were collected from the internet and CDs. These images consist of images of faces, people, animals, scenes, synthetic objects etc... Most of the images have the size 768 × 512 pixels. Five types of deformations were chosen in order to degrade the images. These types can occur in real applications. The types of deformation are: compression in JPEG format (233 images), compression in JPEG2000 format (227 images), Additive white Gaussian noise (AWN) in the RGB components (174 images), Gaussian blur (GB) in RGB components (174 images), and simulated fast fading Rayleigh channel (FF) (174 images). These distortions reflect a wide range of image degradations, from smoothing, to structured distortion, and random noise. The level of distortion was changed to produce images at a wide range of quality, from imperceptible levels to high levels of degradation that would significantly impede cognitive understanding of image content. Table 2 summarizes the properties of these four databases. 4.2 Evaluation metrics and protocol The non-linear mapping is computed among the objective and subjective scores [18]. A set of the predicted Difference Mean Opinion Score (DMOS P) is obtained from the value calculated by the objective quality methods. Five parameters non-linear mapping (C 1, C 2, C 3, C 4 and C 5) are used in this process. This transformation is applied using a logistic function of the equation (12) [19]. 𝐷𝑀𝑂𝑆 𝑝 = 𝐶 1 fun(𝐶 2 , (𝑂𝑀 − 𝐶 3 )) + 𝐶 4 + 𝐶 5 (12) fun(ℎ, 𝑂𝑀 ) = 1 2 − 1 1 + exp(𝑂𝑀 ℎ) (13) Where OM is the value calculated by the objective measure. C 1, C 2, C 3, C 4, C 5 are chosen for the best fit. Then, four metrics are computed to benchmark the proposed method: the Spearman rank-order correlations coefficient (ROCC), the Pearson linear correlation coefficient (CC); and the Root mean square prediction error (RMSE), Kendall rank-order correlation coefficient (KROCC). Figure 4: Categorical Subjective Image Quality (CSIQ) Image database: All 30 Source images. 60 Informatica 46 (2022) 53–65 A. Zeggari et al. The first index is the Spearman rank-order correlations coefficient (ROCC) [10], commonly employed. The term correlation is used to designate the connection or the relation between any two variables. In statistics, this term is utilized to quantify the link between two quantitative variables. This junction can be either symmetric (possibility of permuting the quantitative variables x and y) or asymmetric (one of the values depends on the other, and therefore impossible to permute the quantitative variables x and y). To perform a Spearman rank correlation measurement between two quantitative variables (one representing the metric prediction values, and the other the MOS/DMOS values), the observations must be independent, the link between the two variables must be linear, and the distribution of the values of the variables must not follow a normal law. This method has the particularity of not using the values of the observations but their ranks. In the context of metrics without reference, the calculation proceeds as follows (the first column represents the predictions of the metric, the second column represents the values of the MOS or DMOS): - Sorting of the first column (keeping the association with the values of the second column). - Assign an ascending order number (rank) for the first sorted column. - Sorting of the second column (keeping the association with the last rows). - Assign an ascending number for the second sorted column. - Calculate the square of the difference between each two rows. Spearman's rank correlation coefficient is then calculated by: ) 1 ( )) ( ) ( ( 6 1 2 2 − − − =  n n i DMOS i DMOS ROCC p (14) Where the index i is the square of the difference of each two rows and n is the total number of observations. The second one is the Pearson linear correlation coefficient (CC) between subjective (DMOS) and objective (DMOS P) scores. It supplies an evaluation of the prediction accuracy and it is defined by:    − − − − = = 2 2 1 ) ) ( ( ) ) ( ( ) ) ( )( ) ( ( p p n i p p DMOS i DMOS DMOS i DMOS DMOS i DMOS DMOS i DMOS CC (15) Where the index i denotes the image sample and n denotes the number of samples. The third one is the Root mean square prediction error (RMSE) between subjective (DMOS) and objective (DMOS P) scores. It is defined by: ( )  = − = n i p i DMOS i DMOS n RMSE 1 2 ) ( ) ( 1 (16) Finally, the Kendall rank-order correlation coefficient (KROCC) is defined as 1)N - 0.5(N KROCC D C − = (17) where C stands for the number of concordant pairs between subjective (DMOS) and objective (DMOS P) scores, while D denotes the number of discordant pairs and N is the number of observations. These measures evaluate an objective aptitude model to provide consistently perfect predictions for every kind of images and do not fail extremely for a subset of images, i.e., prediction consistency. ROCC and KROCC evaluate the prediction monotonicity. RMSE and CC judge the prediction accuracy. Values close to one (1) or minus one (-1) are suitable for the best ROCC, KROCC and CC. While a big number is a sign of bad RMSE. 4.3 Discussion and performance comparison Fourteen state-of-the-art measures are compared with GDCM to show the robustness of this latter. MS-SSIM, VSNR, PSNR, SSIM, NQM, DCTex, VIF, GSM, MAD, IFC, GVRO, DTSSIMC, Fsim and GSDM are the state- of-the-art methods used in this comparison. The four metrics CC, KROCC, ROCC, and RMSE are implicated in the measurement of the performance of 14 methods and the proposed one. Tables 3–7 show all these results. The top three measures are highlighted in bold. From the results presented in Tables 3–7, the proposed GDCM method is able to do better than other state-of-the-art algorithms in terms of CC and ROCC Figure 5: Reference images in databases Live. Table 2: Four databases and their characteristics. Database Source Images Distorted Images Distortion Types Image Type Observers TID2008 25 1700 17 color 838 CSIQ 30 866 6 color 35 LIVE 29 779 5 color 161 TID2013 25 3000 24 color 985 Color distortion and edge feature for perceptual quality assessment Informatica 46 (2022) 53–65 61 values. Specifically, GDCM outperforms the first best method in terms of direct average ROCC values and the second best by approximately 0.001 with regard to direct average CC values (see Table 7). However, an interesting result is obtained from the comparison of the GDCM with VIF, MS-SSIM; PSNR, Fsim; GSDM, and DTSSIMC in Tables 5. The values of CC and ROOC are closer to 1; this means that GDCM performs well against these methods or earlier works. In addition, the performance of VIF, MS-SSIM, PSNR, Fsim, GSDM and DTSSIMC in Table 5 is more less than GDCM, for instance VIF values are CC=0.928/ROOC=0.920, MS-SSIM values are CC=0.899/ROOC=0.913, PSNR values are (a) (b) (c) (d) Figure 6: Scatter plots of subjective scores versus scores from the proposed scheme on IQA databases: (a) Live; (b) TID2013; (c) TID2008; (d) CSIQ. (a) (b) (c) (d) (e) (f) Figure 7: Scatter plots of subjective scores versus scores from some of the state-of-the-art algorithms on CSIQ database: (a) PSNR; (b) MS-SSIM; (c) VIF; (d) Fsim ;(e) GSDM (f) DTSSIMc. 62 Informatica 46 (2022) 53–65 A. Zeggari et al. CC=0.800/ROOC=0.801, Fsim values are CC=0.919/ROOC=0.931, GSDM values are CC=0.955/ROOC=0.957 and DTSSIMC values are CC=0.947/ROOC=0.956. PSNR values indicate that this later is not very well harmonized with perceived visual quality. The examination of the results obtained with MS-SSIM, lead us to say that GDCM has a significant performance on MS-SSIM. It can be also observed from Table 8, that the proposed GDCM provides the best results on two out of four IQA benchmark databases. Moreover, it gives the second best CC and ROCC values on TID2013. Its three first places and especially the first ranking among well recognized methods in the literature confirms its location and its robustness and efficiency in the field of image quality assessment. Figure 6 depicts the scatter plots of subjective scores against objective scores predicted by GDCM IQA method. While, figure 7 shows the scatter plots of subjective scores versus scores from some of the state-of- the-art algorithms (VIF, MS-SSIM, PSNR, Fsim, GSDM and DTSSIMC) on CSIQ database. The red curves in Figure 6-7 are obtained by a nonlinear fitting based on Eq. (12). Here X-axis represents the objective score computed by the proposed metric and Y-axis represents the DMOS or MOS obtained through subjective tests. It is obvious that the sample points are much closer to the fitted curve in Figure 6, which indicates that objective scores predicted by GDCM, are more consistent with subjective assessment than other methods. Furthermore, this observation is confirmed by examining Figure 6 (d) and Figure 7: the sample points are much closer to the fitted curve in Figure 6 (d), Whereas, the sample points are less close to the fitted curve especially in figure 7 (a), (b) and (d). Table 3: Live database and performance comparison. Method RMSE CC KROCC ROCC VIF 7.667 0.960 0.827 0.963 IFC 10.264 0.927 0.758 0.926 MS-SSIM 9.259 0.941 0.804 0.951 VSNR 10.469 0.924 0.763 0.928 PSNR 13.360 0.872 0.687 0.876 SSIM 8.945 0.945 0.796 0.948 MAD 6.924 0.967 0.842 0.967 Fsim 7.530 0.961 0.836 0.965 NQM 11.193 0.912 0.741 0.909 DCTex 8.990 0.944 0.807 0.948 GSM 9.038 0.944 0.813 0.955 GSDM 7.526 0.961 0.831 0.962 DTSSIMC 8.2754 0.9530 0.8182 0.9570 GVRO 7.596 0.961 0.831 0.963 GDCM 8.227 0.954 0.822 0.959 Table 4: TID2008 database and performance comparison. Method RMSE CC KROCC ROCC VIF 0.789 0.809 0.587 0.750 IFC 0.911 0.734 0.424 0.568 MS-SSIM 0.717 0.845 0.657 0.854 VSNR 0.981 0.682 0.535 0.705 PSNR 1.100 0.573 0.421 0.579 SSIM 0.855 0.771 0.577 0.775 MAD 0.747 0.831 0.645 0.834 Fsim 0.647 0.876 0.699 0.884 NQM 1.059 0.614 0.461 0.624 DCTex 1.111 0.561 0.410 0.497 GSM 0.715 0.846 0.665 0.855 GSDM 0.644 0.877 0.705 0.891 DTSSIMC 0.621 0.887 0.717 0.897 GVRO 0.645 0.877 0.704 0.885 GDCM 0.631 0.883 0.718 0.901 Table 5: CSIQ database and performance comparison. Method RMSE CC KROCC ROCC VIF 0.098 0.928 0.754 0.920 IFC 0.143 0.838 0.590 0.767 MS-SSIM 0.115 0.899 0.739 0.913 VSNR 0.158 0.799 0.624 0.810 PSNR 0.158 0.800 0.598 0.801 SSIM 0.133 0.861 0.691 0.876 MAD 0.082 0.950 0.797 0.947 Fsim 0.103 0.919 0.769 0.931 NQM 0.176 0.743 0.564 0.740 DCTex 0.161 0.792 0.642 0.804 GSM 0.116 0.898 0.740 0.913 GSDM 0.078 0.955 0.810 0.957 DTSSIMC 0.085 0.947 0.816 0.956 GVRO 0.107 0.927 0.763 0.914 GDCM 0.076 0.958 0.818 0.960 Table 6: TID2013 database and performance comparison. Method RMSE CC KROCC ROCC VIF 1.032 0.772 0.515 0.677 IFC 0.902 0.554 0.394 0.539 MS-SSIM 0.839 0.833 0.605 0.786 VSNR 0.788 0.740 0.508 0.681 PSNR 0.761 0.669 0.470 0.640 SSIM 0.686 0.790 0.559 0.742 MAD 0.596 0.827 0.604 0.781 Fsim 0.568 0.877 0.667 0.851 NQM 0.943 0.686 0.474 0.643 DCTex 0.660 0.650 0.457 0.586 GSM 0.698 0.846 0.626 0.795 GSDM 0.632 0.860 0.635 0.807 DTSSIMC 0.761 0.889 0.689 0.871 GVRO 0.636 0.858 0.631 0.801 GDCM 0.600 0.875 0.685 0.865 Color distortion and edge feature for perceptual quality assessment Informatica 46 (2022) 53–65 63 5 Conclusion In this work, the color distortion is introduced in GSDM. The color image coded in RGB color space in converted to another space including three components Y, I and Q. The deformed and gradient operator are computed from Y component, then the I and Q elements are used to compute the color distortion. The proposed measure is compared with twelve state-of-art methods. 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