gabarda,cristobal 07

Blind image quality assessment throughanisotropy

Salvador Gabarda and Gabriel Cristbal*

Instituto de ptica Daza de Valds (CSIC), Serrano 121, Madrid 28006, Spain*Corresponding author: [email protected]

Received February 26, 2007; revised July 9, 2007; accepted July 18, 2007;posted July 25, 2007 (Doc. ID 80401); published September 26, 2007

We describe an innovative methodology for determining the quality of digital images. The method is based onmeasuring the variance of the expected entropy of a given image upon a set of predefined directions. Entropycan be calculated on a local basis by using a spatial/spatial-frequency distribution as an approximation for aprobability density function. The generalized Rnyi entropy and the normalized pseudo-Wigner distribution(PWD) have been selected for this purpose. As a consequence, a pixel-by-pixel entropy value can be calculated,and therefore entropy histograms can be generated as well. The variance of the expected entropy is measuredas a function of the directionality, and it has been taken as an anisotropy indicator. For this purpose, direc-tional selectivity can be attained by using an oriented 1-D PWD implementation. Our main purpose is to showhow such an anisotropy measure can be used as a metric to assess both the fidelity and quality of images.Experimental results show that an index such as this presents some desirable features that resemble thosefrom an ideal image quality function, constituting a suitable quality index for natural images. Namely, in-focus, noise-free natural images have shown a maximum of this metric in comparison with other degraded,blurred, or noisy versions. This result provides a way of identifying in-focus, noise-free images from other de-graded versions, allowing an automatic and nonreference classification of images according to their relativequality. It is also shown that the new measure is well correlated with classical reference metrics such as thepeak signal-to-noise ratio. 2007 Optical Society of America

OCIS codes: 110.3000, 100.2000, 330.6180, 100.6640.

1. INTRODUCTIONThe objective of a great number of applications of imageprocessing is the search for an in-focus, noise-free versionof an unknown original. Image quality assessment (QA) isnot a minor issue, especially if more than one enhancedimage competes to be the best realization. The naked eyeis surely a good classifier, but an automatized methodwould save time and should simplify the task. Qualityevaluation of images is still an open and challenging prob-lem [1]. Typically, methods for determining the quality ofenhanced images [2,3] require a reference or ground truthimage to fulfill the measure. Measures such as peaksignal-to-noise ratio (PSNR) or root-mean-squared error(RMSE) are simple to calculate, but they are not alwaysin agreement with the perceived visual quality. Signifi-cant improvement has been attained by some image QAmethods that take advantage of known characteristics ofthe human visual system (HVS); for example, Wang andBovik [4] describe a method based on the hypothesis thatthe HVS is highly adapted for extracting structural infor-mation, and they develop a measure of structural similar-ity (SSIM) that compares local patterns of pixel intensi-ties that have been normalized for luminance andcontrast. Sheikh et al. [5] use an information fidelity cri-terion (IFC) for image QA using natural scene statisticsmodels as an alternative to the HVS-based methods. Inanother paper [6], Sheikh et al. explore the relationshipbetween image information and visual quality, and theyintroduce a visual information fidelity (VIF) criterion forfull-reference image QA. The VIF is derived from a statis-

tical model for natural scenes, a model for image distor-tions, and a HVS model in an information-theoretic set-ting. However, when a reference image is not available,only blind image QAmethods may be useful. Sheikh et al.[7] propose the use of natural scene statistics (NSS) mod-els to blindly measure the quality of images compressedby JPEG2000 as a novel way of assessing the quality ofimages afflicted with ringing and blurring distortion re-sulting from JPEG2000 compression. Remarkably, thismethod uses NSS models to provide a reference againstwhich the distorted images can be assessed.A new image QA method that does not require a refer-

ence image to determine the quality of the images underscrutiny is introduced here. This blind image QA methodis based on measuring the anisotropy of the images andhas been confirmed to be robust over an ample set of im-ages and akin to the way the HVS works. Hence, the au-tomatized selection of the best image from a set of pos-sibilities coincides well with the criteria of the HVS, asthe experiments presented here will later corroborate,with a set of natural images.Shannon entropy is classically used as a value to indi-

cate the amount of uncertainty or information in a source[8]. Quality and entropy are somewhat related subjects. Ifthe source is a given image, the obstacle for the entropy tobe considered a quality index is that noise cannot be dis-tinguished from information, noise being a kind of infor-mation itself. From a human observer point of view, ob-jects constitute the areas of interest in a picture, andhumans with good eye correction are easily capable of dis-

B42 J. Opt. Soc. Am. A/Vol. 24, No. 12 /December 2007 S. Gabarda and G. Cristbal

1084-7529/07/120B42-10/$15.00 2007 Optical Society of America

tinguishing the sharpest objects. Noise or blurring is eas-ily identifiable by the visual system. Analytically, entropyincreases with sharpness but, in general, there is not afair correlation when images are noisy. Hence, entropy byitself is not a good indicator of image quality. To overcomethis problem, in this paper we propose to use anisotropyas a suitable measure of image quality.Based on our experiments, we hypothesize that the

degradation processes damage the scenes directional in-formation. Hence, anisotropy, as a directionally depen-dent quality of images, decreases as more degradation isadded to the image.There exists an antecedent of the use of entropy for

identifying the anisotropy of images [9]. Anisotropy is cer-tainly one of the properties of natural images and is re-lated to its directional dependency. Our experiments haveshown that image anisotropy is sensitive to noise andblur; hence quality can be properly measured in this way.Following this line of reasoning, we have extended the ap-plications of entropy to the problem of measuring imagequality in a nonreference scenario. That is, following thisapproach no reference is required to sort images accord-ing to their visual quality. The generalized Rnyi entropyhas been selected to calculate the entropy on a local basisby associating a distribution for each pixel of a digital im-age. In this way, entropy histograms provide a measure ofthe information content of images in the same way as im-age histograms give information about the distribution ofgray levels. Using a proper normalization, a windowedpseudo-Wigner distribution (PWD) can be approximatedas a probability distribution function [10], and then a par-ticular Rnyi-wise entropy can be measured at the pixellevel. This PWD is computed in a 1-D-oriented window,allowing a measure of the entropy in a selected direction.Differences in the directional entropy are taken to mea-sure image anisotropy and hence to estimate of the imagequality. Different techniques have been proposed in theliterature for assessing images when the ground truth isnot available [1114]. In the context of image QA,Dansereau and Kinser were the first to suggest the poten-tial use of the relative Rnyi dimension spectrum as animage quality measure [15]. The main motivation of thispaper is to provide an in-depth study on the use of high-order Rnyi entropies in the area of nonreference imagequality evaluation.This paper is structured as follows: The basic math-

ematical description and theoretical fundamentals of themethod are described in Section 2. Section 3 presents thenew quality metric and its empirical justification. Section4 presents experimental results obtained by applying thismethod to some artificial and real examples. Finally, con-clusions are drawn in Section 5.

2. MATHEMATICAL BACKGROUNDA. Rnyi Entropy MeasuresEntropy is a measure of the information content of givendata. In general, any 2-D array that entails informationcan be considered an image. This suggests that differ-ences in entropy orientations can provide differences inthe information content. That is, information can bestored in an anisotropic way. Entropy can be applied as a

global measure or as a local one, adding the possibility ofdifferent directionalities when dealing with images. En-tropy is an important feature to consider, especially whenorientation inherits some specific information. Subse-quently, directional entropy measurements can be used todetermine differences between different images or tex-tures with different entropic characteristics. Directionalentropy can be achieved by means of the Rnyi entropy.For this reason, Rnyi entropy measurements stand outas a relevant entropic measure in this context.A review of the existing Rnyi measures, which we

summarize here, can be found in [16]. The definition ofentropy was initially proposed independently by Shannon[8] and Wiener [17] as a measure of the information con-tent per symbol, coming from a stochastic informationsource. Later, Rnyi [18] extended this notion to yieldgeneralized entropy. Different distributions have beenconsidered to define some Rnyi entropy measures. Theyhave been introduced in the timefrequency analysis areaby Williams et al. [19], with a significant contribution byFlandrin et al. [20], establishing the properties of suchmeasures. In general, the Rnyi entropy applied to a dis-crete spacefrequency distribution P!n ,k" has the form

R! =1

1 !log2#$

n$kP!!n,k"% . &1'

It is interesting to note that the Shannon entropy givenby

H = $n$kPx!n,k"log2&Px!n,k"' &2'

can be obtained from the Rnyi entropy measure in thelimiting case when !1 [20].Here n and k represent the spatial and frequency vari-

ables, respectively. Also, !"2 are values recommendedfor spacefrequency distribution measures [20]. AlthoughRnyi measures of joint spacefrequency distributionsformally look like the original entropies, they do not havethe same properties, conclusions, and results derived inclassical information theory. For instance, the positivityP!n ,k""0 will not be always preserved, along with theunity energy condition $n$kP!n ,k"=1. In order to reducea distribution to the unity signal energy case, some kindof normalization must be done [19]. The normalizationcan be done in various ways, leading to a variety of differ-ent measure definitions [16,20].

1. Normalization with the Signal Energy

RE! =1

1 !log2($n$k P!!n,k"$n$k P!n,k" ) with ! " 2. &3'

The behavior of this measure is quite similar to thenonnormalized measure form, except in its magnitude.This kind of normalization is important for comparisonbetween various distributions, or with the same distribu-tion when the energy is not unbiased.

S. Gabarda and G. Cristbal Vol. 24, No. 12 /December 2007 /J. Opt. Soc. Am. A B43

2. Normalization with the Distribution Volume

RV3 = 1

2log2($n$k P3!n,k"$n$k *P!n,k"*) . &4'

The volume-normalized form of measure has been usedfor adaptive kernel design [19]. Note that the term withinthe logarithm is just the ratio of norms L3 and L1, whilethe logarithm is a monotonic function. Thus, measure (4)can be considered to be L3 /L1, reducing to the generalcase.

3. Quantum NormalizationQuantum mechanics [21] inspires a normalization by as-similating the spatial/spatial-frequency distribution P ofa given position n with a wave function and deriving itsprobability density function by means of P!n ,k"=P!n ,k"P*!n ,k", followed by a normalizing step to satisfythe condition $n$kP!n ,k"=1.The general case in expression (1) with !=3 gives

R3 = 1

2log2#$

n$kP3!n,k"% . &5'

This measure can be interpreted on a pointwise basis asfollows:

R3!n" = 1

2log2#$

kP3!n,k"% . &6'

The term P in expression (6) also has to be normalizedby Q!n ,k"=P!n ,k"P*!n ,k", followed by P!n ,k"=Q!n ,k" /$kQ!n ,k" to meet the normalizing condition:$kP!n ,k"=1, n :1#n#M, where M is the size of thedata and N /2#k#N /21 the spatial window used tocompute the measure. We have selected this normaliza-tion in particular in the sequel.

B. One-Dimensional Pseudo-Wigner DistributionSpatial-frequency information of a given image can be ex-tracted by associating the gray-level spatial data with oneof the well-known spatial/spatial-frequency distributions[22]. Typically, the Rnyi entropy is applied over one ofthese joint distributions. In this paper the Wigner distri-bution has been selected [23] due to its excellent proper-ties. In such case, any specific pixel n of the image can beassociated to a vector containing its 1-D PWD, calculatedin a neighborhood by means of a small window of lengthN. The use of a windowed 1-D transform for a 2-D signalcan be justified considering three main aspects of theproblem. First, by using a 1-D PWD, data can be arrangedin any desired direction over a 2-D image; second, calcu-lation time is greatly diminished compared to a 2-D ver-sion of the PWD; and third, the 1-D PWD is an invertiblefunction, granting in this way that information is totallypreserved.A discrete approximation of the Wigner distribution

proposed by Claasen and Mecklembruker [24], similar toBrenners expression [25], has been used here:

Wz!n,k" = 2 $m=N/2

N/21

z!n +m"z*!n m"e2i&2$m/N'k. &7'

In Eq. (7), n and k represent the time and frequencydiscrete variables, respectively, and m is a shifting pa-rameter, which is also discrete. Here +z!n", is a 1-D se-quence of data from the image, containing the gray valuesof N pixels, aligned in the desired direction. Equation (7)can be interpreted as the discrete Fourier transform(DFT) of the product z!n+m"z*!nm". Here z* indicatesthe complex conjugate of z. This equation is limited to aspatial interval !N /2 ,N /21 " (the PWDs window), al-lowing information to be extracted locally. By scanningthe image with a 1-D window of N pixels, i.e., by shiftingthe window to all possible positions over the image, thefull pixelwise PWD of the image is produced. The windowcan be tilted in any direction to obtain a directional dis-tribution. Normalizing and associating Wz!n ,k" withP!n ,k" in Eq. (6), the pixelwise information of the imagecan be extracted as follows: Let us consider a discrete se-quence z!n". A PWD, wn!k", can be calculated with N datavalues centered at position n by means of Eq. (7) and as-signed to each position n. This local PWD can be normal-ized using quantum normalization as described in Sub-section 2.A. This normalization identifies the PWD with aprobability distribution Pn, and the Rnyi entropy associ-ated to position n can be computed as

R3!n" = 1

2log2#$

k=1

N

Pn3!k"% . &8'

3. JUSTIFICATION AND DESCRIPTION OFTHE METHODAnisotropy is by definition the property of being direction-ally dependent and is one of the topics considered by someresearchers to find the relationship between the opera-tional structure of the visual system and the naturalworlds content. A directional common pattern for allnatural scenes cannot be determined because naturalscene composition varies, and the directional content dif-fers from sample to sample. Studies carried out by Li etal. [26] indicate that neurons tuned to horizontal aremore prevalent than vertical. Natural scene content hasalso been the subject of anisotropic examination [2730].The relationship between the prevalence of natural scenecontent at different orientations and the visual ability todetect oriented natural scene content has been recentlystudied by Hansen and Essock [31]. Keil and Cristbal[32] conducted a systematic comparison between the con-tent biases at horizontal and vertical as a function of thespatial frequency and found greater horizontal bias atcertain spatial frequencies with a preponderance of verti-cal content at other spatial frequencies. The experimentscarried out by Keil and Cristbal and the differences theyfound in the distribution of energy for natural images inthe spatial-frequency domain suggest that entropic mea-sures such as the Rnyi entropy, based on measuringthe frequency content of images through a directionalPWD, will be an appropriate tool for image anisotropicmeasures.


Natural images can be considered to be constructed bytextures and edges. Generally speaking, any single imageshows a diversity of textures. Such diversity of texturesand edges is the origin of the anisotropy of images. En-tropy can be locally measured through the spatial-frequency content of the image in a directional scheme.Hence, anisotropy is really another kind of informationthat may be the subject of entropic measures. Entropymeasures information. Hence, differently oriented mea-sures will provide different values of entropy according tothe anisotropy of the images. Natural images can be con-sidered random processes. Consequently, anisotropytends to statistically cancel out, and images should be iso-tropic on average if their size were infinite. However, im-age processing techniques and the HVS handle size-limited images. This spatial limitation of the images givessignificance to slight variations in the anisotropy, whichbecome greater as the spot is smaller and relevant whenentropy is considered at the pixel level. These entropy dif-ferences are fundamentally due to the large influence ofedges in the values of entropy, added to the impossibilityof statistically canceling out the anisotropy of edges dueto the limited size of the images. (Consider, for example, aforest with many vertical components due to the stems ofthe trees; here the horizontal component of the entropywill be unbalanced with the vertical component.) Edgesare the origin of the main differences of image entropywhen it is analyzed at the pixel level.To formalize the calculations required to measure the

anisotropy of the images, Eq. (8) will be used. This equa-tion provides a value of entropy R3!n ,%s" for each pixel.Here %s! !%1 ,%2 , . . . ,%S" represents S different orienta-tions taken to measure entropy. To define a figure of meritfor the image, the expected value of this equation is cal-culated as

R!t,%s" =$nR3!n,%s"/M, &9'

where M represents the image size and t! !1,2, . . . ,T" isintroduced to take into account the T different images in-tegrating the data set [t has been omitted in the right sideof Eq. (9) for simplicity]. In all the experiments describedlater, the expected value of the entropy for all images ofthe test set have been measured using six equally spacedpredefined directions (0, 30, 60, 90, 120, and 150), al-though the number of such directions seems to not becritical in the methods performance. Then the variance(standard deviation or range) of these expected values hasbeen selected as an indicator of the anisotropy of the im-ages.Suppose that R&t ,%s' is the expected value of entropy

for image t! !1,2, . . . ,M", measured in directions %s! !%1 ,%2 , . . . ,%S". Then, the standard deviation for the re-sulting set of values, relative to image t, can be defined as

&&t' =-$s=1

S

&'t R&t,%s''2/S, &10'

where 't is the mean of the values R&t ,%s', as defined bythe expression

't =$s=1

S

R&t,%s'/S, &11'

and the range in image t can be defined as

rg&t' =max+R&t,%s', min+R&t,%s',. &12'

To study the statistical performance of the entropy dis-tributions of natural images, a set of 36 images of 256(256 pixels and 8 bits/pixel have been randomly selectedand processed using the method described here (seeFig. 1).First, in order to illustrate the performance of the

method, a set of ten progressively blurred images hasbeen generated from each image in Fig. 1 by iterativelyapplying a blurring point-spread function (PSF) to thesource images (labeled as 0 in the example shown inFig. 2).The maximum blurring appears on the left-hand side of

Fig. 2 (labeled as -10). Also, another set of ten progres-sively noisier images has been generated by iterativelyadding a constant amount of Gaussian noise, startingfrom the same original image. The noisiest image is onthe right-hand side of Fig. 2, labeled as 10. This consti-tutes a set of 21 registered versions of the same view, 20degraded by blur or noise with different strengths plusthe original reference image.An experimental data test has been carried out, con-

sisting in calculating the expectation value of the Rnyientropy for the 21 registered versions, using the imagedata set depicted in Fig. 1. The entropy has been calcu-lated using Eqs. (8) and (9). A fixed window size of N=8has been considered, and a horizontal orientation for thewindows has been applied. Later, the procedure will beextended to any number of orientations. Figure 3 showsthe results of the entropy values obtained from the imagedata set presented in Fig. 2. This experiment has been re-peated for all natural images shown in Fig. 1. Remark-ably, the graphic presented in Fig. 3, which takes into ac-count the expected values of entropy in each set, haspresented an analogous shape for all the 36 natural im-ages considered in this study.The results indicate how entropy increases when blur

diminishes, but it also increases when more and morenoise is added. This excludes entropy as a good indicatorof quality by itself. Only if noise-free versions are com-pared can entropy and quality be directly correlated.These results are in agreement with other theoreticalstudies based on the multiresolution information analysisof images that conclude that entropy per pixel is strictlydecreasing with respect to decreasing resolution [33].Results of the quality metrics given by Eqs. (10) and

(12) are shown in Fig. 4. The same procedure was appliedto all images shown in Fig. 1, obtaining in all cases a simi-lar steady response. It is remarkable to note that the re-sults shown in Fig. 4 closely resemble the performance ofan ideal image QA function [34]. The shapes of suchcurves present the following desirable properties as themost salient features: (i) accuracy, i.e., a distinct maxi-mum is attained for the best quality; (ii) unimodality, i.e.,it has a single maximum for the best quality; and (iii)computational efficiency. The selection of the standard de-


viation and the range of the entropy have been empiri-cally confirmed as a good indicator of anisotropy for natu-ral images. In-focus, noise-free natural images haveshown a maximum anisotropy if compared to other de-graded versions.

4. EXPERIMENTAL RESULTS

The method has been tested for classifying the imagequality results of different algorithms. Figure 5 illus-trates the results of the quality sorting provided by the

Fig. 2. Test scheme consisting in 21 degraded images. Blur decreases from )10 to 0 and noise increases from 0 to 10. The central imageis the original source image.

Fig. 1. Thirty-six images used for empirically determining the directional entropy in natural images. Framed image processing is de-scribed in Fig. 2 and in the text.


method for two well-known images (Lena and MIT) afterthe application of different denoising algorithms [35]. Im-ages labeled as #1 and #7 correspond to the reference orground truth images. In both cases the classification re-

sults match well with the human visual preference andalso with the PSNR. From left to right, images seem todegrade with increasing blur or noise. The standard de-viation of the expected values of the Rnyi directional en-tropy has been considered to achieve the classification,and the resulting values have been normalized between 0and 1 in order to facilitate the visual assessment. Table 1shows the quantitative results provided by the describedmethod in comparison with the PSNR and the SSIM met-ric [3].Similar results have been observed with other natural

images (not shown here). Nevertheless, images to be clas-sified by this method must fulfill some requirements in or-der to guarantee the reliability of the measurement. Im-ages to be classified must be registered, and degradationmust be uniform. To illustrate this assumption, anotherexample in the area of superresolution (SR) imaging [36]is shown in Fig. 6. The images shown in Fig. 6(a) presenta spatial-variant blur as two 3-D objects compete to be infocus at the same time. Hence, as the images are 2-D rep-resentations of 3-D objects, different areas in the sameimage may suffer from different amounts of degradation.Bearing in mind that in this method the quality is mea-sured as an average value, classification cannot be com-

Fig. 4. A. Standard deviation of the expected values of the Rnyi directional entropy for the images shown in Fig. 2. B. Range of theexpected values of the Rnyi directional entropy for the images in Fig. 2. The variability refers to six different equally spaced orientationsof the entropy in the image. The maximum variability corresponds to the original image, as an in-focus, noise-free version of the test setdefined in Fig. 2.

Fig. 5. Upper row (from left to right): original Lena image (#1) and progressively degraded blurred and noisy versions. Bottom row (fromleft to right): original MIT image (#7) and progressively degraded blurred and noisy versions. Images are courtesy of Sylvain Fischer [35].

Fig. 3. Expected value of the pixelwise Rnyi entropy of the 21images of the test set presented in Fig. 2.


pletely satisfactory; i.e., some areas are in focus whileother areas are out of focus in the same photogram.Hence, on average, images are well classified but, in sepa-rate regions (the face of the child, the shirt, the head inthe foreground, etc.) some disagreement with the visualappearance is possible. Figure 6(b) shows another ex-ample in the same SR area where the sorted quality of theimages correlates well with the visual judgment. In thisapplication domain (as in the case of image fusion) it isvery common that the reference image is absent, hinder-ing the assessment of the different results.In order to determine whether this method is in agree-

ment with human judgment, we have also conducted a setof experiments with a group of four images taken from theLIVE database [37] proposed by Sheikh et al. [38], whichcan be considered to be good representatives of naturaland artificial images. In [38] they present the results ofan extensive subjective QA study in which a total of 779distorted images were evaluated by human subjects, andthey use the results to evaluate the performance of sev-eral prominent full-reference image QA algorithms.Tables 25 present and compare the results obtained witha group of four images (the luminance component only)extracted from the above-mentioned database, after mea-suring their quality by means of the method describedhere. It is necessary to remark on the good performance of

the current method for smooth distortion (blur) and ran-dom noise (see Tables 2 and 3). Structured distortion suchas in the case of JPEG compression presents special ar-rangements of equal-valued pixels along privileged direc-tions (horizontal and vertical). Blocking artifacts can beartificially introduced by the JPEG compression proce-dure, which can produce an erroneous estimate of the an-isotropy measure. A feasible solution for reducing theblocking artifacts can be based on applying a deblockingfiltering as it was proposed in [39]. The second approachis to consider that structured geometrical distortion in-creases the anisotropy of JPEG images due to the pres-ence of zero-entropy values in the histogram. The currentmethod is initially intended to be used for the QA of natu-ral images. However, a slight modification of this measurewill allow its application to JPEG compressed images.The modification is based on introducing a correcting fac-tor that accounts for the number of zero-entropy values inthe directional entropy histograms. This factor penalizesthe presence of geometrically equal-valued pixels that areresponsible for the high zero-entropy counts in JPEG im-ages. A high zero-entropy count rarely appears in the en-tropy histograms of natural images. Therefore such crite-rion can be used when natural and JPEG images arecompared. Suppose that L is the size of the image and S isthe number of directions used to measure the images an-isotropy. Suppose also that K is the total number of zero-entropy values found in the S orientations while measur-ing the entropy. Then

& = # KSL%*% &13'provides a corrected measure of anisotropy for JPEG im-ages. In Eq. (13) & is given by Eq. (10) and * is a param-eter that penalizes the strength of the zero-entropycounts over the original anisotropy measure and whosevalue has been empirically determined to be *=0.1. Table

Table 1. Comparison of Different Image QualityMeasures

Lena PSNR SSIM &&t' MIT PSNR SSIM &&t'

#1 1 1 #7 1 1#2 26.01 0.7923 0.82 #8 21.77 0.6618 0.77#3 25.51 0.7766 0.80 #9 21.24 0.6273 0.74#4 24.99 0.7459 0.72 #10 20.57 0.5917 0.66#5 24.36 0.7129 0.71 #11 20.00 0.5574 0.65#6 20.34 0.5357 0.55 #12 15.56 0.4002 0.39

Fig. 6. Classification obtained with two sets of test images in a superresolution scenario. From left to right, image quality decreases anda quantitative figure of merit (standard deviation of directional entropy per pixel) is given at the bottom of each image. Images arecourtesy of Filip roubek.


4 shows how the corrected metric successfully discountsthe blocking artifact in the case of JPEG compressed im-ages and provides a good sorting estimate of their quality.

The current procedure for the tested data set produces agood match with human judgment, although the authorsrecognize that extensive testing with ground truth data isrequired for this method to be widely accepted as a QAmetric. This work has concentrated on the development ofa new objective quality metric, and we used the LIVE da-tabase as a reference for the subjective assessment withhuman subjects. Further work will explore the influenceof the combined presence of multiple artifacts such asblockiness and noisiness.

5. CONCLUSIONSA new method of image QA has been introduced in thispaper. The new metric provides an image quality measurewithout a reference or ground truth image, facilitating ingeneral a sorting mechanism for selecting the best imageamong a set of processed images. Besides that, a distinctfeature of this measure is that it is capable of distinguish-ing the presence of noise in images by decreasing its valuewhen noise is present. The method is based on measuringthe averaged anisotropy of the image by means of a pix-elwise directional entropy. The robustness of the methodhas been experimentally validated in the case of natural

Table 3. Algorithm Evaluation Using the Four Imagesa

Buildings&&k'/

(PSNR) Lighthouse&&k'/

(PSNR) Statue&&k'/

(PSNR) Stream&&k'/

(PSNR)

#159(0.000)

1 #164(0.00)

1 #148(0.000)

1 #151(0.000)

1

#103(0.031)

0.99(33.61)

#43(0.019)

0.99(37.56)

#85(0.015)

0.96(39.46)

#138(0.031)

0.98(33.6)

#46(0.058)

0.94(28.24)

#114(0.039)

0.97(31.63)

#55(0.046)

0.82(30.2)

#88(0.062)

0.93(27.63)

#130(0.2890)

0.40(15.49)

#40(0.062)

0.93(27.58)

#25(0.109)

0.56(23.12)

#2(0.187)

0.63(18.48)

#61(0.4062)

0.26(13.38)

#96(0.171)

0.69(19.08)

#91(0.203)

0.38(18.14)

#106(0.312)

0.36(14.86)

#4(1.9960)

0.03(8.65)

#66(1.000)

0.12(10.19)

#145(1.00)

0.05(9.63)

#131(0.500)

0.21(12.28)

aBuildings, Lighthouse, Statue, and Stream taken from the LIVE database for WHITE NOISE degradation. The standard deviation of the noise is indicated below the

reference number of each image &columns 1, 3, 5, and 7'. The corresponding PSNR has been included in columns 2, 4, 6, and 8.


Buildings&&k'/

(PSNR) Lighthouse&&k'/

(PSNR) Statue&&k'/

(PSNR) Stream&&k'/

(PSNR)

#159(0.000)

1 #164(0.00)

1 #148(0.000)

1 #151(0.000)

1

#45(0.5624)

0.71(29.41)

#4(0.4478)

0.82(39.15)

#98(0.8489)

0.58(31.38)

#71(0.4192)

0.90(37.4)

#7(0.8489)

0.49(24.29)

#102(0.8220)

0.46(28.32)

#77(1.3072)

0.41(28.6)

#18(0.7629)

0.55(25.29)

#62(0.9348)

0.45(23.52)

#15(1.1353)

0.32(25.93)

#131(1.8228)

0.28(26.98)

#126(0.834)

0.51(24.55)

#134(1.5364)

0.24(20.62)

#97(1.4791)

0.23(24.5)

#54(2.166)

0.22(26.24)

#50(1.020)

0.42(23.23)

#73(2.6249)

0.07(18.64)

#24(14.999)

0.003(18.5)

#120(3.999)

0.05(24.02)

#58(3.0833)

0.07(19.57)

aBuildings, Lighthouse, Statue, and Stream taken from the LIVE database for BLUR degradation. The standard deviation of the Gaussian kernel is indicated below

the reference number of each image &columns 1, 3, 5, and 7'. The corresponding PSNR has been included in columns 2, 4, 6, and 8.

Table 4. Algorithm Evaluation Using the FourImagesa

Buildings &&k' Lighthouse &&k' Statue &&k' Stream &&k'

#157(1.77)

1 #3(0)

1 #13(2.77)

1 #212(0)

1

#227(0)

0.86 #57(2.6)

0.88 #70(2.19)

0.94 #137(1.683)

0.85

#163(1.03)

0.71 #231(1.29)

0.64 #130(1.10)

0.89 #185(1.00)

0.73

#43(0.58)

0.45 #44(0.42)

0.29 #208(0)

0.84 #16(0.57)

0.63

#162(0.267)

0.35 #86(0.39)

0.26 #221(0.165)

0.71 #85(0.41)

0.57

#204(0.247)

0.33 #161(0.19)

0.17 #11(0.29)

0.68 #100(0.29)

0.51

#131(0.18)

0.16 #217(0.20)

0.36

aBuildings, Lighthouse, Statue, and Stream taken from the LIVE data-

base for JPEG compression. The compression bitrate is indicated below the referencenumber of each image &columns 1, 3, 5, and 7'.


images, and results have been used to determine the rela-tive quality of diverse processed images after applyingdifferent image processing algorithms. The experimentalevaluation of the data set used demonstrates the effec-tiveness and promise of the proposed technique, althoughsome assumptions such as registration and spatial-invariant degradation should be fulfilled by the imagesunder scrutiny to obtain the best results.

ACKNOWLEDGMENTSThis research has been supported by the followingprojects: TEC2004-00834, TEC2005-24739-E, TEC2005-24046-E, and 20045OE184 from the Spanish Ministry ofEducation and Science and PI040765 from the SpanishMinistry of Health. We thank S. Fischer and F. Sroubekfor facilitating use of the pictures of Figs. 5 and 6, respec-tively.

REFERENCES1. Z. Wang and A. Bovik, Why is image quality assessment so

difficult? IEEE International Conference on AcousticsSpeech and Signal Processing (IEEE, 2002), pp. 33133316.

2. Z. Zhang and R. S. Blum, A categorization of multiscale-decomposition-based image fusion schemes with aperformance study for a digital camera application, Proc.IEEE 87, 13151328 (1999).

3. Z. Wang and A. C. Bovik, A universal image qualityindex, IEEE Signal Process. Lett. 9, 8184 (2002).

4. Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli,Image quality assessment: from error visibility tostructural similarity, IEEE Trans. Image Process. 13,600612 (2004).

5. H. R. Sheikh, A. C. Bovik, and G. DeVeciana, Aninformation fidelity criterion for image quality assessmentusing natural scene statistics, IEEE Trans. Image Process.14, 21172128 (2005).

6. H. R. Sheikh and A. C. Bovik, Image information andvisual quality, IEEE Trans. Image Process. 15, 430444(2006).

7. H. R. Sheikh, A. C. Bovik, and L. K. Cormack, No-reference quality assessment using natural scene statistics:JPEG2000, IEEE Trans. Image Process. 14, 19181927(2005).

8. C. E. Shannon and W. Weaver, The Mathematical Theory ofCommunication (University of Illinois Press, 1949).

9. E. N. Kirsanova and M. G. Sadovsky, Entropy approach in

the analysis of anisotropy of digital images, Open Syst.Inf. Dyn. 9, 239250 (2002).

10. W. J. Williams, M. L. Brown, and A. O. Hero, Uncertainity,information and timefrequency distributions, Proc. SPIE1566, 144156 (1991).

11. P. Marziliano, F. Dufaux, S. Winkler, and T. Ebrahimi,Perceptual blur and ringing metrics: application toJPEG2000, Signal Process. 19, 163172 (2004).

12. N. Cvejic, C. N. Canagarajah, and D. R. Bull, Image fusionmetric based on mutual information and Tsallis entropy,Electron. Lett. 42, 626627 (2006).

13. C. S. Xydeas and V. Petkovic, Objective image fusionperformance measure, Electron. Lett. 36, 308309 (2000).

14. G. Qu, D. Zhang, and P. Yang, Information measure forperformance of image fusion, Electron. Lett. 38, 313315(2002).

15. R. Danserau and W. Kinsner, New relative multifractaldimension measures, in IEEE International Conference onAcoustics Speech and Signal Processing (IEEE, 2001), pp.17411744.

16. L. Stankovic, A measure of some timefrequencydistributions concentration, Signal Process. 81, 621631(2001).

17. N. Wiener, Cybernetics (Wiley, 1948).18. A. Rnyi, Some fundamental questions of information

theory, in Selected Papers of Alfrd Rnyi, Pl Turn, ed.(Akadmiai Kiad, 1976), Vol. 3, pp. 526552 [Originally inMagy. Tud. Akad. III Oszt. Kzl. 10, 251282 (1960)].

19. T. H. Sang and W. J. Williams, Rnyi information andsignal dependent optimal kernel design, in IEEEInternational Conference on Acoustics Speech and SignalProcessing (IEEE, 1995), Vol. 2, pp. 9971000.

20. P. Flandrin, R. G. Baraniuk, and O. Michel,Timefrequency complexity and information, in IEEEInternational Conference on Acoustics Speech and SignalProcessing (IEEE, 1994), Vol. 3, pp. 329332.

21. R. Eisberg and R. Resnick, Quantum Physics (Wiley, 1974).22. L. D. Jacobson and H. Wechsler, Joint spatial/spatial-

frequency representation, Signal Process. 14, 3768(1988).

23. E. Wigner, On the quantum correction for thermodynamicequilibrium, Phys. Rev. 40, 749759 (1932).

24. T. A. C. M. Claasen and W. F. G. Mecklenbruker, TheWigner distributiona tool for time frequency analysis,Parts IIII, Philips J. Res. 35, 217250, 276300, 372389(1980).

25. K. H. Brenner, A discrete version of the Wignerdistribution function, in Proceedings of EURASIP, SignalProcessing II: Theories and Applications (North Holland,1983), pp. 307309.

26. B. Li, M. R. Peterson, and R. D. Freeman, Oblique effect: aneural bias in the visual cortex, J. Neurophysiol. 90,204217 (2003).


Buildings &&k' Lighthouse &&k' Statue &&k' Stream &&k'

#199(1.666)

1 #174(1.54)

1 #162(0.74)

1 #217(1.48)

1

#222(0.84)

0.96 #51(0.6505)

0.97 #102(2.41)

0.99 #17(0.40)

0.98

#13(0.40)

0.89 #149(0.364)

0.96 #116(0.222)

0.97 #8(0.71)

0.93

#33(0.37)

0.88 #106(0.242)

0.92 #227(0.05)

0.97 #71(0.19)

0.79

#29(0.20)

0.79 #91(0.242)

0.92 #92(0.377)

0.95 #175(0.050)

0.58

#156(0.12)

0.69 #202(0.05)

0.75 #169(0.07)

0.85

aBuildings, Lighthouse, Statue, and Stream taken from the LIVE database for JPEG2000 compression. The compression bitrate is indicated below the reference

number of each image &columns 1, 3, 5, and 7'.


27. E. Switkes, M. J. Mayer, and J. A. Sloan, Spatialfrequency analysis of the visual environment: anisotropyand the carpentered environment hypothesis, Vision Res.18, 13931399 (1978).

28. R. J. Baddeley and P. J. B. Hancock, A statistical analysisof natural images matches psychophysically derivedorientation tuning curves, Proc. R. Soc. London, Ser. B246, 219223 (1991).

29. P. J. B. Hancock, R. J. Baddeley, and L. S. Smith, Theprincipal components of natural images, Network Comput.Neural Syst. 3, 6170 (1992).

30. J. Haung and D. Mumford, Statistics of natural imagesand models, in Proceedings of the ICCV, 1, 541547 (1999).

31. B. C. Hansen and E. A. Essock, A horizontal bias inhuman visual processing of orientation and itscorrespondence to the structural components of naturalscenes, J. Vision 4, 10441060 (2004).

32. M. S. Keil and G. Cristbal, Separating the chaff from thewheat: possible origins of the oblique effect, J. Opt. Soc.Am. A 17, 697710 (2000).

33. R. Romn, J. J. Quesada, and J. Martnez,Multiresolution-information analysis for images, SignalProcess. 24, 7791 (1991).

34. Y. Qu, Z. Pu, H. Zhao, and Y. Zhao, Comparison ofdifferent quality assessment functions in autoregulativeillumination intensity algorithms, Opt. Eng. (Bellingham)45, 117201 (2006).

35. S. Fischer, F. Sroubek, L. Perrinet, R. Redondo, and G.Cristbal, Self-invertible 2D Gabor wavelets, Int. J.Comput. Vis. available at http://www.springerlink.com/content/07q411454q407047/fulltext.pdf.

36. F. Sroubek, G. Cristbal, and J. Flusser, Combinedsuperresolution and blind deconvolution, in InformationOptics: 5th International Workshop (American Institute ofPhysics, 2006), paper CP860, pp. 1526.

37. H. R. Sheikh, Z. Wang, L. Cormack, and A. C. Bovik, LIVEimage quality assessment database, Release 2, 2005[Online]. Available at http://live.ece.utexas.edu/research/quality.

38. H. R. Sheikh, M. F. Sabir, and A. C. Bovik, A statisticalevaluation of recent full reference image qualityassessment algorithms, IEEE Trans. Image Process. 15,34403451 (2006).

39. M. Y. Shen and C. C. Jay Kuo, Review of postprocessingtechniques for compression artifact removal, J. VisualCommun. Image Represent 9, 214 (1998).


gabarda,cristobal 07

Documents