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BELIF: BLIND QUALITY EVALUATOR OF LIGHT FIELD IMAGE WITH TENSOR
STRUCTURE VARIATION INDEX
Likun Shi Shengyang Zhao Zhibo Chen∗
CAS Key Laboratory of Technology in Geo-spatial Information Processing and Application System
University of Science and Technology of China, Hefei 230027, China
ABSTRACT
With the development of immersive media, Light Field Image
(LFI) quality assessment is becoming more and more impor-
tant, which helps to better guide light field acquisition, pro-
cessing and application. However, almost all existing LFI
quality assessment schemes utilize the 2D or 3D quality as-
sessment methods while ignoring the intrinsic high dimen-
sional characteristics of LFI. Therefore, we adopt the tensor
theory to explore the LF 4D structure characteristics and pro-
pose the first Blind quality Evaluator of LIght Field image
(BELIF). We generate cyclopean images tensor from the orig-
inal LFI and then the features are extracted by the tucker de-
composition. Specifically, Tensor Spatial Characteristic Fea-
tures (TSCF) for spatial quality and Tensor Structure Vari-
ation Index (TSVI) for angular consistency are designed to
fully assess the LFI quality. Extensive experimental results
on the public LFI databases demonstrate that BELIF signifi-
cantly outperforms the existing image quality assessment al-
gorithms.
Index Terms—Light field, Image quality assessment,
Objective model, Tensor, Angular consistency.
1. INTRODUCTION
As a recent emerging media modality, Light Field Image
(LFI) has attracted widespread attention. Unlike traditional
2D and 3D technology, light field can describe the distri-
bution of light rays in free space. Specifically, LFIs can
simultaneously record the direction and intensity information
of radiance, which ideally provides abundant depth cues and
6 degree-of-freedom (DOF) viewing experience. Therefore,
monitoring the quality of LFI is critical to better guiding the
procedure of light field acquisition, processing and applica-
tion techniques.
The LFI is a 4D signal composed of multiple Sub-
Aperture Images (SAIs), which can be represented as a 2D
image array, as shown in Fig.1. Here the uand vdimen-
sions are referred to as the angular dimensions and sand t
dimensions are referred to as the spatial dimensions. Due
This work was supported in part by NSFC under Grant 61571413,
61632001. *Corresponding author. (Email: chenzhibo@ustc.edu.cn)
Fig. 1. Illustration of the Light Field Image (LFI).
to the high dimensional characteristic of the LFI, its quality
is affected by three factors, spatio-angular resolution, spatial
quality and angular consistency [1]. Here, spatio-angular
resolution refers to the number of SAIs in a LFI and the
resolution of a SAI. Spatial quality indicates the quality of
SAIs and angular consistency measures the visual coherence
between SAIs. Since spatio-angular resolution is determined
by the acquisition devices, this paper focuses on the effects of
spatial quality and angular consistency. Currently, LFI qual-
ity evaluation mainly concentrates on subjective evaluation.
Since the real light field display is still under exploration [2],
some research works attempt to display LF with the available
facilities. For example, Paudyal et al. [3] and Viola et al. [4]
analyzed the effect of different compression methods on the
quality of LFIs based on 2D display and Adhikarla et al. [5]
and Shi et al. [6] considered the quality effects from LFIs
compression, rendering and synthesis.
However, subjective evaluation is resource and time con-
suming, which is not applicable for real applications. There-
fore an effective objective quality assessment model is neces-
sary. In general, image quality assessment (IQA) algorithms
can be categorized as full-reference (FR), reduced-reference
(RR) and no-reference (NR) according to the availability of
original image information. The FR-IQA methods measure
the difference between the reference image and distorted im-
age. For example, structure similarity between reference and
distorted images is measured in SSIM [7], binocular rivalry
difference is calculated in [8] and morphological pyramid de-
Fig. 2. Flow diagram of the proposed BELIF model.
composition and mean squared errors on them are utilized in
MP-PSNR[9] And the RR-IQA methods utilize partial infor-
mation of the reference image for quality assessment, such
as [10, 11, 12]. The NR-IQA method only measures the dis-
torted images, which is more applicable in most real scenar-
ios without having access to the original reference image. For
example, Natural Scene Statistic (NSS) theory is employed
in NIQE [13] and BRISQUE [14] and binocular fusion and
binocular rivalry are simulated in BSVQE [15].
However, none of aforementioned schemes consider the
intrinsic high dimensional characteristics of LFI, especially
the distortion caused by angular consistency. Therefore, con-
sidering both the high dimensionality property of the LFI and
potential applicability of the proposed quality evaluator, we
propose the first NR-LFI quality assessment scheme based on
tensor theory. Mathematically, a LFI is a 4D tensor. The
tensor theory can effectively describe the characteristics and
distributions in the high-dimensional space. It has been suc-
cessfully applied to many fields of computer vision, such as
compression and recognition [16]. In this work, we propose
the first Blind quality Evaluator of LIght Field image (BELIF)
based on the tensor theory, in which a novel Tensor Structure
Variation Index (TSVI) is designed to measure angular con-
sistency degradation. Specifically, we first mimic the prop-
erties of the binocular vision to generate cyclopean images
and decompose the cyclopean image array along the angular
dimension to obtain the tensor decomposition components.
Secondly, we extract Tensor Spatial Characteristic Features
(TSCF) to measure the degradation of spatial quality. Thirdly,
TSVI is calculated by analyzing the structural similarity dis-
tribution between the first decomposition component and LFI
cyclopean images. Finally, a regression model is applied to
train and predict the quality of distorted LFI. Extensive exper-
iment results verify that BELIF is superior to existing objec-
tive algorithms and achieves the state-of-the-art performance.
The remainder of the paper is organized as follows. Sec-
tion 2 describes the proposed model in detail. In Section 3,
we illustrate the experimental results. Finally, Section 4 con-
cludes the paper.
(a) (b)
(c) (d)
Fig. 3. Tucker decomposition components. (a) First compo-
nent; (b) Second component; (c) Third component; (d) energy
distribution of all decomposition components.
2. PROPOSED BELIF MODEL
In this section, we describe the proposed model in detail. As
shown in Fig. 2, after generating cyclopean images based
on binocular vision theory, we utilize Tucker decomposition
to decompose it along the angular dimension. Then, TSCF
and TSVI are proposed to monitor spatial quality and angular
consistency respectively. Finally, regression model is used to
predict LFI quality.
2.1. LFI Cyclopean Images
As the LFI can provide binocular cues directly, we mimic
the response of HVS to estimate the cyclopean image that
is formed in the observer’s mind when a stereo image pair
is stereoscopically presented [17]. Since the cyclopean im-
age contains both left and right view information and takes
into account the influence of binocular visual characteristics,
it can reflect the quality of the received image pair [8]. In our
model, horizontally adjacent SAIs in LFI are treated as left
and right views, respectively. Then, we synthesise the cyclo-
pean image Cu,v, according to [18],
Cu,v =Wu,v ×Iu,v +Wu,v+1 ×Iu,v+1 (1)
where we define the SAI as Iu,v, and (u, v)∈ {U, V }denotes
the angular coordinate. Wu,v and Wu,v+1 are the weights
defined in [18]. Finally, a cyclopean image array is obtained
with angular resolution of U×(V−1).
2.2. Tucker Decomposition
Images in the cyclopean image array have high texture sim-
ilarity, indicating that the cyclopean image array has a large
amount of redundant information in the angular dimension.
To alleviate this problem, we adopt tensor decomposition to
remove redundant information from the angular dimension.
Specifically, the Tucker decomposition is used to achieve di-
mensionality reduction [16]. It decomposes a tensor into a
core tensor multiplied by a matrix along each dimension. So
for cyclopean image array C, we have
C≈G×1A(1) ×2A(2) ×3A(3) (2)
where we reshape the cyclopean image array into 3D tensor
along the angular dimension. The tensor G∈RR1×R2×R3
is the core tensor whose entries illustrate the level of interac-
tion between the different components. A(1) ∈RK1×R1and
A(2) ∈RK2×R2are the factor matrices in spatial dimension
and A(3) ∈RK3×R3is the angular dimension factor matrix.
In our model, we set Kn=Rn, where n= 1,2,3.
The angular decomposition components can then be ob-
tained by multiplying the core tensor with the factor matri-
ces A(1) and A(2) along each mode in the spatial dimension,
which can be given by
T=G×1A(1) ×2A(2) (3)
Here we utilize the alternating least squares method pro-
vided by the tensor toolbox [19] to implement the Tucker de-
composition. Fig. 3(a)-(c) show the first three components
and the energy of each component is shown in Fig. 3(d). Ob-
viously, the texture information and energy mainly concen-
trate in the first component, which represents the basic texture
structure information of the LFI. It is also observed that the
second and third components contain the high frequency in-
formation with relatively higher energy. We find the first three
components contains more than 80% energy, so we treat them
as three most important dimensionality reduced images.
2.3. Features Extraction
2.3.1. Tensor Spatial Characteristic Features (TSCF)
In practical applications, operations such as compression in-
evitably lead to deterioration of the LFI spatial quality. To
measure changes in spatial quality, we extract the TSCF fea-
ture. First, we analyze the global statistics of the first com-
ponent and extract the NSS feature fnss. Specifically, mean
subtracted contrast normalized (MSCN) coefficients are ob-
tained and the statistical distribution is fitted using the zero-
mean asymmetric generalized gaussian distribution (AGGD)
model [14]. In addition, it is observed that the distortion will
change the local informatioin in the first three components.
Then both spatial and spectral entropy are computed on 8×8
blocks without overlapping [20]. Here spectral entropy is cal-
culated after excluding DC coefficients in the DCT domain.
Finally, the skewness and mean value of entropy flocal are
extracted. Further we compute mean value, entropy, kurto-
sis and skewness of energy distribution as supplementary fea-
tures fenergy . Finally, we combine all these features to obtain
the TSCF FT SC F ,
FT SC F ={fnss, flocal , fenerg y }(4)
2.3.2. Tensor Structure Variation Index (TSVI)
In addition to spatial quality, angular consistency also affects
the quality of the LFIs. Usually, angular reconstruction oper-
ations, such as interpolation, will break angular consistency.
To measure the degradation of angular consistency, we pro-
pose the Tensor Structure Variation Index (TSVI). Specifi-
cally, we measure the structural similarity Sbetween each
image of the cyclopean image array and the first decomposi-
tion component,
Su,v =Fss(Cu,v , T1)(5)
where T1is the first decomposition component and (u, v)∈
{U, V −1}is the angular coordinate of the cyclopean image
array. Fss is the function to calculate structural similarity, we
utilize the popular SSIM [7] in the paper.
The distribution of two LFIs selected from Win5-LID [6]
is shown in Fig. 4. When the angular consistency is not de-
stroyed, the distribution of structural similarity is smooth, as
shown in Fig. 4(a). However, when the angular consistency is
disrupted by interpolation distortion, the distribution of struc-
tural similarity changes significantly. Fig. 4(b)-(d) show the
structural similarity distribution of the LFIs introducing the
nearest neighbor interpolation distortion. As the angular con-
sistency deteriorates, the degree of variation in the structural
similarity distribution of the LFI gradually increases.
Finally, we treat the structural similarity distribution as a
matrix and extract the mean, standard deviation, and singular
values as feature FT SV I ,
FT SV I ={avg(S), std(S), sv d(S)}(6)
3. EXPERIMENT RESULTS
3.1. LFI Databases
In our experiment, we conduct comparison experiments on
Win5-LID [6] and MPI-LFA [5] databases. The Win5-LID
database comprises 220 quality annotated LFIs based on 10
reference LFIs that are subject to 6 different types of distor-
tions at different distortion levels. Distortion types include
JPEG2000, HEVC, linear interpolation (LN), nearest neigh-
bor interpolation (NN), and two CNN models. The associated
overall mean opinion score (MOS) value is also provided for
each LFI.
The MPI-LFA contains 336 quality annotated LFIs. 14
reference LFIs are distorted by 3D extension of HEVC, LIN-
EAR, NN, optical flow estimation (OPT), quantized depth
maps (DQ) and gaussian blur (GAUSS) with six degra-
dation levels for each distortion type. For quality assess-
ment, authors denote measured values as just-objectionable-
differences (JODs), which is more similar to difference-
mean-opinion-score (DMOS) [21]. The lower value indicates
the worse quality.
(a) (b) (c) (d)
Fig. 4. Distribution of structural similarity with different nearest neighbor distortion levels from Win5-LID database [6]. Above
is the ’Bike’ LFI and below is the ’Dish’ LFI. (a) is the original image, and the distortion levels are gradually increased from
(b) to (d).
Table 1. Performance Comparison.
Win5-LID MPI-LFA
Metrics SROCC LCC RMSE SROCC LCC RMSE
PSNR 0.6026 0.6189 0.8031 0.8078 0.7830 1.2697
SSIM [7] 0.7346 0.7596 0.6650 0.7027 0.7123 1.4327
VIF [22] 0.6665 0.7032 0.7270 0.7843 0.7861 1.2618
FSIM [23] 0.8233 0.8318 0.5675 0.7776 0.7679 1.3075
MSSIM [24] 0.8266 0.8388 0.5566 0.7675 0.7518 1.3461
IWSSIM [25] 0.8352 0.8435 0.5492 0.8124 0.7966 1.2340
IFC [26] 0.5028 0.5393 0.8611 0.7573 0.7445 1.3629
NIQE [13] 0.2086 0.2645 0.9861 0.0665 0.1950 2.0022
BRISQUE [14] 0.6687 0.7510 0.5619 0.6724 0.7597 1.1317
NFERM [27] 0.6328 0.7213 0.5767 0.6454 0.7451 1.1036
Chen [8] 0.5269 0.6070 0.8126 0.7668 0.7585 1.3303
SINQ [18] 0.8029 0.8362 0.5124 0.8524 0.8612 0.9939
BSVQE [15] 0.8179 0.8425 0.4801 0.8570 0.8751 0.9561
3DSwIM [28] 0.4320 0.5262 0.8695 0.5565 0.5489 1.7063
MW-PSNR Reduc [29] 0.5326 0.4766 0.8989 0.7217 0.6757 1.5048
MW-PSNR Full [29] 0.5147 0.4758 0.8993 0.7232 0.6770 1.5023
MP-PSNR Reduc [30] 0.5374 0.4765 0.8989 0.7210 0.6747 1.5067
MP-PSNR Full [9] 0.5335 0.4766 0.8989 0.7203 0.6730 1.5099
APT [31] 0.3058 0.4087 0.9332 0.0710 0.0031 2.0413
BELIF 0.8719 0.8910 0.4294 0.8854 0.9096 0.7877
3.2. Comparison with the Existing Metrics
Currently there is no LFI objective quality evaluation model.
In order to demonstrate the effectiveness of BELIF, we com-
pare several FR and NR IQA metrics, including seven 2D-FR
metrics [7, 22, 23, 24, 25, 26], three 2D-NR metrics [13, 14,
27], one 3D-FR metric [8], two 3D-NR metrics [15, 18], five
multi-view FR metrics [28, 29, 9, 30] and one multi-view NR
metric [31]. Correlation between MOS and predicted results
is computing by using SROCC, PCC, and RMSE [8]. The
SROCC measures the monotonicity while PCC evaluates the
linear relationship between predicted score and MOS. The
RMSE provides a measure of the prediction accuracy. The
value of SROCC and PCC closing to 1 represent high pos-
itive correlation and a lower RMSE value indicates a better
performance. Then the support vector regression (SVR) with
a radial basis function kernel [32] is chosen as the regression
model. We randomly select 80% of the database as training
set, while the remaining 20% as test set. 1000 times cross-
Table 2. Ablation Study Results.
Win5-LID MPI-LFA
SROCC LCC RMSE SROCC LCC RMSE
BELIF-FTSVI 0.7902 0.8473 0.5051 0.8678 0.8916 0.8188
BELIF 0.8719 0.8910 0.4294 0.8854 0.9096 0.7877
validations are performed. The median of correlation coeffi-
cients are used as the final results.
The results of all methods on Win5-LID and MPI-LFA
are shown in Table 1. Obviously, BELIF outperforms all the
existing algorithms on both databases. The reason is that ex-
isting 2D and 3D algorithms primarily measure the degrada-
tion of spatial quality without considering the angular consis-
tency in the 4D LFI. Although multi-view IQA methods can
measure the distortion caused by angular reconstruction, they
don’t take into account the compression distortion or similar
distortions. Therefore we can conclude that BELIF can effec-
tively capture the degradation in spatial quality and angular
consistency.
Additionally, we trained BELIF on the Win5-LID database,
and tested it on the same distortions in the MPI-LFA database.
The SROCC value can reach 0.8309, which proves that BE-
LIF has good generality.
3.3. Ablation Study
To demonstrate the validity of proposed TSVI, we perform
an ablation study and the results are shown in Table 2. Obvi-
ously, TSVI can significantly improve the performance of the
model.
4. CONCLUSION
In this paper, we have presented the first Blind quality Evalu-
ator of LIght Field image (BELIF), which is based on tensor
decomposition theory. The BELIF can effectively assess the
distortion of the spatial quality and angular consistency. And
the results show that BELIF outperforms the existing metrics.
In the future, we’ll extend this framework for quality evalua-
tion of light field video signals.
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