Neurocomputing 215 (2016) 21–31

Contents lists available at ScienceDirect

Neurocomputing
journal homepage: www.elsevier.com/locate/neucom

Reorganized DCT-based image representation for reduced reference
stereoscopic image quality assessment
Lin Ma a, Xu Wang b,c,n, Qiong Liu d, King Ngi Ngan eaHuawei Noah's Ark Lab, Hong Kong
College of Computer Science and Software Engineering, Shenzhen University, Shenzhen 518060, ChinacNanjing University of Information Science & Technology, Nanjing 210044, Chinad
Department of Electronics & Information Engineering, Huazhong University of Science & Technology, Wuhan 430074, Chinae
Department of Electronic Engineering, The Chinese University of Hong Kong, Hong Kongb

art ic l e i nf o

a b s t r a c t

Article history:
Received 28 January 2015
Received in revised form
17 June 2015
Accepted 20 June 2015
Available online 10 June 2016

In this paper, a novel reduced reference (RR) stereoscopic image quality assessment (SIQA) is proposed bycharacterizing the statistical properties of the stereoscopic image in the reorganized discrete cosine
transform (RDCT) domain. Firstly, the difference image between the left and right view images is computed. Afterwards, the left and right view images, as well as the difference image, are decomposed byblock-based discrete cosine transform (DCT). The DCT coefﬁcients are further reorganized into a three-level
coefﬁcient tree, resulting in ten RDCT subbands. For each RDCT subband, the statistical property of thecoefﬁcient distribution is modeled by the generalized Gaussian density (GGD) function. And the mutual
information (MI) and energy distribution ratio (EDR) are employed to depict the statistical properties
across different RDCT subbands. Moreover, EDR can further model the mutual masking property of thehuman visual system (HVS). By considering the GGD modeling behavior within each RDCT subband and MI
together EDR characterizing behavior across RDCT subbands, the statistical properties of the stereoscopic
image are fully exploited, including the left view, right view, and the difference image. Experimental results
demonstrated that the statistical properties of the difference image can well represent the perceptual
quality of the stereoscopic image, which outperforms the representative RR quality metrics for stereoscopic
image and even some full reference (FR) quality metrics. By considering the left view, right view, anddifference image together, the performances of the proposed RR SIQA can be further improved, which
presenting a more closely relationship between the quality metric output and human visual perception.
& 2016 Elsevier B.V. All rights reserved.

Keywords:
Stereoscopic image quality assessment(SIQA)
Reduced reference (RR)
Reorganized discrete cosine transform(RDCT)
Human visual system (HVS)

1. Introduction
Image perceptual quality assessment plays the essential role in
the image processing and communication [1,2], such as image
capturing, compression, storage, transmission, displaying, printing,sharing, and so on. Therefore, there are many research works aim todevelop image quality metrics for guiding the performance optimization during each step of image processing [3,4] and communication. Human eyes are the ultimate receivers of the images. The
subjective test process is regarded as the most reliable way toevaluate the perceptual quality of the image. However, the subjective test process is time-consuming, which is impractical for the
optimization process of the online image processing. Therefore, thenCorresponding author at: College of Computer Science and Software Engineering, Shenzhen University, Shenzhen 518060, China.
E-mail addresses: forest.linma@gmail.com (L. Ma),wangxu.cise@gmail.com (X. Wang), q.liu@hust.edu.cn (Q. Liu),knngan@ee.cuhk.edu.hk (K.N. Ngan).

http://dx.doi.org/10.1016/j.neucom.2015.06.116
0925-2312/& 2016 Elsevier B.V. All rights reserved.

objective quality metrics that can automatically evaluate the image
perceptual quality and guide the image processing applications aredemanded.
Nowadays, with the rapid developments of content generationand display technology, three-dimensional (3D) applications andservices are becoming more and more popular for visual quality ofexperiences (QoE) of human viewers. The 3D contents displaying
on the 3D devices have brought new entertainments and more
vivid experiences to the consumers, which attract more and more
attentions from not only researchers but also the industries. For
these applications, the quality of 3D content is the most criticalpart to provide the visual QoE. However, in the 3D processing
chain including capturing, processing [5–7], coding [8,9], transmitting, reconstruction, retrieving, etc., artifacts are inevitably introduced due to the resource shortage in processing [10]. Therefore, how to automatically evaluate the perceptual quality of 3D
content [11] becomes a challenging issue in 3D visual signal processing. Moreover, it is claimed that the artifacts of 3D content

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L. Ma et al. / Neurocomputing 215 (2016) 21–31

affect more on human visual system (HVS) [12,13], compared withthe conventional 2D contents. Therefore, the realization of the HVS
properties on 3D content is researched to help more accurately
evaluate perceptual quality of the 3D contents.
According to the availability of the reference image, the conventional 2D image quality assessment (IQA) methods can be divided into
three categories, speciﬁcally the full reference (FR) [14–16], no reference (NR) [17–22], and reduced reference (RR) [22–28], respectively.
FR metrics require the full assess of the original image to evaluate the perceptual quality of the distorted image. The original
image is assumed to be artifact free and of perfect quality. Such
metrics can be employed to guide the perceptual quality optimization during image/video compression, watermarking, and so on.
The most appealing quality metrics are the mean square error(MSE) and its related peak signal-to-noise ratio (PSNR), because of
their simplicity, clear physical meaning, and easy optimization.
However, MSE and PSNR do not correlate with HVS properties.
Therefore, many FR metrics are developed to incorporate the HVS
properties and image signal properties. Wang et al. developed themost popular image quality metric structural similarity (SSIM) [14]that captures the structure information loss to depict the perceptual
quality of the distorted image. A wavelet-based visual signal-tonoise ratio (VSNR) is developed to capture the distortions in wavelet
domain [15]. A simple quality metric considering texture masking
and contrast sensitivity function is developed for perceptual image
coding [29]. In [16], Ma et al. proposed to incorporate the horizontal
effect of HVS into SSIM for a better image quality metric.
However, in real-world applications, we are not able to accessthe original image for quality analysis in most cases, where only the
distorted image is available. The NR quality metrics are thus employed. Many researchers employ the behaviors of speciﬁc distortions for the NR quality assessment, such as the blocking artifact of
JPEG coded images, ringing artifact of the JPEG 2000 coded images,
and so on. As JPEG 2000 employs the wavelet transform to compress the image, the wavelet statistical model is utilized to capture
the compression distortion [18]. Liang et al. [19] combined the
sharpness, blurring, and ringing measurements together to depict
the perceptual quality of the JPEG 2000 coded image. The distribution of the DCT coefﬁcient after quantization is modeled in [20]to predict the PSNR value of the JPEG coded image. Furthermore,
Ferzli et al. [21] did the psychophysical experiment to test theblurring tolerance ability of the HVS, based on which the just-noticeable blur (JNB) model is developed. These methods employ the
behaviors of speciﬁc distortions to predict the degradation level.
Therefore, if a new distortion is introduced, these methods canhardly evaluate the perceptual quality of the distorted image. In
order to compromise between the FR and NR IQAs, RR IQAs aredeveloped. It is expected that the RR methods can effectively
evaluate the image perceptual quality based on a limited number of
RR features extracted from the reference image. Only a small
number of bits are required for representing the extracted features,
which can be efﬁciently encoded and transmitted for the quality
analysis. Consequently, it will be very useful for the quality monitoring during the image transmission and communication.
For RR quality metrics, only partial information of the original
image is available for quality analysis, which can be further categorized into the following three classes.

 Distortion-based RR metrics: The behaviors of the distortions aremodeled for RR quality metric design. Wolf et al. [30,31]
proposed to extract a set of spatial and temporal features formeasuring the distortions introduced in the standard video
compression and communication environment. The featuresthat are associated with the blurring, blocking, and frame
differences are extracted in [32] to depict the compression
artifacts introduced by MPEG-2. These RR quality metrics aredesigned for some speciﬁc distortions, which cannot be effectively applied to the other images of different distortions.
Therefore, a general RR IQA for evaluating the image perceptual
quality of different distortions is required.
 HVS-based RR metrics: HVS properties should be considered for
quality assessment, as the human eyes are the ultimate receivers. Le Callet et al. [33] employed a neural network to train
and evaluate the perceptual qualities of video sequences basedon the perceptual-related features extracted from the video
frames. In [34,35], the perceptual features motivated from thecomputational models of low level vision are extracted as the
reduced descriptors to represent the image perceptual quality.
The merits from the contourlet transform, the contrast sensitivity function, and Webers law of just noticeable difference areincorporated to derive an RR IQA [36], which are employed forevaluating the perceptual qualities of the JPEG and JPEG 2000
coded images. Recently, an RR IQA [37] for wireless imaging isdeveloped by considering different structural information thatis observed in the distortion model of wireless link.
 Statistics-based RR metrics: The statistical modeling of the image
signal has been investigated for the image perceptual quality
assessment for RR IQAs. In [38,23], Wang et al. proposed awavelet-domain natural image statistic metric (WNISM), whichmodels the marginal probability distribution of the wavelet
coefﬁcients of a natural image by the generalized Gaussian
density (GGD) function. The Kullback–Leibler distance (KLD) isused to depict the distribution difference. To improve theperformance and reduce the number of features, the probability
distribution was represented by the Gaussian scale mixture(GSM) model in wavelet domain [39]. In [24–26], the RR features
are extracted in the reorganized domain. In [24], the DCT
coefﬁcients are ﬁrst reorganized into several representative
subbands, whose distributions are modeled by the GGD. The
city-block distance (CBD) is utilized to capture the image perceptual quality. In [40], the statistics of image gradient magnitude are modeled by the Weibull distribution to develop an RR
image quality metric. Also the statistics of the edge [41] areutilized for developing the RR IQA. In [42], the authors measure
the differences between the entropies of wavelet coefﬁcients of
the reference and distorted image to quantify the image information change, which can indicate the image perceptual quality.
In this paper, we proposed a novel RR SIQA based on the statistical modeling of the stereoscopic image. The difference image iscomputed by referring to the left view and right view image. After
performing the block-based DCT and reorganization process, thecoefﬁcients of the images (left view, right view, and the different
image) are reorganized into different RDCT subbands. The statistical property within each RDCT subband is exploited by the GGDmodeling of the coefﬁcient distribution. The statistical property
across RDCT subbands is modeled by the energy distribution ratio(EDR), which can be further employed for modeling the HVSmutual masking property. The main contributions of our proposed
method are listed as follows.

 The statistical property of stereoscopic image is studied forperceptual quality analysis. The statistical properties of theobtained difference image are ﬁrstly investigated in the RDCT
domain. By considering the difference image, the left and rightview images are considered together for perceptual quality
analysis, which matches the HVS perception of the stereoscopic
image.
 The statistical properties of the difference image are characterized from two perspectives, speciﬁcally the within andacross RDCT subband statistical properties, respectively. The
statistical properties depicted within and across the RDCTL. Ma et al. / Neurocomputing 215 (2016) 21–31

subbands can help capture the distortions introduced to thestereoscopic image.
 The difference image is demonstrated to be most important for
SIQA, compared to the sole left view and right view image.
Therefore, the proposed RR SIQA metric can be viewed as ascalable approach. If only a few RR features are constrained, we
can only extract the RR features from the difference image for
quality analysis. Otherwise, all the RR features are extracted for
quality analysis from the images, including the left view, rightview, and difference image.
The rest of this paper is organized as follows. Section 2 overviews the related work. Section 3 illustrates the proposed RR SIQA
model. Experimental results are provided in Section 4. Finally,
conclusions are given in Section 5.

2. Related work
As 3D images are prevailing, the quality evaluation of 3Dimages is demanded for the quality control and optimization for
better QoE of human viewers. Existing perceptual quality metrics
for 3D images can be roughly divided into two categories, named
quality model extended from 2D image quality assessment (IQA)
metrics and the quality model speciﬁcally designed for 3D images.
The ﬁrst category simply extends the 2D IQA models to thestereoscopic image. Such models treat each view image of the stereoscopic image independently. By fusing the obtained quality index of each view image, the quality value of the stereoscopic image
is determined. In [43], Hewage et al. investigated the correlation
between subjective quality scores and three quality metrics, including PSNR, Video Quality Model (VQM) [44], and SSIM [14] for3D video content. It is demonstrated that the VQM metric performs
better than the other two metrics for predicting the overall perceptual quality of the stereoscopic image. The quality metric for 3D
image in [45] is also extended from 2D IQAs. These extended metrics treat each view image independently, which does not consider
the binocular vision properties. However, such binocular vision
properties are critical for the 3D image perception, which make theextended quality metrics generate unsatisfactory performances.
The other category considers the speciﬁc HVS properties ofviewing 3D images, such as the binocular vision and depth perception properties. In [46], Benoit et al. fused the depth (or disparity) information and 2D quality metrics to evaluate the 3D image
quality. Ref. [47] investigated the integration of disparity information into 2D quality metrics. Boev et al. [48] combined the monoscopic quality component and the stereoscopic quality component
to develop a stereo-video quality metric, where the cyclopean image concept was ﬁrst introduced by fusing the left and right views.
To further improve the performance of 3D IQA, the binocular fusion
and rivalry properties are investigated. The binocular spatial sensitivity (BSS) weighted metric is developed [49] based on the binocular just noticeable difference model [50]. Chen et al. [51] developed a framework for assessing the quality of stereoscopic
images that have been afﬂicted by possibly asymmetric distortions.
The linear rivalry model was employed to exploit the binocular
rivalry property in [52]. However, the features employed in thebinocular vision properties based metric are local, which may notwork well when the original 3D images are inaccessible.
For 3D RR IQA metrics, image features including the distortion
driven features such as binary edge mask [53,54], and HVS features
such as contrast sensitivity index [55], are extracted and compared for
quality analysis, which correlate with HVS perception and image statistical properties. The marginal distributions of disparity [56] subband
coefﬁcients can be well ﬁtted by the GGD model, which is similar tothe luminance images. This property was employed as prior23

information to improve the performance of Bayesian disparity estimation [57]. In [27], Wang et al. extracted the RR features in thecontourlet domain for 3D image quality assessment. After receiving
the RR features, the RR metrics evaluate the perceptual quality of the
distorted images by referring to the corresponding extracted RR
features.

3. Proposed reduced reference (RR) stereoscopic image quality
assessment (SIQA)
3.1. Statistical properties of the stereoscopic image
The statistical properties of conventional 2D images have been extensively studied, such as the GGD modeling of the wavelet coefﬁcientin [23], the GSM modeling in wavelet domain [39], GGD modeling in
RDCT domain [24]. However, there are no literatures discussing thestatistical modeling of the stereoscopic image, speciﬁcally jointly considering the left view and right view image together. As mentioned
before, HVS perception properties of the stereoscopic images signiﬁcantly affect the quality analysis of the stereoscopic image. It is
expected that an accurate modeling of the statistical properties of thestereoscopic image can help to capture the quality degradation. In thissection, we focus on the statistical modeling of the stereoscopic image
by jointly considering the left view and right view image.
The correlation between the left view and right view image canbe exploited by performing the disparity map estimation between
the two images. The disparity map depicts the pixel replacement of
one view image referring to the other image. By using the disparity
map, we can obtain the view difference image between the two view
images. Such difference image introduces the view disparities to thehuman eyes, which are critical to generate the 3D experiences of thestereoscopic image. Therefore, the statistical properties of such difference image are investigated in this section. However, as we target
at an RR SIQA, we need to consider the RR feature extraction in thereceiver side, speciﬁcally the statistical feature extraction. The features in the receiver side should be easy for computation and extraction following the same procedure as the sender side. Therefore,
we cannot perform the disparity map estimation in the sender andreceiver side. Firstly, the computational complexity is high. Secondly
the disparity map estimated in the reference and distorted stereoscopic images will be different. Therefore, we employ a straightforward and simple way to generate the difference image by subtracting
one view image from the other view image. The statistical properties
of such difference image are studied. And the experimental results in
Section 4 will illustrate the performance improvements by employing the difference image, not only for our proposed RR SIQA, but also
for the other RR SIQAs as well as the FR SIQAs.
Supposing the left view image is Il and the right view image isIr, the difference image Id is obtained by:

Id = Ir − Il.

(1)

Il − Ir can also be employed to obtain Id, which makes no differences to the statistical modeling. The corresponding images of Il, Ir,
and Id are illustrated in Fig. 1. Only the luminance component of
the image is illustrated, which mostly affects the HVS perception.
The difference image is processed as Id + 128 for better visualization. The pixel value distribution of the difference image is illustrated in Fig. 1(d), where the red line denotes the pixel value
distribution of the difference image. It can be observed that the
pixel value distribution presents a high kurtosis distribution (witha sharp peak at zero and a fat-tail distribution). As discussed in[24,13], the high kurtosis distributions can be well modeled by
GGD, which is deﬁned in:

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L. Ma et al. / Neurocomputing 215 (2016) 21–31

Fig. 1. The stereoscopic image and the generated difference image. (For interpretation of the references to color in this ﬁgure caption, the reader is referred to the web
version of this paper.

Pα, β (x) =|x| ββe−( α )⎛ 1⎞2αΓ ⎜ ⎟
⎝ β⎠(2)where β > 0 and α are the two parameters of the GGD function. Γis the Gamma Function denoted by:Γ (x) =∞

∫0 t x − 1e−t dt(3)αmodels the width of the peak (standard deviation), while β isinversely proportional to the decreasing rate of the peak. α and βalso refer to the scale and shape parameters, respectively. The blueline indicates the GGD modeling of the difference image coefﬁcient distribution. It can be observed that the blue and red lines
overlap with each other, which demonstrates an accurate GGDmodeling of the coefﬁcient distribution. The city-block distance(CBD) [24,26] is employed to capture the distribution difference,
which is deﬁned as:
hL

dCBD (p, q) = ∑ |p (i) − q (i)|
i=1

(4)

where p and q are two coefﬁcient distributions, and hL denotes thenumber of histogram bins.
As illustrated in [24,26], the coefﬁcient distribution of the natural
image in RDCT domain can be well modeled by GGD. In this paper, we
make the ﬁrst attempt to employ the RDCT decomposition to process
the difference image between left and right view images. We investigate whether the RDCT coefﬁcient distribution of the difference
image can be accurately modeled by GGD and whether such modelingfeatures can be employed as the stereoscopic image features, which
can further help for stereoscopic image quality assessment.
Firstly, the difference image as in Fig. 1(c) is obtained. Afterwards,

the block-based DCT is employed to transform the image pixel values
to the DCT domain. Speciﬁcally, the 8  8 block-based DCT is employed. The obtained image after performing 8  8 DCT is illustrated
in Fig. 2(a). After obtaining the DCT coefﬁcients, the reorganization
process as introduced in [24] is applied, which generate the corresponding RDCT representation as illustrated in Fig. 2(b). For better
visualization, the coefﬁcients of the DCT and RDCT representations
are rescaled in the range of [0,255]. For the reorganization process,the 8  8 DCT coefﬁcients are ﬁrstly decomposed into ten groups.
Then the coefﬁcients of all the 8  8 DCT blocks are grouped andorganized together according to their positions. The reorganization
process results in a three level coefﬁcient tree with ten RDCT subbands S0, … , S9 , as shown in Fig. 2(b). The RDCT representation
presents a similar appearance like a wavelet representation, which
exhibits structural similarity between subbands and coefﬁcientmagnitude decaying toward high frequency subbands.
As discussed in [26], the RDCT coefﬁcient distribution of thenatural image can be well depicted by GGD. In this paper, we will
investigate how the GGD function models the coefﬁcient distribution of the difference image and its RDCT subbands. As illustrated inFig. 1(d), GGD is demonstrated to accurately model the coefﬁcient
distribution of the difference image with the CBD value equals to
0.1824. The GGD modeling of the RDCT subband coefﬁcient distribution is illustrated in Fig. 3. It can be observed that the coefﬁcient distribution of the RDCT subband can be more accurately
modeled by GGD, compared with the difference image in Fig. 1(d).
We also employ the CBD as deﬁned in Eq. (4) to evaluate the GGDmodeling accuracy, which is also illustrated in Fig. 3. It can be observed that only two subbands S1 and S2 generate larger CBD values
than the CBD value of the difference image. And the average CBDvalue over all the 9 subbands is 0.129322, which is much smaller
than the CBD value of the difference image. It means that the GGD is

L. Ma et al. / Neurocomputing 215 (2016) 21–31

25

Fig. 2. The DCT and RDCT representation of the difference image.

Fig. 3. The coefﬁcient distribution of each RDCT subband and its GGD modeling curve.

more suitable to model the RDCT subband coefﬁcient distribution of
the different image.
Therefore, in this paper, other than directly modeling the
coefﬁcient distribution of the difference image, the coefﬁcient
distributions of the RDCT subbands are modeled to extract thecorresponding RR features for quality analysis. As the difference
image is considered, we explicitly jointly consider the left andright view image, which matches the HVS perception of the stereoscopic image. The prior RR IQAs for stereoscopic image extract
the RR features on single view image, which do not consider theinter-view image statistical properties for stereoscopic image
quality assessment.
3.2. Proposed reduced reference stereoscopic image quality assessment metricIn this paper, the features extraction and quality analysis
schemes in [26] are employed to predict the perceptual quality of
degraded stereoscopic image. Fig. 4 provides the framework of our
proposed metric.

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L. Ma et al. / Neurocomputing 215 (2016) 21–31

Fig. 4. The framework of the proposed SIQA metric.

3.2.1. Feature extraction
In the sender side, the left/right/difference images of original
stereoscopic image are decomposed and reorganized into RDCT
representation as shown in Fig. 2. Afterwards, the following features are extracted from the RDCT subbands.

 GGD model parameters: For the three horizontal RDCT subbands,
S1, S4 and S7, the distribution of subband coefﬁcients is ﬁtted by
GGD model. Then, the model parameters α, β and dCBD are
calculated based on Eqs. (2) and (4). Therefore, there are nine
GGD model parameters in total extracted.
 Mutual information (MI): MI features can describe the essential
relationship between the RDCT subbands, which are inﬂuenced
by introduced distortion. In this paper, two MI values of theparent–child correlation between the subband pairs (S1, S4 ) and(S4, S7 ), three MI values of the cousin–child correlation between
the subband pairs (S1, S2 ), (S4, S5 ) and (S7, S8 ), and three MI values of the brother–child correlation between the subband pairs(S1, S3 ), (S4, S6 ) and (S7, S9 ) are calculated as RR features. Thus,
there are eight MI values in total extracted to represent theinter-subband dependencies.
 Energy distribution ratio (EDR): EDR is a global feature which cancapture the frequency proportion changes caused by introduced
distortions. The FRD features are deﬁned as

M+H
EDR =
,
L

(5)

where L, M, H are the sums of absolute DCT coefﬁcient values in
the low frequency (S0, S1, S2, S3 ), medium frequency (S4, S5, S6 )and high frequency (S7, S8, S9 ) RDCT subbands, respectively.
For each image component (left/right/difference image), we employed three horizontal RDCT subbands for GGD modeling and
CBD calculation. Each RDCT subband requires two GGD modelingparameters and one CBD parameter. Moreover, eight MI features
are extracted to depict the relationship between horizontal RDCT
subbands and other RDCT subbands. Additionally, one EDR feature
is extracted to globally depict the frequency proportion of theimage. Therefore, in total, we have 3 × 3 + 8 + 1 = 18 RR features
extracted for each image. For the method with only difference
image, we have 18 RR features. For the method with left view,
right view, and difference image, we have 18 × 3 = 54 RR features.

indexes will be determined to measure the perceptual quality
degradation caused by the introduced distortion.

 CBD: The distance between the RDCT subband m original anddistorted stereoscopic image is deﬁned as
m, v

m, v

, pd

hL

m, v
m, v
(i) − pd (i) ,o)= ∑ p

(6)

i=1

m, v
m, v
where po and pd are the coefﬁcient distributions of original

and distorted stereoscopic images, and v ∈ {left image, rightm, v
image, difference image}. Since po is not available in the receiver side, the distance can be approximated as
m, v

(

m, v

dCBD po, pd) = d (p , p

m, v

m, v

m, v

m, v
CBD

where dCBD (pom, vpαm, v, β
m, v

side.

m, v
o

m, v

, pαm, v, β

m, v

m, v
αm, v, βm, v) − d (p
m, v
CBD

m, v
m, v
αm, v, βm, v , pd), (7)) is the parameters from the senderis the estimated coefﬁcient distribution of theoriginal stereoscopic image based on the GGD model parameters αm, v and βm, v .
 Differences between the MI values: The differences between theMI values of the original and distorted stereoscopic images are
determined byvvv

dMI (Sm, v, Sn, v ) = MIo (Sm, v, Sn, v ) − MId (Sm, v, Sn, v ),(8)v
where MIo (Sm, v, Sn, v ) is the MI value of the RDCT subband Sm, v
v
and Sn, v in the original stereoscopic image, and MId (Sm, v, Sn, v ) is

the MI value of the RDCT subband Sm, v and Sn, v in the distorted
stereoscopic image.
 Similarity between the EDR values: To measure the inﬂuence of
the introduced distortion on the HVS-related features. The similarity between the EDR values of the original and distorted
stereoscopic images are deﬁned as

⎧
ξv
v
v
⎪ v
v EDR o < EDRd
⎪ ξ + EDR ovdEDR = ⎨ξvvv⎪⎪ ξ v + EDR v EDR o ≥ EDRd ,
⎩
d

(9)

where
v

v

ξ v = |EDR o − EDRd | .
v

3.2.2. Quality analysis and poolingIn the receiver side, the extracted features of the original anddistorted stereoscopic image are compared to predict the stereoscopic image perceptual quality. First, the following three distance

m, v

(

dCBD pov(10)

EDRo and EDRd are the EDR values of the original and distorted
stereoscopic images, respectively. ξv in the denominator isemployed to scale dEDRv into the range [0,1]. With such scaling
process, the mutual masking properties have been considered[58]. The mutual masking effect is determined by the minimum

L. Ma et al. / Neurocomputing 215 (2016) 21–31

value of the thresholds calculated from the original and distorted image. Therefore, the computed EDR value can depict the
texture information of the image. The mutual masking effect of
the HVS perception is modeled as Eq. (9), where the smaller
value of EDRov and EDRdv is employed to model the masking
effect. In this way, only the image is highly textured in both thereference and distorted images (large EDRov and EDRdv values)
can produce a signiﬁcant masking effect.
After obtaining the CBD values and the similarity index between the ERD values, the quality values for image component v isdeﬁned as
m, v

Qv = c1 × ∑ dCBD + c2 ×v
v
(Sm, v, Sn, v ) + c3 × dEDR .
∑ dMI(m, n)

m(11)

In this paper, the parameters c1, c2 and c3 are set as 0.4883, 0.0313
and 0.6719, respectively. To scale the quality values, the quality
values Qv are transformed by a logarithm process:⎛Qv
Q s = log10 ⎜ 1 +

v⎞

⎟.
D0 ⎠

⎝

(12)

D0 is a scale factor to adjust the variation of Qv. In this paper, D0 is
set as 0.0001 for simplicity.
Furthermore, the ﬁnal perceptual quality of the distorted stereoscopic image is determined asv

Q fin = ∑ Q s .
v(13)

4. Experimental results
In this section, we implement the proposed RR-SIQA metricand make performance comparison with the state-of-the-art
methods. To validate the robustness of proposed metric, it is necessary to evaluate the SIQA metrics on different 3D image quality
databases (IQDs). Currently, there are two categories for existing
3D IQDs. One is symmetric IQD [59] where the left/right views of
the stereoscopic image are symmetrically distorted. The othercategory is the asymmetric IQD [13] where the left/right views of
the stereoscopic image are degraded with different distortion
types and levels. In this paper, we evaluate the performance on
both symmetric and asymmetric IQDs. The detailed information of
the selected IQDs is described as follows: LIVE 3D IQD Phase I (LIVE-Phase-I) [60] consists of 20 outdoor
stereoscopic scenes. Each scene contains one stereoscopic
pairs (left/right view) and the corresponding range maps ofthe views. All the reference stereoscopic images are withresolution 640  360. For each reference stereoscopic image,its left/right views are symmetrically degraded by ﬁve different distortion types with different degradation levels. The
distortion types include JPEG compression (denoted as JPEG),
JPEG2000 compression (denoted as JP2K), white noise contamination (denoted as WN), Gaussian blur (denoted as
GBLUR), and fast fading channel distortion of JPEG2000 compressed bitstream (denoted as FF). The database contains 365
subject-rated stereoscopic images (80 each for JP2K, JPEG, WN
and FF; 45 for GBLUR).
 LIVE 3D IQD Phase II (LIVE-Phase-II) [51] aims to build a diverse
database that consists of both symmetrically and asymmetricallydistorted stereoscopic pairs. The distortion types include JPEG, JP2K,
WN, GBLUR and FF. The database consists of 360 subject-rated
stereoscopic images (72 each for JP2K, JPEG, WN, GBLUR and FF).

27

For fair comparison, both 2DIQA extension model and binocularvision inspired metric (denoted as SIQA model) are evaluated in
the experiment. Two FR-SIQA models, including FI-PSNR [61] andMJ3DQA [51] are implemented in the experiment. To verify theeffectiveness of proposed RR-SIQA metric, three different RR-SIQA
metrics, including DNT [39], RDCT [26] and contourlet domain
based model (denoted as CT [27]) are employed as the benchmark.
We proposed two RR quality metrics, speciﬁcally the Proposed-I
and Proposed-II. Proposed-I only performs the RR quality analysisof the difference image, while Proposed-II performs the RR quality
analysis of left view, right view, and the different image.
To remove nonlinearity introduced by the subjective ratingprocess and facilitate empirical comparison of different IQA metrics, the nonlinear least-squares regression function nlinﬁt ofMatlab is employed to map the objective quality score q to thepredicted subjective quality score DMOSp. The mapping function isthe ﬁve parameters logistic function

DMOSp =

p1
p1−
+ p4 ·q + p5 ,2
1 + exp (p2 ·(q − p3 ))(14)

where p1, p2, p3, p4 and p5 are the parameters of the logistic
function. Three criteria are employed to evaluate the mapping
performance: (1) correlation coefﬁcient (CC): accuracy of objective
metrics; (2) Spearman's rank order correlation coefﬁcient(SROCC): monotonicity of objective metrics; and (3) root meansquared-error (RMSE). The scatter plots of subjective DMOS against
the predicted DMOSp of RR-SIQA metrics on the 3D IQDs are provided in Fig. 5. It is easy to observe that the our proposed RDCTbased RR-SIQA metrics can achieve the best performance on theentire database for both symmetric and asymmetric IQDs. Detailed
experimental results are provided in Table 1.
The performances of different IQAs over different stereoscopic
image quality databases are illustrated in Table 1 and Fig. 5. It can beobserved that the proposed method can outperform the other RR
and even some FR metrics on both LIVE-Phase-I and LIVE-Phase-II,with larger LCC/SROCC and smaller RMSE values. We comparedsome quality metrics extended from conventional 2D images, such
as PSNR, SSIM, VSNR, and so on. From Table 1, experimental results
demonstrate that PSNR performs badly, although it requires thewhole reference image for perceptual quality analysis. The reason isthat PSNR only measures the pixel absolute differences, which does
not take the HVS property into consideration. For SSIM, the structural distortions are measured rather than the absolute pixel value
differences, which are sensitive to the HVS perception. Therefore,
SSIM demonstrates a better performance than PSNR. However, SSIM
also requires the whole reference image for quality analysis. For MSSSIM, a multi-scale SSIM is applied to the stereoscopic image, which
generates a better performance than SSIM. However, compared theperformance of SSIM and MS-SSIM on LIVE-Phase-I and LIVE-PhaseII, it can be observed that SSIM and MS-SSIM perform worse on
LIVE-Phase-II. Therefore, SSIM and MS-SSIM are not able to handle
the quality assessment of stereoscopic images with non-symmetricdistortions. For other FR quality metrics extended from 2D images,
such VIF and UQI, as the reference stereoscopic image is available
and complex HVS and image signal properties have been studied,the performances are much better for both the symmetric and nonsymmetric distortions. For the FR quality metrics speciﬁcally designed for stereoscopic image, FI-PSNR and MJ3DQA, the performances are not good enough, even worse than the metrics extended
from conventional 2D metrics. The reason may be attributed to thatthe mechanism of binocular summation is still an open issue. Thus
the computation model of the rivalry property may not be accurateenough for assessing the perceptual quality of stereoscopic images.
Consequently, the performances of existing binocular vision inspired
metrics are limited, such as FI-PSNR and MJ3DQA.

28L. Ma et al. / Neurocomputing 215 (2016) 21–31

Fig. 5. Scatter plots of subjective DMOS vs. predicted DMOSq of SIQA metrics on the 3D IQDs. (a)–(e) Results on the LIVE-Phase-I database. (f)–(j) Results on the LIVE-Phase-II database.

For the RR quality metrics, we compare our proposed methodwith DNT [39], RDCT [26], and CT [27], which are extended fromthe conventional 2D RR metrics. These RR metrics will perform thequality analysis for the left and right view image independently.

Then the average quality index is regarded as the perceptual
quality of the stereoscopic image. RDCT tries to depict the coefﬁcient distribution in the RDCT domain as the RR features. As
shown in Fig. 2, RDCT presents similar signal decomposition

L. Ma et al. / Neurocomputing 215 (2016) 21–31

29

Table 1
Performance of the SIQA metrics for LIVE-Phase-I and LIVE-Phase-II databases in terms of CC, SROCC and RMSE.
Criteria

CC

Type

FR

RR

SROCC

FR

RR

RMSE

FR

RR

MetricLIVE-Phase-I [60]LIVE-Phase-II [51]

JP2K

JPEG

WN

GBLUR

FF

ALL

JP2K

JPEG

WN

GBLUR

FF

ALL

PSNR
SSIM
MS-SSIM
VSNR
VIF
UQI
FI-PSNR [61]
MJ3DQA [51]
DNT [39]
RDCT [26]CT[27]DWT-I
DWT-II
Proposed-I
Proposed-II

0.78780.87530.93350.89050.9381
0.95100.85750.86150.93800.91570.92520.91770.91870.9216
0.91820.11900.48930.66630.41180.68200.77370.3266
0.29140.69030.72280.55740.65920.66670.71790.72220.9352
0.9421
0.95220.91090.93180.92700.92890.95020.92310.91180.9196
0.89270.888
0.91270.91310.76940.91800.94490.90150.96520.95680.81910.9086
0.96360.92040.9596
0.92840.9226
0.93110.92470.71070.72380.80830.78700.86160.87910.7096
0.67830.85890.80730.83390.79240.79470.79660.80680.83550.87660.92970.89040.92530.94180.87330.87910.86080.90420.89980.7061
0.66290.90330.90560.47260.9301
0.95100.69420.82650.85090.92470.96120.93930.74680.95240.86390.7856
0.89660.80940.66960.72530.83890.65670.83220.83450.77510.82180.89190.75470.8971
0.76330.75590.74780.7544

0.41610.66590.83240.43080.82370.79840.66770.74670.86260.82430.77380.7826
0.79930.80980.82200.92800.84210.79950.97100.98710.98030.73840.95580.9701
0.9694
0.94330.97520.96140.96900.97210.77430.86690.87400.8717
0.9466
0.96150.71570.88880.90850.89250.90300.92960.90780.91000.9016

0.73170.8024
0.79380.77680.84080.86390.64500.88370.54170.8004
0.5216
0.71610.67430.84310.8179PSNR
SSIM
MS-SSIM
VSNR
VIF
UQI
FI-PSNR [61]
MJ3DQA [51]
DNT [39]
RDCT [26]CT [27]DWT-I
DWT-II
Proposed-I
Proposed-II

0.79930.85840.89780.83180.90220.90770.85220.81990.90290.88530.88810.87830.87530.89180.88660.12120.43610.59850.40630.58340.73740.25680.24620.65970.62170.50250.60930.61980.60880.61630.9316
0.93790.94230.90490.93250.92550.92970.93270.92330.91330.91490.88990.88320.91320.91240.90200.87930.92820.8306
0.93120.92740.93940.90040.93890.86920.92900.88670.88380.89540.87910.58750.58610.73490.72950.80370.83290.65990.64460.82240.69430.78580.67220.6722
0.6636
0.69640.83410.87650.92250.88180.92050.93730.86440.86030.85920.90420.89220.70720.65760.90340.90520.70980.9206
0.94730.65420.81960.85090.91480.94270.92510.74190.94960.85320.77120.87880.79390.65570.70270.81720.75770.82580.83450.74370.81590.88590.72910.88970.72430.71640.73730.72880.52340.67890.82710.62440.7782
0.7984
0.66810.75830.82460.75670.77090.69280.7286
0.73190.74920.86500.83580.80100.89520.95010.98030.70880.8901
0.91380.88220.89290.90590.895
0.87850.88680.76600.83480.83040.83480.93300.96150.69450.84970.86220.88450.85240.92050.89220.89540.8886

0.71840.79250.77190.73550.81710.86390.64560.87750.57290.76980.61230.70830.65510.80930.7938PSNR
SSIM
MS-SSIM
VSNR
VIF
UQI
FI-PSNR [61]
MJ3DQA [51]
DNT [39]
RDCT [26]CT [27]DWT-I
DWT-II
Proposed-I
Proposed-II

7.9761
6.26174.64265.89284.48454.00336.6623
6.57714.48895.20584.91335.14495.11455.02685.12946.49275.70294.8762
5.95894.7822
4.14326.2512
6.25544.73104.51885.42924.91744.874
4.55254.52295.8916
5.57755.0822
6.8631
6.03806.24096.16125.1833
6.39736.83076.53507.49547.6512
6.79696.7843

11.91445.73954.73866.2635
3.78364.20878.30266.04633.86725.66014.07485.37995.58235.27945.51058.7411
8.57347.31597.66636.30725.92268.75459.13046.36297.33306.8571
7.5856
7.54327.51197.34119.01047.89136.03987.4643
6.21975.5143
7.98867.81648.34557.00507.1557
11.611
12.2777.0353
6.95429.44143.93433.31327.71136.03055.62834.0781
2.95383.6752
7.12433.26705.39496.62854.74416.29067.29096.75805.34287.40345.44245.40936.20275.59314.44036.44014.33696.34176.42656.51766.44398.58605.47254.0621
6.61514.15694.41335.45724.87613.70774.15014.64334.56334.40524.30044.17435.18777.50938.36313.32652.23142.74959.3891
4.09493.3802
3.41784.62283.0791
3.83133.43793.26357.28215.73645.59085.63963.7104
3.16218.03625.27334.80955.19044.94484.24174.82654.77004.97797.69366.73666.8644
7.1083
6.10995.68458.62555.2841
9.48766.76599.63037.87838.33536.06946.4939property with wavelet transform. Therefore, in order to further
demonstrate the effectiveness of the proposed RDCT, we compare
the performance of RDCT with discrete wavelet transform (DWT)of the RR IQA for stereoscopic images. For fair performance comparison, only RDCT is replaced by DWT, while the other processesof the proposed RR IQA remain unchanged. The experimental results are also illustrated in Table 1. It can be observed that the
proposed method using RDCT can signiﬁcantly outperform the one
using DWT. Therefore, the RDCT is more suitable for GGD modeling and CBD calculation, which can further beneﬁt the performance improvement, compared with DWT. Moreover, it can beobserved that RDCT performs better than DNT and CT. DNT and CT
are also designed by depicting the coefﬁcient distribution in the
wavelet domain. Therefore, the RDCT coefﬁcient distribution isdemonstrated to beneﬁt more for the RR quality analysis than the
wavelet coefﬁcient distribution.
Moreover, RDCT performs comparatively with the methods of
Proposed-I and Proposed-II on LIVE-Phase-I. However, the performance of Proposed-I and Proposed-II on LIVE-Phase-II is much worse
than that on LIVE-Phase-I. The difference of the two databases is thesymmetric property of the distortions, which introduced different

distortion levels to the left and right view image, respectively. For
LIVE-Phase-I, the distortions introduced in left and right view image
are the same. No perceptual quality difference exists between the left
and right view images. The two view images will be perceived andcontributed equally to the ﬁnal stereoscopic image quality perception. However, for the non-symmetric distortions, the left and rightview images present different distortions. The HVS perception ofsuch stereoscopic images will be signiﬁcantly affected. There exist
complicated binocular perception properties of stereoscopic images,
such as the binocular masking effect and error tolerance effect between the two view images. As such, the simple averaging process ofthe quality values of left and right view image cannot well depict thereal quality perception behavior of HVS. Therefore, we cannot makesure a good performance of proposed RR IQA on LIVE-Phase-II. It isalso the main reason why the other RR and FR metrics perform quite
well on LIVE-Phase-I but poorly on LIVE-Phase-II. Therefore, we thinkthat the perceptual qualities of the left and right view image need tobe jointly analyzed to match the HVS perception behavior for the
non-symmetric distortions. In this paper, we proposed to employ thedifference image to depict the stereoscopic image quality. The distortion difference between left and right view image can be more

30

L. Ma et al. / Neurocomputing 215 (2016) 21–31

clearly depicted, which will help more accurately analyze the degradation level of the stereoscopic image. However, this joint consideration is simple and straightforward. In the future, we will consider more accurately modeling the relationship between the left andright view image to derive better RR IQAs for stereoscopic images.
Besides, the performance of Proposed-I is slightly worse thanthat of Proposed-II on LIVE-Phase-I, while better than that of Proposed-II on LIVE-Phase-II. It means that the difference image iscapable to capture the introduced distortions, speciﬁcally for the
non-symmetric distortions. However, the performance of RDCT
demonstrates that the qualities of the left and right view images arealso helpful for SIQA. It arises an open question that how we canjoint consider the left, right view, and difference images to generate
a better RR SIQA. By considering the Proposed-I and Proposed-II, thedifference image is most important for quality analysis. The proposed RR SIQA metric can thus be viewed as a scalable approach. If
only a few RR features are constrained, we only extract the RR
features from the difference image for quality analysis. If more RR
features are tolerant, we can extract all the RR features from theimages, including the left view, right view, and difference image for
quality analysis. Such process can help to improve the performancesof the stereoscopic images with symmetric distortions.

5. Conclusion
In this paper, we propose a novel RR-SIQA metric based on thenatural image statistics in RDCT domain. For the coefﬁcient in the
RDCT subband of luminance image and difference image of thestereoscopic images, the marginal distribution of the coefﬁcients isapproximately GGD distributed. For each RDCT subband of theluminance image and difference map of the stereoscopic images,
the model parameters and ﬁtting error of the GGD distribution, MI
and ERD values are extracted as feature parameters. At the receiverside, the 3D visual quality is predicted by measuring the distance
between the features. Experiments show that the proposed metrichas good consistency with 3D subjective perception of human.

Acknowledgments
This work was supported in part by the National Natural Science Foundation of China under Grants 61501299 and 61471178, inpart by the Guangdong Nature Science Foundation under Grant
2016A030310058, in part by the Shenzhen Emerging Industries oftheStrategic
Basic
Research
Project
under
GrantsJCYJ20150525092941043 and JCYJ20130326105637578, in part by
the Project 2016049 supported by SZU R/D Fund, in part by the
grant from the Research Grants Council of the Hong Kong SAR,
China (Project CUHK 415712), and in part by the Priority Academic
Program Development of Jiangsu Higher Education Institutions(PAPD) and Jiangsu Collaborative Innovation Center on Atmospheric Environment and Equipment Technology (CICAEET) fund.

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Lin Ma received the B.E., and M.E. degrees from Harbin
Institute of Technology, Harbin, China, in 2006 and2008, respectively, both in computer science. He received his Ph.D. degree in Department of Electronic
Engineering at the Chinese University of Hong Kong
(CUHK) in 2013. He is now a Researcher with Huawei
Noah's Ark Lab, Hong Kong.
He was a Research Intern in Microsoft Research Asia
from October 2007 to March 2008. He was a Research
Assistant with the Department of Electronic Engineering, CUHK, from November 2008 to July 2009. He was a
Visiting Student with the School of Computer Engineering, Nanyang Technological University (NTU),

31

from July 2011 to September 2011. His current research interests include multimodal matching, deep learning, image/video processing, and quality assessment.
He got the best paper award in Paciﬁc-Rim Conference on Multimedia (PCM)
2008. He was awarded the Microsoft Research Asia fellowship in 2011. He was aﬁnalist to HKIS young scientist award in engineering science in 2012.

Xu Wang received the B.S. degree from South China
Normal University, Guangzhou, China, in 2007, and M.S.
degree from Ningbo University, Ningbo, China, in 2010.
He received his Ph.D. degree from the Department ofComputer Science, City University of Hong Kong, Hong
Kong, in 2014. In 2015, he joined the College of Computer Science and Software Engineering, Shenzhen
University as an Assistant Professor. His research interests are 3D video coding and 3D image quality
assessment.

Qiong Liu received her B.S. degree in Computer Scienceand Technology from Central China Normal University
and Ph.D. degree in National Engineering ResearchCenter for Multimedia Software from Wuhan University in 2008. She is now the faculty of Division ofCommunication and Intelligent Network, WNLO. Her
research interests include multi-view video coding,
depth estimation for multi-view video, low complexity
video coding, region-of-interest video compression,scalable video coding and video surveillance

King Ngi Ngan received his B.Sc. (Hons) and Ph.D. degrees, both in Electrical Engineering from Loughborough University, UK, in 1978 and 1982, respectively. He
joined the Department of Electronic Engineering, theChinese University of Hong Kong as Chair Professor in
2003. He has been appointed Chair Professor at the
University of Electronic Science and Technology,
Chengdu, China, under the National Thousand Talents
Program since 2012. Previously he was a Full Professor
at the School of Computer Engineering, Nanyang
Technological University, Singapore, and the School ofElectrical, Electronic and Computer Engineering, University of Western Australia, Australia. He was appointed as Honorary Professor of Tunku Abdul Rahman University in Malaysia,
Adjunct/Visiting Professor of Zhejiang University, Shanghai Jiaotong University,
Shanghai University, Huazhong University of Science and Technology and Huaqiao
University in China, Distinguished Adjunct Professor of the National Sun Yat-sen
University in Taiwan, and Adjunct Professor of the University of Western Australia
and RMIT University in Australia. He served as the External Examiner for the B.Eng.
degree program of Malaysia's Multimedia University, and was appointed as IEEE
Distinguished Lecturer of the IEEE Circuits and Systems Society in 2006–2007.
Prof. Ngan is active in many professional activities. He was an associate editor of
the Journal on Visual Communications and Image Representation, U.S.A., and anarea editor of EURASIP Journal of Image Communications, and served as an associate editor of IEEE Transactions on Circuits and Systems for Video Technology
and Journal of Applied Signal Processing. He chaired a number of prestigious international conferences on video signal processing and communications and servedon the advisory and technical committees of numerous professional organizations.
He co-chaired the IEEE International Conference on Image Processing (ICIP) in 2010
in Hong Kong. He has published extensively including 3 authored books, 6 edited
volumes and over 300 refereed technical papers in the areas of visual signal processing, image/video coding and multimedia communications, which are his main
research interests. He also holds 11 patents on image coding/transmission
techniques.