Christophe Charrier

Abdelhakim Saadane

Christine Fernandez-Maloigne

Dimension reduction-based attributes selection in no-reference learning-based image quality algorithms

published or not. The documents may come

Dimension reduction-based attributes selection in no-reference learning-based image quality algorithms

Introduction

Lossy image compression techniques such as JPEG2000 allow high compression rates, but only at the cost of some perceived degradation in image quality. The way to evaluate the performance of any compression scheme is a crucial step, and more precisely available ways to measure the quality of compressed images. There is a very rich literature on image quality criteria, generally dedicated to specific applications (optics, detector, compression, restoration, . . . ). From several years, a number of researches have been conducted to design robust No-Reference Image Quality Assessment (NR-IQA) algorithms, claiming to have made headway in their respective domains. NR-IQA algorithms generally follow one of three trends. 1) Distortion-specific approaches: These employ a specific distortion model to drive an objective algorithm to predict a subjective quality score. These algorithms quantify one or more distortions such as blockiness [START_REF] Muijs | A no-reference blocking artifact measure for adaptive video processing[END_REF][START_REF] Song | A new no-reference assessmet metric of blocking artefacts on HVS masking effect[END_REF], blur [START_REF] Parvezsazzad | Noreference image quality assessment for jpeg2000 based on spatial features[END_REF][START_REF] Barland | Blind quality metric using a perceptual map for jpeg2000 compressed images[END_REF] or ringing [START_REF] Hantao | A no-reference metric for perceived ringing artifacts in images[END_REF][START_REF] Hu | Jpeg ringing artifact visibility evaluation[END_REF] and score the image accordingly. 2) Training-based approaches: these train a model to predict the image quality score based on a number of features extracted from the image [START_REF] Luo | A training-based no-reference image quality assessment algorithm[END_REF][START_REF] Tsoy | Noreference image quality assessment through interactive neuroevolution[END_REF][START_REF] Babu | No-reference JPEG image quality assessment using GAP-RBF[END_REF][START_REF] Moorthy | Visual importance pooling for image quality assessment[END_REF][START_REF] Moorthy | A two-step framework for constructing blind image quality indice[END_REF]. 3) Natural scene statistics (NSS) approaches: these rely on the hypothesis that images of the natural world (i.e. distortion free images) occupy a small subspace of the space of all possible images and seek to find a distance between the test image and the subspace of natural images [START_REF] Moorthy | A two-step framework for constructing blind image quality indice[END_REF][START_REF] Gabarda | Blind image quality assessment through anisotroy[END_REF][START_REF] Brandao | No-reference image quality assessment based on dct-domain statistics[END_REF].

Yet, all existing algorithms fail for at least one to correctly predict the quality of an image when degradation has not been learned. Degradation is not necessarily the same for the trial algorithms. Taking into account those failure cases will help to design a robust NR-image quality assessment algorithm. In this paper, we develop a NR-image quality assessment algorithm based on an attribute selection approach. All the attributes are extracted from usually used and well-known NR-IQA training-based algorithms. The trial NR-IQA algorithms used are the following: 1) BIQ-An [START_REF] Gabarda | Blind image quality assessment through anisotroy[END_REF], 2) BIQI [START_REF] Moorthy | A two-step framework for constructing blind image quality indice[END_REF], 3) DIIVINE [START_REF] Moorthy | Blind image quality assessment: From natural scene statistics to perceptual quality[END_REF], 4) BLIINDS [START_REF] Saad | A DCT statisticsbased blind image quality index[END_REF], 5) BLIINDS-2 [START_REF] Saad | Blind image quality assessment: A natural scene statistics approach in the dct domain[END_REF], 6) BRISQUE [START_REF] Mittal | No-reference image quality assessment in the spatial domain[END_REF], 7) NIQE [START_REF] Mittal | Making a "completely blind" image quality analyzer[END_REF]. The implementations of the algorithms were either publicly available on the Internet or obtained from the authors. A features vector is constructed from all attributes and a attribute selection process is designed to only keep descriptors that have been identified as meaningful with respect to the image. The rest of paper is organized as follows. Section II presents the used databases. The proposed new NR-IQA is given in Section III. The performance is evaluated in Section IV and a conclusion is made in Section V.

NR-IQA algorithms and image databases

Databases description

To provide comparison of NR-IQA algorithms, three publicly available databases are used: 1) LIVE database [START_REF]LIVE Image Quality Assessment Database[END_REF], 2) TID2008 database [START_REF] Ponomarenko | Color image database for evaluation of image quality metrics[END_REF] and 3) CSIQ image database [START_REF] Larson | Most apparent distortion: full-reference image quality assessment and the role of strategy[END_REF]. The LIVE database contains 29 original images on which five kinds of distortions have been applied to generate 770 degraded images. The TID2008 database contains 1700 distorted versions of 25 original images (from Kodak Lossless True Color Image Suite) applying 17 distortion types. The CSIQ database consists of 30 original images, each distorted using six types of distortions at four to five different levels as detailed above.

NR-IQA 1 NR-IQA 2 NR-IQA k      f 1 f 2 . . . f i         f i+1 . . . f i+ j       f l . . .

Tampere Image Database 2008 (TID2008)

The Tampere Image Database 2008 (TID2008) was created in 2008, for the evaluation of full-reference image quality assessment metrics and developed at the Tampere University of Technology, in Finland. The TID2008 contains 25 reference images and 1700 distorted images corresponding at 17 types of distortions on 4 levels. Reference images are obtained by cropping from Kodak Lossless True Color Image Suite (http://r0k.us/graphics/kodak/). All images are in BMP format at 384X512 pixels resolution. A software which developed based on Swiss System is using to conduct the psychophysical experiment. Mean Opinion Scores (MOS) were calculated from the subjective data. The MOS were 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. Subjective evaluations were made in standard PC laboratory or via the internet. http://www.computervisiononline.com/ dataset/tid2008-tampere-image-database-2008

Categorical Subjective Image Quality (CSIQ) Database

The Categorical Subjective Image Quality (CSIQ) Database was released by the Computational Perception and Image Quality Lab, at the Oklahoma state University, in 2010. It consists of 30 original images, each is distorted using six different types of distortions at four to five different levels of distortion. CSIQ images are subjectively rated base on a linear displacement of the images across four calibrated LCD monitors placed side by side with equal viewing distance to the observer.

The database contains 5000 subjective ratings from 35 different observers, and ratings are reported in the form of Difference of Mean Opinion Scores (DMOS). Subjective evaluations were made on pre-calibrated display and viewing distance is 70cm. http://vision.okstate.edu/?loc=vqa\_samviq

NR-IQA scheme design

General Scheme

All the trial NR-IQA methods applies the same principle: after computing a set of different features, a combination of this set is performed in different ways. In this paper, the design a NR-IQA algorithm is based on a new selection process of relevant attributes provided by different common NR-IQA methods. Fig 1 displays the general scheme of the proposed method. From all trial NR-IQA schemes, all features are computed. This yields to a set of n features. From this initial set a subset of M attributes is generated (under the constraint that M ≤ n) in order to keep the most relevant features with respect to some criteria. Then a combination of these M features is performed to design a NR-IQA algorithm scoring with a high correlation level with human judgments of image quality.

Attributes selection criteria

Given a set of visual attributes describing an image, we use a Manifold Learning method to project the data on a new lowdimensional space. Thus, nonlinear new discriminant features of the input data are yielded. The obtained low dimensional submanifold is used as a new representation that is transmitted to design the proposed NR-IQA algorithm.

When data objects are described by a large number of features (i.e., the data are of high dimension) it is often beneficial to reduce the dimension of the data. Dimension reduction can be beneficial not only for reasons of computational efficiency but also because it can improve the accuracy of the analysis. To deal with this issue, dimension reduction techniques are often applied as a data pre-processing step or as part of the data analysis to simplify the data model. This typically involves the identification of a suitable low-dimensional representation for the original high-dimensional data set. Dimensionality reduction methods can be divided into two sets whether the transformation is linear or nonlinear. We detail here the principles of Laplacian Eigenmaps (LE) [START_REF] Belkin | Laplacien eigenmaps for dimensionality reduction and data representation[END_REF] that will be used in this study.

Let

X = {x 1 , x 2 , • • • , x n } ∈ IR p be n sample vectors.
Dimensionality reduction consists in finding a new low-dimensional representation in IR p with q p. Given a neighborhood graph G associated to the vectors of X, one considers its adjacency matrix W where weights W i j are given by a Gaussian kernel

W i j = k(x i , x j ) = e - ||x i -x j || 2 σ 2 . ( 1
)
Let D denote the diagonal matrix with elements D ii = ∑ j W i j and ∆ denote the un-normalized Laplacian defined by ∆ = D -W . Laplacian Eigenmaps dimensionality reduction consists in searching for a new representation {y 1 , y 2 , • • • , y n } with y i ∈ IR n , obtained by minimizing 1 2 ∑ i j This is achieved by finding the eigenvectors y 1 , y 2 , • • • , y n of matrix ∆. Dimensionality reduction is obtained by considering the q lowest eigenvectors (the first eigenvector being discarded) with q p and is defined by the following operator h LE : x i → (y 2 (i), • • • , y q (i)) where y k (i) is the i th coordinate of eigenvector y k .

y i -y j 2 W i j = Tr(Y T ∆Y) with Y = [y 1 , y 2 , • • • , y n ].

Final quality score calculation

Once the laplacian eigenmaps is performed on initial data, all generated eigenvectors are descending ordered by their associated eigenvalues. Then data are projected on this eignespace. Let fi ) be the i-th projected data. The final quality score based on a selection process, namely Feature Selection-based Image Quality Index (FSIQI) can be expressed as a M-parameters function :

FSIQI = M ∏ i=1 ( fi ) α i (2)
where α i is a weight factor applied to the i-th projected data fi ) and M is the number of considered attributes. The main objective is to find optimal exponent values of (2).

The associated error function

From (2), the search for the exponent values seeks to minimize the error function

E(α i ; i = 1, • • • , M) = (3) min ∑ K j=1 (DMOS j -FSIQI j (α i )) 2
where K is the number of tested images for which the DMOS values are provided, and FSIQI j (.) are the quality computed rates obtained following a logistic regression as depicted in [START_REF] Vqeg | Final report from the video quality experts group on the validation of objective models of video quality assessment[END_REF].

In other words, the goal is to estimate the M exponent values that minimize the error function E(.). Since the error function is non-convex and may contain numerous local optima, the choice of search strategy to optimize it is important.

Search strategy

The Genetic Algorithm (GA) is a population-based stochastic search procedure that finds exact or approximate solutions to optimization and search problems. Modeled on the mechanisms of evolution and natural genetics, genetic algorithms uses directed random searches to locate optimal solutions in multimodal landscapes. Their basic principles were first introduced by Holland in 1975 [START_REF] Holland | Adaptation in natural and artificial systems[END_REF].

Usually, a simple GA is composed of three operations: selection, genetic operation, and replacement. GAs use a population, which is composed of a group of chromosomes, to represent the solutions of the system. Defining the solution representation of the system is the first task when applying GAs. The solution in the problem domain can then be encoded into the chromosome in the GA domain, and vice versa. Initially, a population is randomly generated. The fitting function then uses values from objective functions to evaluate the quality of fit of each chromosome. Next, a particular group of chromosomes is chosen from the population to be parents. The offsprings are then generated from these parents using genetic operations (crossover and mutation). The ----------0-01-11---1 100-01-111-1-1 100-01-000-010 0000010 DIIVINE --1-10--------111--01 100--0-111-101 10--00-00--000 0000-10 BLIINDS 00---00 000--10 -------000---0 1-1-10-000-0-0 000-0-0 00000-1 fitness of the offspring is then evaluated and used in replacement processes in order to replace the chromosomes in the current population by the selected off-spring. The GA cycle is then repeated until a desired termination criterion is satisfied, or the objective value is below the threshold. In this paper, M is the number of features used to compute FSIQI values. In that case, the GA domain represents a M-dimensional space in which one point is expressed as (α i , • • • , α M ), and the fitness function is defined by [START_REF] Parvezsazzad | Noreference image quality assessment for jpeg2000 based on spatial features[END_REF].

BLIINDS 2 011-10- 011--1- 111---1 ------- 111-101 ----0-- 0---0-0 0--0-00 BIQ-An 000-0-0 000-010 0-0-01- 000-010 -------000-010 000-010 0000010 NIQE 011-10- 01--11- 111-1-1 ----1-- 111-101 ------- 0-----0 --00-1- BRISQUE 111-101 11--111 111-1-1 1---1-1 111-101 1-----1 ------- --0--00 FSIQI 1111101 1111-01 11111-0 1--1-11 1111101 --11-0- --1--11 -------

Performance Evaluation

Apparatus FSIQI results are compared to results provided by all trial NR-IQA algorithms. To preform this evaluation, the Spearman Rank Order Correlation Coefficient (SROCC) is computed between the DMOS values and the predicted scores obtained from NR-IQA algorithms. Since the LIVE database has been used to find optimal α i and M parameters, both TID2008 and CSIQ databases will serve as test set.

In addition, to ascertain which differences between NR-IQA schemes performance are statistically significant, we applied an hypothesis test using the residuals between the DMOS values and the ratings provided by the IQA algorithms. This test is based on the t-test that determines whether two population means are equal or not. This test yields us to take a statistically-based conclusion of superiority (or not) of an NR-IQA algorithm.

How to choose M value ?

In order to investigate the optimal α i values and the M parameters needed to design FSIQI algorithm, we used the LIVE database as training set to compute initial features.

Finding the number M is rely to figure out the dimension i of the eigenspace. This can be expressed as ∀i ∈ [1, . . . , n],

arg min i (SROCC(FSIQI(i)) -SROCC(FSIQI(i + 1)) < ε) (4)
In this study ε = 0.1, and we found that for eigenspaces of more than 8 dimensions, corresponding SROCC values are very close and consecutive differences are lower than ε. This, only the 8 first eigenvectors are considered to define the eigenspace on which initial features will be projected on.

Comparison results

In order to evaluate the performance of the FSIQI algorithm, a comparison of SROCC values obtained from all trial NR-IQA schemes is performed on both TID2008 and CSIQ database. Table 2 presents obtained results when SROCC is computed between predicted scores and MOS values for the CSIQ Images database for all trial NR-IQA algorithms and the proposed one. One can observe that the performance of the trial NR-IQA algorithm vary according to degradation even if NIQUE and BRISQUE seem to be better than the remaining ones. However, FSIQI the proposed method, presents high performance whatever the degradation (except for the last one (Global contrast decrement)).

Table 3 presents obtained results when SROCC is computed between predicted scores and MOS values for the TID Images database subsets which are not common to the LIVE database and for all trial NR-IQA algorithms and the proposed one. One can also notice that the performance of the 7 trial NR-IQA algorithms are highly dependent on the considered degradation. BIQI performs better for masked noise, DIIVINE for high frequency noise, BLIINDS-II for additive noise, quantization noise and image denoising and JPEG2000 transmission errors, NIQE for spatially correlated noise and impulse noise. By contrast, FSIQI, equals or outperforms the best trial NR-IQA algorithm regardless of the considered degradation. Moreover, the SROCC value of FSIQI metric is equal or greater than 0.772 for the first seven degradations. For a learning-based metric as FSIQI, this performance remains very interesting since the training set and the test set have no common degradations. used to provide statistical significance of NR-IQA/DMOS on TID database. Each entry in this table is coded using 12 symbols. The position of each symbol corresponds to one subset of the TID database as expressed in table 3. Each symbol gives the result of the hypothesis test on the subset. If the symbol equals '1', the NR-IQA on the row is statistically better than the NR-IQA on the column ('0' means worse, '-' is used when NR-IQAs are indistinguishables). On can observe that difference between quality scores predicted with FSIQI and any trail algorithms is most of the time significant when the entire database is considered or when any subset is used. Since the learning process is applied on LIVE database to design FSIQI, this result illustrates its capability to judge well image quality when applied degradations are not learnt.

Tables 5 shows similar results when CSIQ database is considered. The position of the symbol represents the tested subsets: Additive pink Gaussian noise, JP2K, JPEG, Gaussian noise, Gaussian blur, Global Contrast Decrements, all data. Considering the global performance on all data subsets, FSIQI over performs all other tested NR-IQA methods, except BLIINDS. Yet for one particular degradation (Global Contrast Decrements associated to the 6th digit), FSIQI seems to be less efficient than other trial algorithms to predict quality scores.

Finally, to compare the computational complexity of the proposed algorithm, we measured the average computation time required to assess an image of size 512 × 578 (using a computer with Intel Core-I7 processor at 2.2GHz). Table 6 reports the measurement results, which are rough estimates only, as no code optimization has been done on our Matlab implementations. It can be observed that the proposed method is one of the time consuming method but less than BLIINDS. This is not really surprising, since FSIQI consists in using all attributes of prior NR-IQA algorithms (around 180 attributes) to compute final score in another space.

Yet, one can remark that since the dimensionality of the eigenspace is to be equal 8, this means that the fundamental NR-IQA problem exists in a space of around 8 attributes.

Conclusion

We have used a selection process of quality attributes based on manifold to design a new NR-IQA scheme, named FSIQI. Considering all attributes used by seven trial NR-IQA algorithms, a high dimensional feature vector is obtained and the reduced applying laplacian eigenmaps. We have shown the new FSIQI algorithm only needs eight features to performs well in this new representation space of features. The method correlates highly with human perception of quality, and outperforms recent NR-IQA algorithms.

Figure 1 .

 1 Figure 1. General scheme of the proposed NR-IQA algorithm based on combination of features.

  -1001-1111 1111--110111 ------------

Trial NR-IQA schemes

  All attributes considered in this paper are extracted from NR-IQA learning-based metrics summarized in Table1. This table also gives the number of attributes used by each algorithm.

	NR-IQA algo-	comments	#	at-
	rithm		tributes
	BIQI	Machine learning-based ap-	18
		proach (SVM).
	DIIVINE	Classification (SVM) and Re-	88
		gression (SVR)
	BLIINDS	Machine learning-based ap-	12
		proach (Probabilistic model)
	BLIINDS-II	Machine learning-based ap-	12
		proach (Probabilistic model)
	BIQ-An	Renyi entropy measure along	6
		various orientations
	NIQE	Space domain natural scene	18
		statistic model
	BRISQUE	Natural scene statistic-based	18
		distortion-generic

Table 1 : NR-IQA trial Algorithms

 1

Table 2 : SROCC values computed between predicted scores and MOS values for the CSIQ Images database.

 2

	CSIQ subset	BIQI DIIVINE BLIINDS BLIINDS-II BIQ-An NIQE BRISQUE FSIQI
	JP2k	0.708	0.830	0.575	0.895	0.460	0.906	0.866	0.901
	JPEG	0.867	0.799	0.264	0.901	0.012	0.883	0.903	0.902
	Gaussian Noise	0.324	0.176	0.293	0.379	0.091	0.299	0.252	0.402
	Add. Gaussian Pink Noise	0.879	0.866	0.555	0.801	0.303	0.810	0.925	0.917
	Gaussian Blur	0.771	0.871	0.774	0.891	0.739	0.892	0.903	0.894
	Global Contrast Decrement	0.585	0.396	0.078	0.012	0.767	0.232	0.029	0.156
	Cumulative subsets	0.619	0.596	0.170	0.577	0.286	0.628	0.566	0.699
	TID2008 subset	BIQI DIIVINE BLIINDS BLIINDS-II BIQ-An NIQE BRISQUE FSIQI
	Additive noise in color compo-
	nents is more intensive than addi-tive noise in the luminance com-	0.46	0.366	0.441	0.778	0.117	0.742	0.495	0.781
	ponent
	Spatially correlated noise	0.589	0.722	0.245	0.446	0.311	0.758	0.584	0.746
	Masked noise	0.897	0.872	0.688	0.866	0.175	0.854	0.623	0.895
	High frequency noise	0.787	0.864	0.583	0.586	0.016	0.687	0.582	0.855
	Impulse noise	0.406	0.188	0.039	0.719	0.110	0.812	0.723	0.788
	Quantization noise	0.747	0.824	0.663	0.839	0.570	0.817	0.799	0.772
	Image denoising	0.306	0.759	0.509	0.760	0.481	0.605	0.570	0.796
	JPEG2000 transmission errors	0.367	0.021	0.211	0.606	0.262	0.493	0.260	0.489
	Non eccentricity pattern noise	0.010	0.032	0.033	0.142	0.067	0.016	0.163	0.131
	Local blockwise distortions of different intensity	0.022	0.060	0.150	0.457	0.124	0.183	0.175	0.421
	Mean shift (intensity shift)	0.024	0.050	0.355	0.057	0.384	0.138	0.091	0.312
	Cumulative subsets	0.282	0.145	0.072	0.342	0.037	0.134	0.225	0.451

This cost function encourages nearby sample vectors to be mapped to nearby outputs.

Table 3 : SROCC values computed between predicted scores and MOS values for the TID Images database subsets for which associated degradations are not common with LIVE database subsets.

 3

Table 4 : Statistical significance matrix of NR-IQA/DMOS on TID database subsets. Each entry in the table is a codeword consisting of 12 symbols. The position of the symbol represents the tested subsets as mentioned in the first column of Table 3. Each symbol gives the result of the hypothesis test on the subset: '1' means that the algorithm for the row is statistically better that the algorithm for the column, '0' means it is worse, and '-' means it is indistinguishable.

 4

	BIQI	DIIVINE BLIINDS BLIINDS-II	BIQ-An	NIQE	BRISQUE	FSIQI
	BIQI

Table 5 : Statistical significance matrix of NR-IQA/DMOS on CSIQ database subsets. Each entry in the table is a codeword consist- ing of 7 symbols. The position of the symbol represents the tested subsets: Additive pink Gaussian noise, JP2K, JPEG, Gaussian noise, Gaussian blur, Global Contrast Decrements, all data. Each symbol gives the result of the hypothesis test on the subset: '1' means that the algorithm for the row is statistically better that the algorithm for the column, '0' means it is worse, and '-' means it is indistinguishable.

 5

Table 4

 4

	gives obtained results when a One-sided t-test is

Table 6 : Comparison of computational time (in second/image)

 6

Author Biography

Christophe Charrier (M'10) received the M.S. degree from the Nantes University of Science and Technology, Nantes, France, in 1993, and the Ph.D. degree from the University Jean Monnet, Saint-Etienne, France, in 1998. He has been an Associate Professor with the GREYC laboratory at the University of Caen, France, since 2001. In 2008, he was a Visiting Scholar with the Laboratory for Image and Video Engineering, University of Texas, Austin. From 2009 to 2011, he was an Invited Professor with the Computer Department, University of Sherbrooke, Sherbrooke, QC, Canada. He is now the head of the E-Payment & Biometrics research team. His current research interests include digital image and video coding, processing, quality assessment, computational vision, and biometrics data quality.

Abdelhakim Saadane received his Ph.D. degree in Signal Processing and Telecommunications from University of Rennes1. He is currently associate professor at the Polytechnic school of Nantes University and a member of the SIC laboratory in XLIM Institute. His research activities are focused on the Human Visual System modeling and its use in applications such as coding, quality assessment, watermarking and user experience. He is a member of French National Color Imaging Group and serves as a member of division 8 of CIE.

Christine Fernandez-Maloigne is currently Vice-Rector of Poitiers University, in charge of International Relations. She is also director of a CNRS research federation (MIRES), which gathers 560 researchers in the South-West of France, in the area of mathematics, image processing, computer graphic, computer science and communication systems. Her research activities are focused on colour imaging, including fundamental researches about introduction of human visual system models in multiscale colour image processes as well as practical applications. She was cofounder member of the French National Colour Imaging Group (GFINC) in 2000, now part of the CFC (Centre Franc ¸ais de la Couleur). Currenlty, Christine Fernandez-Maloigne is French representative of the CIE Division 8 (Commission Internationale de l'Eclairage, Image Technology Division) since 2006 and secretary of this division since may 2015. She is also deputy Editorin-chief of JOSA A.


Xinwei Liu

Marius Pedersen

Christophe Charrier

Patrick Bours

CAN NO-REFERENCE IMAGE QUALITY METRICS ASSESS VISIBLE WAVELENGTH IRIS SAMPLE QUALITY?

Keywords: Quality assessment, visible wavelength, iris biometrics, no-reference, image quality metric

The overall performance of iris recognition systems is affected by the quality of acquired iris sample images. Due to the development of imaging technologies, visible wavelength iris recognition gained a lot of attention in the past few years. However, iris sample quality of unconstrained imaging conditions is a more challenging issue compared to the traditional near infrared iris biometrics. Therefore, measuring the quality of such iris images is essential in order to have good quality samples for iris recognition. In this paper, we investigate whether general purpose no-reference image quality metrics can assess visible wavelength iris sample quality.

INTRODUCTION

The iris is one of the most commonly used modalities for biometric recognition and it is a mature technology used in many government and civilian applications (e.g. border control in the United Kingdom and United Arab Emirates). However, most of the existing systems rely on heavy imaging constraints captured in a stop-and-stare interface, at close distances and using near infrared (700-900 nm) wavelengths with sufficient quality. In recent years, thanks to the development of imaging technologies, there are more and more iris recognition systems that operate in the visible wavelength (VW) and in less constrained environments [START_REF] Matey | Iris recognition in less constrained environments[END_REF][START_REF] Fancourt | Iris recognition at a distance[END_REF][START_REF] Smith | Extended evaluation of simulated wavefront coding technology in iris recognition[END_REF][START_REF] Park | A real-time focusing algorithm for iris recognition camera[END_REF][START_REF] Raja | Smartphone based visible iris recognition using deep sparse filtering[END_REF][START_REF] Raja | Visible iris imaging: A novel imaging solution for improved iris recognition[END_REF][START_REF] Boyce | Multispectral iris analysis: A preliminary study[END_REF]. The VW iris imaging systems lead to acquire degraded iris samples due to less constrained environments that makes the sample quality assessment a major issue. Existing iris sample quality assessment methods [START_REF] Kalka | Image quality assessment for iris biometric[END_REF][START_REF] Chen | Localized iris image quality using 2-d wavelets[END_REF] cannot handle the specificity of VW iris data and there are quite a few approaches developed for such iris images [START_REF] Proenc ¸a | Quality assessment of degraded iris images acquired in the visible wavelength[END_REF]. Since VW iris images are much closer to ordinary color images than near infrared iris images, it is interesting to investigate whether general purpose noreference image quality metrics (IQMs) can assess VW iris samples due to the lack of methods specific for VW iris image quality assessment. Towards this goal, we propose to 1) conduct the iris sample quality assessment by using no-reference IQMs, and 2) evaluate the performance of no-reference IQMs based on the performance of iris recognition system in order to answer 'Can no-reference IQMs assess visible wavelength iris sample quality?'.

In this paper, we introduce the related works of this research field in Section 2. In Section 3, the experimental setup is presented. Then the experimental results will be illustrated in the next section. Finally, the conclusions and future works are presented in Section 5.

RELATED WORK

With some minor exceptions, the large majority of the existing iris recognition methods (both near infrared and VW iris) follow the statistical pattern recognition model and can be separated into four stages: segmentation, normalization, feature extraction and comparison [START_REF] Proenc ¸a | The ubiris. v2: A database of visible wavelength iris images captured on-the-move and at-adistance[END_REF]. The human iris is an internal organ, naturally protected, visible from the exterior and enables data acquisition. VW iris recognition systems will inevitably constitute a tradeoff between data acquisition constraints and recognition accuracy. This research topic receives growing interest and several recent publications focus on this aspect. The 'Iris-on-the-move' project [START_REF] Matey | Iris recognition in less constrained environments[END_REF] is an example of an image acquisition system to make the recognition process less intrusive for subjects. Fancourt et al. [START_REF] Fancourt | Iris recognition at a distance[END_REF] presented that it is possible to acquire sufficiently high-quality images at a distance of up to 10 meters. Smith et al. [START_REF] Smith | Extended evaluation of simulated wavefront coding technology in iris recognition[END_REF] investigated that the iris structure can be captured in the VW spectra, discovering the possibility of using multispectral data to improve recognition performance. Park and Kim [START_REF] Park | A real-time focusing algorithm for iris recognition camera[END_REF] captured out of focus VW iris images. Raja et al. [START_REF] Raja | Smartphone based visible iris recognition using deep sparse filtering[END_REF] first developed a new recognition scheme and adapt it to smartphone based VW iris images, and then proposed an improved VW iris imaging solution for increasing the performance of VW iris recognition system [START_REF] Raja | Visible iris imaging: A novel imaging solution for improved iris recognition[END_REF]. Boyce et al. [START_REF] Boyce | Multispectral iris analysis: A preliminary study[END_REF] studied the image acquisition wavelength of revealed components of the iris, and identified the important role of iris pigmentation.

In order to ensure high performance of biometric system based on VW iris, the challenge is to assess the iris quality during the acquisition process [START_REF] Liu | Image-based attributes of multi-modality image quality for contactless biometric samples[END_REF]. However, only a few pub-lications investigated VW iris quality and most of these works are from Proenc ¸a et al. [START_REF] Proenc ¸a | Quality assessment of degraded iris images acquired in the visible wavelength[END_REF][START_REF] Proenc ¸a | The ubiris. v2: A database of visible wavelength iris images captured on-the-move and at-adistance[END_REF]. Due to the limited number of approaches for VW iris sample quality assessment, meanwhile, VW iris images are much closer to ordinary color images than near infrared iris images, it is interesting to investigate whether no-reference IQMs can assess VW iris samples. No-reference IQMs provide quality assessment of an image without the need of any reference image or its features and they are mostly for natural images. The properties of noreference IQMs make it possible to use them to assess VW iris images. There are many no-reference IQMs, for more details we refer to [START_REF] Kamble | No-reference image quality assessment algorithms: A survey[END_REF].

EXPERIMENTAL SETUP

The iris recognition system used in this paper is OSIRIS (Open Source for IRIS) version 4.1 [START_REF] Sutra | A biometric reference system for iris, osiris version 4.1[END_REF]. The OSIRIS reference system is an open source iris recognition system developed in the framework of the BioSecure project [START_REF] Sutra | A biometric reference system for iris, osiris version 4.1[END_REF]. The VW iris database used in this paper is part of the GC 2 multimodality biometric database. This database is on the final stage of the development by the authors of this paper and will be available soon to the research field. The iris database contains 50 subjects, both left and right eyes are acquired by two different cameras: a Canon D700 camera with Canon EF 100mm f/2.8L Macro Lens (18 Megapixels) and a Google Nexus 5 smartphone embedded camera (8 Megapixels). 15 samples are taken for each camera per eye. In order to avoid that segmentation errors corrupt the results for OSIRIS system, 31 and 25 subjects are selected from reflex camera and smartphone, which were accurately segmented based on visual inspection. Totally, 1680 iris samples (930 from reflex camera and 750 from smartphone) are used in this paper. Only small natural distortions appear in the images. Some examples from the database are shown in Figure 1.

We select 13 no-reference IQMs which are commonly used in the research field and their Matlab code are publicly available: BIQI [START_REF] Moorthy | A two-step framework for constructing blind image quality indices[END_REF], BLIINDS2 [START_REF] Saad | Dct statistics model-based blind image quality assessment[END_REF], BRISQUE [START_REF] Mittal | Noreference image quality assessment in the spatial domain[END_REF], IL-NIQU2 [START_REF] Zhang | A featureenriched completely blind image quality evaluator[END_REF], JNBM [START_REF] Ferzli | A no-reference objective image sharpness metric based on the notion of just noticeable blur (jnb)[END_REF], SSEQ [START_REF] Liu | Noreference image quality assessment based on spatial and spectral entropies[END_REF], CONTRAST [START_REF] Fang | No-reference quality assessment of contrast-distorted images based on natural scene statistics[END_REF], DCTSP [START_REF] Han | Novel no-reference image blur metric based on block-based discrete cosine transform statistics[END_REF], PWN [START_REF] Zhu | A no-reference objective image quality metric based on perceptually weighted local noise[END_REF], AQI and AQIP [START_REF] Gabarda | Blind image quality assessment through anisotropy[END_REF], SSH [START_REF] Leclaire | No-reference image quality assessment and blind deblurring with sharpness metrics exploiting fourier phase information[END_REF], and SH [START_REF] Blanchet | An explicit sharpness index related to global phase coherence[END_REF]. BIQI is a two-step framework based on natural scene statistics. BLIINDS2 is a distortion-agnostic metric based on a natural scene statistics model of discrete cosine transform coefficients. BRISQUE is a natural scene statisticbased distortion-generic model that operates in the spatial domain. ILNIQU2 integrates the features of natural image statistics derived from multiple cues and learns a multivariate Gaussian model of image patches from a collection of pristine natural images. JNBM is a perceptual-based image sharpness/blurriness metric. SSEQ is based on spatial and spectral entropies. CONTRAST is a method for contrast distorted images based on the principle of natural scene statistics. DCTSP is a algorithm for blurred images and it is based on block-based discrete cosine transform statistics and

EXPERIMENTAL RESULTS

Distribution and mean of comparison scores

In order to evaluate the performance of the IQMs, we first plot the original comparison score for both reflex camera and smartphone in Figure 2 (a) and (b). The x axis represents the score and the y axis represents the quantity of the comparison. The histograms of the comparison score are obtained from the genuine (comparison between samples from the same subject) and imposter (comparison between samples from different subjects) comparisons for all image samples. The line plots correspond to the fitted normal distributions and the mean of the score is given as well. In general, high quality biometric samples could generate relatively good genuine comparison scores (in our case, the score closer to zero the more similar two iris samples), which are well separated from impostor comparison scores [START_REF] Grother | Performance of biometric quality measures[END_REF]. This can be observed from Figure 2 (a) and (b). Then we show two examples of the histogram of the genuine comparison scores when omitting low quality samples by using selected no-reference IQMs in Figure 2 (c) and(d). Grother et al. [START_REF] Grother | Performance of biometric quality measures[END_REF] proposed to use qualitybin based approaches to evaluate the image quality assessment methods. They believed if a certain percentage of low quality samples are excluded from the dataset, the comparison score would decrease (in our case) and the Equal Error Rate (EER) (when False Match Rate (FMR) and False None Match Rate (FNMR) are equal) would decrease as well. Because the scale of the quality score for each IQM is different and the linearity of the quality score is unknown, we omit the percentile low quality samples and keep 75%, 50%, and 25% of high quality samples for each of the IQMs. We conduct an inspection for all omitted low quality samples in order to ensure that at least there is one sample per subject. In the two plots, the red continuous line represents the original comparison score; the green '-.' line represent the comparison scores when we keep the 75% highest quality iris samples; the blue colon line represents the comparison scores when we keep the 50% highest quality iris samples; and the magenta dot line represents the comparison scores when we keep the 25% highest quality iris samples. We only illustrate the best IQM for reflex camera and smartphone, and for the rest of IQMs we only plot the mean values with omitting low quality samples in Figure 2 (e) and (f). From Figure 2 (c) and (d) we can see that, there is only slightly left shift for genuine score.

In Figure 2 (e) and (f), all mean values of comparison score become lower when omitting more low quality samples for smartphone, however, the mean values become higher at 50% (equals to right shift in previous plots) for reflex camera when using ILNIQU2 and PWN to omit low quality samples. The rest of the no-reference IQMs have similar performance with these two IQMs. The above findings indicate that the selected no-reference IQMs fail to assess the iris image quality well according to the performance of OSIRIS system. AQIP and BIQI have lowest mean of comparison score for reflex camera and smartphone, respectively, while ILNIQU2 and PWN have the highest mean of comparison score compared to the others.

DET curves and EER

An IQM is useful if it can at least give an ordered indication of an eventual performance. Rank-ordered Detection Error Trade-Off (DET) characteristics curve is one of the most commonly used and widely understood method used to evaluate the performance of quality assessment approaches. The DET used here plots FNMR versus FMR. As mentioned before, we also obtain EER as an indicator to examine the performance of IQMs. Figures 3 (a) and (b) illustrate the two examples of DET curves with EER for data with and without omitting low quality samples for reflex camera by using AQIP, and for smartphone by using BIQI . Since all DET curves for both reflex camera and smartphone are very similar we only show two examples here. If a DET curve is closer to the left-bottom point, it means that this set of data lead to a higher iris recognition performance. Meanwhile, the lower EER values the better system performance. From Figure 3 (a) and (b) we can see that, the DET curves with omitting low quality samples (magenta, blue, and green lines, same as Figure 2) are on the right-top side or very close to DET curve without omitting low quality samples (the red continuous line). Figure 3 (c) and (d) represent the EER values from all IQMs for reflex camera and smartphone, respectively. From Figure 3 (c) and (d) we can observe that, most of the EER values with omitting low quality samples are higher than EER values without omitting low quality samples (the red dash line represents the EER calculated from original comparison score). This means that there is no system performance improvement after omitting low quality samples. However, the EER values from BIQI and SSEQ when keeping 75% of the high quality score are lower than original EER value for reflex camera, and EER values from CONTRAST when keeping 50% and BLIINDS2 when keeping 75% of the high quality score are lower than original EER value for smartphone. Additionally, we calculate EER values for both cameras by omitting lowest quality iris sample one by one until only one highest quality iris sample remains. Figure 4 (a) and (b) illustrate the change of EER values for both cameras. The x axis represents the number of omitted low quality samples. The y axis represents the EER value. We slightly shift the plot to the right-top side for each IQM in order to show the results more clear. As introduced before, when we omit low quality iris samples, the EER value will decrease if the IQMs can predict iris sample quality. From both plots in Figure 4 we can see that, there is no obvious decrease for EER values (from the left to the right) until only a few high quality samples left. However, for most of the IQMs, we can find an increase or fluctuation in the EER values at the end of the line. Another interesting finding is that, most of the lines have a big drop in the end due to only high iris samples are remains, except the second last line (BLIINDS2) for both cameras and the fourth last line (ILNIQU2) for smartphone. This means that high quality iris samples given by BLIINDS2 and ILNIQU2 cannot enhance the performance of the OSIRIS system compared to low quality samples.

Computational complexity

We also notice that some of the no-reference IQMs are designed for real images so they are time consuming, which is not suitable for real time iris recognition. The IQMs whose computation speed is less than 1 second: BIQI, JNBM, SSEQ, DCSP, PWN, SSH, and SH; whose computation speed is between 1 and 5 seconds: BRISQUE, ILNIQU2, CONTRAST, AQI, and AQIP; and whose computation speed is more than 5 seconds: BLIINDS2.

CONCLUSIONS AND FUTURE WORKS

In this paper, we evaluate the performance of no-reference IQMs on VW iris images. From the experimental results we can conclude that, the selected 13 no-reference IQMs cannot assess well the quality of VW iris samples from selected GC 2 database. By looking at EER values, only BIQI and SSEQ increase the performance when keeping 75% of the high quality samples for reflex camera; only CONTRAST and PWN increase the performance when keeping 50% and 75% of the high quality samples for smartphone, respectively. Since all these IQMs are designed for natural images but VW iris images contain rich texture information with unique structure components. Therefore, VW iris images are different from natural images, so it can be the reason for the low performance. Another possible reason when these IQMs fail to assess iris sample quality can be that, the quality attributes ap- plied in these IQMs do not appear in some of the iris images and these attributes are not sensitive for OSIRIS iris recognition system. The contribution of this work can be used for the development of quality assessment methods for VW iris, moreover, for contactless biometric modalities. The experimental results indicate that biometric modality specific IQMs might be required. It has been shown that red channel has more discriminatory information than the other channels. It is interesting to investigate if the experimental results will be different if only red channel is used. Other VW iris databases and iris recognition systems could also be used to evaluate the performance of selected metrics.

Fig. 1 .

 1 Fig. 1. Iris samples from the database. The first two samples are from reflex camera and the last two are from smartphone.

Fig. 2 .

 2 Fig. 2. Comparison scores and their mean values with and without omitting low quality samples.

Fig. 3 .

 3 Fig. 3. Examples of DET curves with EER for original comparison score with and without omitting low quality samples.

Fig. 4 .

 4 Fig. 4. EER values with omitting low quality iris samples one by one until the best quality sample left. The x axis represents the number of omitted low quality samples. The y axis represents the EER value. We slightly shift the plot to the right-top side for each IQM in order to show the results more clear.

* This research is supported by the Conseil Regional Basse-Normandie Grant 14P02048 and Research Council of Norway through project number 221073: HyPerCept -Color and Quality in Higher Dimensions.


Christophe Charrier

Abdelhakim Saadane

Christine Fernandez-Maloigne

No-Reference Learning-based and Human Visual-based Image Quality Assessment Metric

Keywords: image quality assessment, no reference, human visual system, visual sub-bands, multivariate Gaussian distribution

With the rapid growth of multimedia applications and technologies, objective image quality assessment (IQA) became a topic of fundamental interest. No-Reference (NR) IQA algorithms are more suitable to real-world applications where the original image is not available. In order to be more consistent with human perception, this paper proposes a new NR-IQA metric where the input image is firstly decomposed to several frequency sub-bands which mimic the human visual system (HVS). Then, the statistical features are extracted from these frequency bands and used to fit a multivariate Gaussian distribution (MVGD). Finally, the model obtained by training predicts the quality of the input image. Experimental results demonstrate the method effectiveness and show its robustness when tested by different databases. Moreover, the predicted quality is more consistent with human perception.

Introduction

From the last two decades, a great number of researches have been conducted to design robust No-Reference Image Quality Assessment (NR-IQA) algorithms. As they don't use the reference image, these algorithms can be embedded in the development of new multimedia services. NR-IQA algorithms aim at predicting image quality from objective features extracted from distorted images. To reach this goal, these algorithms, either assume a priori knowledge of involved distortions, or look for a generic approach by directly assessing the image quality regardless the type of image distortion [START_REF] Zhang | Review on universal no-reference image quality assessment algorithm[END_REF]. For specific approaches, metrics are mainly designed to quantify distortions induced by image encoders such as JPEG and JPEG2000. In studies [START_REF] Gao | A de-blocking algorithm and a blockiness metric for highly compressed images[END_REF] [3], the block effect is estimated in the spatial domain while studies [START_REF] Wang | Blind measurement of blocking artifacts in images[END_REF] [START_REF] Liu | Efficient dct-domain blind measurement and reduction of blocking artifacts[END_REF] quantify the same effect in the frequency domain. Assessment algorithms for blur effect are proposed in [START_REF] Ferzli | A no-reference objective image sharpness metric based on the notion of Just Noticeable Blur (JNB)[END_REF] [START_REF] Sang | No-reference blur image quality assessment based on gradient similarity[END_REF] . Distortions induced by JPEG2000 such as blur and ringing are considered in [START_REF] Sazzad | No reference image quality assessment for JPEG2000 based on spatial features[END_REF] [START_REF] Barland | Reference free quality metric for JPEG-2000 compressed images[END_REF]. The blur effect is characterized by an increase of the spread of edges while the ringing effect produces halos and/or rings near sharp object edges. As a result, the proposed metrics are generally based on the measurement of edges spreading. All of these metrics are interesting and some of them perform very well. However they remain limited by the distortions that they have to know.

Generic approaches aim to be universal and look to address all applications fields. Usually, the generic approaches follow two trends: Signal based approach that extracts and analyzes features in image signals and visually based approach that aims to mimic the human visual system (HVS) properties. Signal based approaches present a good trade-off between performance and complexity. Generally, these approaches require two steps. In the first one, relevant features are extracted while in the second, these features are pooled in order to produce the quality score of the image under test. The first step has been the subject of several investigations [START_REF] Wang | Image quality assessment: From error measurement to structural similarity[END_REF] [11] [START_REF] Wee | Image quality assessment by discrete orthogonal moments[END_REF]. In contrast, the second step usually uses conventional combinations. To overcome this drawback, statistical modeling of natural images has been considered where the features extraction procedure is followed by a learning step. In the case of no-reference metrics which is the context of this paper, these learning methods can well map features and subjective assessments [START_REF] Babu | No-reference JPEG image quality assessment using GAP-RBF[END_REF] [14] [15] [16] [17] [START_REF] Mittal | Making a "completely blind" image quality analyzer[END_REF]. Since the result of evaluation ultimately depends on the final observer, the visuallybased trend looks for designing metrics according to HVS behavior when assessing quality. Several metrics based on one or more HVS properties, are proposed in literature. The HVS sensitivity to image signals is used in [START_REF] Chandler | VSNR: A wavelet-based visual signal-to-noise ratio for natural images[END_REF] [START_REF] Sheikh | Image information and visual quality[END_REF]. The HVS sensitivity to spatial frequencies, luminance and/or structural information is pointed out in [START_REF] Larson | Most apparent distortion: Full-reference image quality assessment and the role of strategy[END_REF] [27] [START_REF] Callet | Frequency and spatial pooling of visual differences for still image quality assessment[END_REF]. Nowadays, several HVS models are proposed in image quality assessment and their experimental results are very promising.

The goal of this paper is to combine the advantages of visually-based methods and the interesting results [START_REF] Gastaldo | Supporting visual quality assessment with machine learning[END_REF] of learning techniques in the context of NR-IQA metrics. More specifically, it uses the spatial frequency sensitivity of HVS to decompose the test image, extracts the statistical features of each visual sub-band and combines them using a multivariate Gaussian distribution, to assess the quality.

The rest of this paper is organized as follows: The proposed metric is presented in Section II. The visual sub-band decomposition is described in Section III. The experimental results are shown and discussed in section IV.

The LEVIQI Index

General framework

Fig. 1 gives the overall framework of the proposed method.

The first block models the spatial frequency selectivity of the human visual system and performs a perceptual decomposition on both training and testing images. The steerable pyramid [START_REF] Liu | Image fusion by using steerable pyramid[END_REF] is used to achieve the perceptual decomposition described in Section 2.2. The steerable pyramid is a multi-scale, multi-orientation ans self inverting image decomposition. With this decomposition, the image is divided into a set of sub-bands localized in scale and orientation. An example of the first level image decomposition where four oriented band-pass filters are used, is given Fig. 2.

The second block extracts the statistical features of each filtered visual channel. Instead of looking to define new features, this paper will exploit some features derived from well-known metrics.

The computed features and the DMOS (Difference of Mean Opinion Scores) values of training images are then used by the learning block to fit an IQA Multivariate Gaussian Distribution. Due to its simple parametric form, the MVGD is widely used for modeling vector-features signals and has been a sound choice in many image and video applications. Therefore, the resulting model, namely LEarning-based and Visual-based Image Quality Index (LEVIQI) is given by:

LEV IQI (x) = 1 (2π) k/2 |Σ| 1/2 exp - 1 2 (x -β) T Σ -1 (x -β) (1)
where x = (f 1 , ..., f k , DM OS) corresponds to the extracted features to which is added the DMOS of training distorted images. β and Σ denote the mean and covariance matrix of the MVGD model and are estimated using the maximum likelihood method. The features extracted from testing images with DMOS values lying between 0 and 100 with a step of 0.5, are fed into the learned LEVIQI to assess objective quality of image under test. The DMOS of the test image is the one that maximizes the distribution p (x, β, Σ). The probabilistic model is trained on the LIVE IQA database, for which, one has access to DMOS values. To ensure a robustness of results, multiple training sets were constructed. In each, the image database was subdivided into distinct training and test sets (completely content-separate). For each train set, 80% of the LIVE IQA Database content was chosen, inducing that the remaining 20% is considered for the test set. Specifically, each training set contained images derived from 23 original images, while each test set contained the images derived from the remaining 6 original images. 1000 randomly chosen training and test sets were obtained and the prediction of the quality scores was run over the 1000 iterations.

Visual Sub-band decomposition

It is well known that the retinal image is processed by different frequency channels that are narrowly tuned around specific spatial frequencies and orientations. Numerous According to these experiments, most of the proposed decompositions suggest a spatial frequency bandwidth of approximately one octave and an orientation sensitivity that varies between 20 • and 60 • depending on the spatial frequency. This study uses the decomposition of Fig. 3. Discussed in [START_REF] Daly | A visual model of optimizing the design of image processing algorithm[END_REF], this decomposition uses a radial frequency selectivity that is symmetric on a log-frequency axis with bandwidths nearly constant at one octave. It consists of one isotropic low-pass and three band-pass channels. The angular selectivity is constant and equal to 30 • .

Selected features

All features considered in this paper are extracted from nine commonly used learningbased NR-IQA metrics : 1) BRISQUE [START_REF] Mittal | No-reference image quality assessment in the spatial domain[END_REF], 2) QAC [START_REF] Xue | Learning without human scores for blind image quality assessment[END_REF], 3) BLIINDS-II [START_REF] Saad | Blind image quality assessment: A natural scene statistics approach in the dct domain[END_REF], 4) NIQE [START_REF] Mittal | Making a "completely blind" image quality analyzer[END_REF], 5) DIIVINE [START_REF] Moorthy | Blind image quality assessment: From natural scene statistics to perceptual quality[END_REF], 6) BIQI [START_REF] Moorthy | A two-step framework for constructing blind image quality indice[END_REF], 7) IL-NIQE [START_REF] Zhang | A feature-enriched completely blind image quality evaluator[END_REF], 8) SSEQ [START_REF] Liu | No-reference image quality assessment based on spatial and spectral entropies[END_REF] and 9) OG-IQA [START_REF] Liu | Blind image quality assessment by relative gradient statistics and ada boosting neural network[END_REF]. A reason of the choice of those trial algorithms is motivated by the fact that the code of all of them is publicly available.

Yet, since around 200 features are available from all the trial algorithms, only the most relevant are selected. Furthermore, some of them modelize similar visual characteristics, e.g., luminance sensitivity, sub-band anisotropy, and so on. So, it is not necessary to select features which modelize similar characteristics.

All features are computed for all original images (and their associated degraded version) of the LIVE IQA database [33]. Then, the Spearman Rank-Order Correlation Coefficient (SROCC) between values of features and subjective DMOS is computed. Finally, only the 10 highest correlated attributes are considered to design LEVIQI under the constraint that the selected features do not modelize similar characteristics. 1 presents the selected distinct features. Yet, these attributes have not been used as they have been defined in their associated NR-IQA schemes, but have been modified to adapt the visual sub-band decomposition.

GGD fit parameters:

The first set of features, derived from BRISQUE, includes the shape parameter α and the variance σ 2 of generalized Gaussian distribution (GGD) fit of the MSCN (mean subtracted contrast normalized) coefficients for each sub-band. The MSCN coefficients refer to the transformed luminances Î(i, j) given by:

Î(i, j) = I (i, j) -µ (i, j) σ (i, j) + C , (2)
where (i,j) are spatial indices, C=1, and µ (i, j) =

3 k=-3 3 l=-3 ω k,l I k,l (i, j) , and σ (i, j) = 3 k=-3 3 l=-3 ω k,l (I k,l (i, j) -µ (i, j))
2 , ω is a 2D circularly-symmetric Gaussian weighting function.

The shape α and the variance σ 2 parameter of the GGD are computed over all subbdands and then pooled by computing the lowest 10th percentile average of the local α scores and the local σ 2 scores across the sub-bands.

Coefficient of Frequency Variation: This feature, derived from BLIINDS2, is defined for each subband as:

ζ = σ |X| µ |X| = Γ (1/γ) Γ (3/γ) Γ 2 (2/γ) -1 (3)
where σ |X| and µ |X| are the standard deviation and mean of the frequency coefficient magnitudes |X|, respectively. The feature ζ is computed for all sub-bands of the image and pooled by taking the highest 10th percentile and over all of the sub-band scores of the image.

Energy Sub-band ratio Measure: This attribute, also derived from BLIINDS2, is used to capture local spectral signature. This feature is defined as:

R n,k = E n,k -1 n-1 j<n E j,k E n,k + 1 n-1 j<n E j,k (4)
where E n,k = σ 2 n,k is the average energy in the frequency sub-band n for a given radial band k, where n ∈ {1, 2, 3, . . . , 6} and k ∈ {1, 2, 3}. The mean of (R n,k ) n∈[2,...,6] is computed on the three radial bands k of the image and pooled by computing the highest 10th percentile average of the scores of the image.

Across scale and Spatial correlations These two features are derived from features designed for DIIVINE. In order to capture the statistical dependencies between highpass (HP) responses of natural images and their band-pass (BP) counterparts, a structural correlation is modeled as ρ = (2σ xy + C 2 )/(σ 2

x + σ 2 y + C 2 ) where σ xy is the cross-variance between the windowed regions from the BP and HP bands, and σ 2

x , σ 2 y are their windowed variances respectively; C 2 is a stabilizing constant. The mean of the 18 correlation values (corresponding to the 18 sub-bands) is computed.

In order to capture spatial correlation statistics, the joint empirical distribution between coefficients at (i, j) and the set of spatial locations at a distance of τ is computed for each d θ 1 , θ ∈ {0 o , 30 o , 60 o , 90 o , 120 o , 150 o }. The correlation between these two variables denoted X and Y is estimated by:

ρ (τ ) = E P XY (x,y) X -E P X(x) [X] T Y -E P Y (y) [Y ] σ X σ Y (5)
where E P X(x) [X] is the expectation of X with respect to the marginal distribution p X (x) (similarly for Y and (X,Y)). ρ (τ ) is plotted for various distance across distortions and the obtained curve is fitted with a 3 rd order polynomial. The coefficients of the polynomial and the error between the fit and the actual ρ (τ ) form an 30 dimensional feature vector (5 values for each direction). The mean of ρ (τ ) is computed over the three radial bands and pooled by computing the highest 10th percentile average of the scores.

Local spatial and spectral entropy features:

The spatial entropy is computed on the obtained image after applying the first non-directional lower-pass filter applying.

Concerning the spectral entropy, a modified version of the attribute designed for SSEQ is defined. The variance across the six orientations per radial band var

(E [R θ ]) is computed. (E [R θ ]
) is the average of the Renyi entropy R θ [n] per orientation for the three sub-bands (one per radial band) of orientation θ.

Finally, the mean of the three variance values per radial band is computed.

Chromatic Statistics: This attributed is derived from IL-NIQE and is computed on the color image before applying the DCP transform. From the RGB coordinates system, a logarithmic-scale opponent color space RGB is defined as

R = log R -µ R , G = log G -µ G and B = log B -µ B
where µ R (resp. µ G and µ B ) is the mean log R (resp. log G and log B) over the image. Finally, the following linear color transform is applied on the RGB color space as

l 1 = (R + G + B)/ √ 3, l 2 = (R + G -2B)/ √ 6, l 3 = (R -G)/ √ 2.
The distributions of each channel l 1 , l 2 , l 3 conforms to a Gaussian probability law. In this paper, only the chromatic channels l 2 and l 3 are considered, since l 1 refers to a luminance channel. Finally, the two model parameters µ C and σ 2 C are estimated using a multivariate Gaussian model.

Performance evaluation 3.1 Experimental setup

Trial databases: To provide comparison of NR-IQA algorithms, two publicly available databases are used: 1) TID2013 database [START_REF] Ponomarenko | Image database TID2013: Peculiarities, results and perspectives[END_REF] and 2) CSIQ database [START_REF] Larson | Most apparent distortion: full-reference image quality assessment and the role of strategy[END_REF]. Since the LIVE database [33] has been used to train both the proposed metric and most of the trail NR-IQA schemes, it has not been used to evaluate performances of NR-IQA methods.

The TID2013 database contains images with multiple distortions. This database consists of 25 original images on which 24 different type of distortions have been applied using five degradation levels per distortion. A total of 3000 distorted images are generated. It is worth noting that seven new types of degradations have been introduced with respect to the 17 types of degradation existing in the previous version of the database, known as TID2008. The database contains 524340 subjective ratings from 971 different observers, and ratings are reported in the form of MOS.

The CSIQ Database consists of 30 original images, each is distorted using six different types of distortions at four to five different levels of distortion. A total of 866 distorted images have been generated. The database contains 5000 subjective ratings from 35 different observers, and ratings are reported in the form of DMOS. 2. SROCC values computed between predicted scores using NR-IQA schemes from which some attributes are extracted to design LEVIQI and MOS values for TID2013 Images database.

Trial NR-IQA: To assess the performance of the proposed metric, nine commonly used NR-IQA schemes are used to compare LEVIQI with. The trial metrics are those mentioned in section 2.3. Only NR-IQA schemes whose at least one feature has been adapted to design LEVIQI index, i.e., BRISQUE, BLIINDS2, DIIVINE, SSEQ and ILNIQE are used to compare the performance of LEVIQI with. Statistical Significance and hypothesis testing: Results obtained from the proposed metric are compared to results provided by all trial NR-IQA algorithms. To perform this evaluation, the Spearman Rank Order Correlation Coefficient (SROCC) is computed between the DMOS values and the predicted scores obtained from NR-IQA algorithms. In addition, to ascertain which differences between NR-IQA schemes performance are statistically significant, we applied an hypothesis test using the residuals between the DMOS values and the ratings provided by the IQA algorithms. This test is based on the t-test that determines whether two population means are equal or not. This test yields us to take a statistically-based conclusion of superiority (or not) of an NR-IQA algorithm.

Experimental results

Table 2 gives SROCC mean values computed between predicted scores from NR-IQA schemes from which some extracted features are used to design LEVIQI and MOS values for the TID2013 Images database. When considering the whole database, LEVIQI overperforms BRIQUE, BLIINDS2, DIIVINE, SSEQ ad ILNIQE. In 67% of cases (16 subsets out of 24), scores predicted by LEVIQI allow to have a better correlation (higher SROCC value) with human judgments than that of any other tested NR-IQA. For the remaining cases (8 remaining subsets), the performance of LEVIQI is very close to the best values. If we consider multidistorted images associated to the seven last subset of Table 2, LEVIQI performs better than trial quality schemes except for 'Multiplicative Gaussian Noise' and 'Comfort Noise'. Yet, obtained SROCC values are highly competitive with the best quality index.

Similar results as those of Table 2 are given in Table 3 for CSIQ Images database. For this database also, The global performance (SROCC value of cumulative subsets) of LEVIQI is higher than that of trial metrics. More specifically, LEVIQI performs better 4 times over 6. For the two remaining distortions 'Gaussian Noise' and 'Additive Gaussian Pink Noise', LEVIQI presents the second best performance. 3. SROCC values computed between predicted scores from which some attributes are extracted to design LEVIQI and MOS values for CSIQ Images database.

In addition, Table 4 gives obtained results when a One-sided t-test is used to provide statistical significance of NR-IQA/LEVIQI quality scores on the 6 multidistortions subsets of TID2013 database (the 6 last subsets in Table 2). Each entry in this table is coded using six symbols. The position of each symbol corresponds to one subset ( first position corresponds to 'Change of Color Saturation' subset, second position for 'Multiplicative Gaussian Noise' subset etc..). Each symbol gives the result of the hypothesis test on the subset. If the symbol equals '1', the NR-IQA on the row is statistically better than the NR-IQA on the column ('0' means worse, '-' is used when NR-IQAs are indistinguishable). Results confirm that, most of the time, LEVIQI is more consistent with human judgments than trial NR-IQA schemes from which some features have been extracted. As multidistortions subsets are not common to LIVE database, these results are more reliable. In a similar way, Table 5 gives obtained results when a One-sided t-test is used to provide statistical significance of NR-IQA/LEVIQI quality scores on CSIQ database. One can notice that distortions present in CSIQ database are also present in LIVE database. For these learned distortions, LEVIQI exceeds in several cases all of the trial NR-IQA schemes. Finally, to compare the computational complexity of the proposed algorithm, we measured the average computation time required to assess an image of size 512 × 512, using a computer with Intel Core-I7 processor at 2.2GHz.

Conclusion

In this paper, a machine learning-based and human vision-based quality index called LEVIQI has been proposed in the purpose of no reference quality evaluation. The model utilizes ten derivative relevant attributes from five well-known and highly competitive NR-IQA schemes. The selected attributes address human vision characteristics such as frequency sensitivity, chromatic sensitivity, anisotropy and contrast sensitivity. These attributes have been adapted to be computed on 18 sub-bands generated from three different radial bands and six different orientations, to simulate human perception sensitivity. Obtained results show that the performance of LEVIQI is competitive with top-performing NR-IQA schemes. The potential of this model to be used in real applications is the subject of investigations where real-time implementation of LEVIQI index is considered using efficient vectorization.

Fig. 1 .

 1 Fig. 1. Overall framework of the proposed method.

Fig. 2 .Fig. 3 .

 23 Fig. 2. Steerable pyramid-based image decomposition. Illustration of the first level image decomposition (radial selectivity) where four oriented band-pass filters are used (angular selectivity). The second level of decomposition is the result of the same process performed on low-pass filter 1 (low-pass filter 0 downsampled by the factor 2)

Table 1 .

 1 Selected features to design LEVIQI

	Feature from Description

Table 4 .

 4 Statistical significance comparison of trial NR-IQA/LEVIQI quality scores on TID2013 database multidistortions subsets.

		BRISQUE	BLIINDS2	DIIVINE	SSEQ	ILNIQE
	LEVIQI	1111111	1111111	10111-1	11111--	110-1--

Table 5 .

 5 Statistical significance comparison of NR-IQA/LEVIQI quality scores on CSIQ database subsets.

		BRISQUE	BLIINDS2	DIIVINE	SSEQ	ILNIQE
	LEVIQI	1-1-111	--11111	1111111	1101111	---111-

Table 6 .

 6 Table 6 reports the measurement results, which are rough estimates only, as no code optimization has been done on our Matlab implementations. LEVIQI is superior to DIIVINE and BLIINDS2 while inferior to BRISQUE and SSEQ and similar to ILNIQE. Comparison of computational time (in second/image)

	NR-IQA BRISQUE BLIINDS2 DIIVINE	SSEQ	ILNIQE	LEVIQI
	time	1.33	87.13	27.33	2.69	11.85	12.38