Chengyue Ma

Karam Naser

Vincent Ricordel

Patrick Le Callet

Chunmei Qing

An adaptive Lagrange multiplier determination method for dynamic texture in HEVC

Keywords: Lagrange multiplier, rate-distortion optimization, Dynamic textures

I. INTRODUCTION

In recent year, since people does not satisfy with the normal fidelity in the traditional forms of videos, high definition (HD) and ultra HD (UHD) videos have been increasingly popular with the rapid development of cameras. However, it is a great challenge to transmit and store the huge amount of the videos data for the practical applications. The ITU-T Visual Coding Experts Group (VCEG) and the ISO-IEC Moving Picture Experts Group (MPEG) have developed a new video standard, namely, high efficiency video coding (HEVC). Compared with the previous video coding standards, HEVC achieves compression more efficiency by using variable size for coding units and prediction units, advanced motion vector prediction and adaptive loop filtering. With the improvement, HEVC is expected to be widely used in various applications, such as digital satellite broadcasting, entertainment, online education, and so on.

Following the classical coding framework, rate distortion optimization (RDO) techniques have been exploited in HEVC to identify the optimal encoding setting for achieving the optimal rate distortion (RD) performance. However, the Lagrange RDO technique can not accurately reflect the perceptual visual quality due to two reasons. Firstly, the Lagrange multiplier only relates to the quantization parameter but ignores the characteristic of the input video. Secondly, the coding efficiency in RDO is measured by the objective criterion( i.e., Sum of square error, SSE), which can not accurately reflect the perceptual visual quality. In other words, HEVC does not fully consider the perceptual characteristics of the input video during the encoding process. Therefore, for improving the efficiency of video coding while keeping the high quality, it is required to use the characteristics of the Human Visual System (HVS).

For developing an adaptive Lagrange multiplier, some methods have already been proposed in the published literatures. [START_REF] Li | Laplace Distribution Based Lagrangian Rate Distortion Optimization for Hybrid Video Coding[END_REF] presented a Laplace-based Lagrange multiplier according to the Laplace distribution of transformed residuals. [START_REF] Zeng | Perceptual adaptive Lagrangian multiplier for high efficiency video coding[END_REF] proposed an adaptively adjusting Lagrange multiplier in the RDO process based on the perceptual sensitivity of the input CTU. [START_REF] Jung | Perceptual rate distortion optimization for video coding using free-energy principle[END_REF] obtained an adaptive Lagrange multiplier based on the free-energy principle which represents the disorderly concealment effect in human eyes. [START_REF] Yang | Perceptual feature guided rate distortion optimization for high efficiency video coding[END_REF] introduced an adjusting Lagrange multiplier based on the gradient magnitude of the input CTU.

Besides, another solution for the perceptual video coding is to incorporate the existing visual quality assessment (VQA) metrics which can more suitable describe the human perception into the video codec. For example, [START_REF] Wang | Perceptual video coding based on SSIM-inspired divisive normalization[END_REF] proposed a normalization factor based on DCT domain-SSIM index to transform the DCT residual into the perceptually uniform space together with a new distortion model of improving the perceptual coding efficiency. [START_REF] Huang | Perceptual Rate-Distortion Optimization Using Structural Similarity Index as Quality Metric[END_REF] introduced the SSIM to replace the SSE as the quality metric and developed a SSIMbased RDO using the coding information of the key frame.

Although there are already some proposed methods for improving the Lagrange multiplier and the quality measurement in RDO, most of these methods only consider one perceptual characteristic while improving the rate distortion optimization techniques. It is not enough since human visual system would be affected by many factors. Therefore, it is necessary to incorporate many factors that would affect human visual and give each factor a suitable weight according to the experiment for improving the RDO more likely considering the characteristics of the HVS.

Moreover, dynamic texture is also a major research topic in the field of video coding. Dynamic textures are sequences of frames of moving scenes that exhibit temporal regularity, intended in a statistical sense, like sea-waves, smoke, foliage, whirlwind but also talking faces, traffic scenes etc. Since dynamic texture usually cost much but not important in human visual system. Therefore, many algorithm for dynamic texture synthesis is presented as it is easy to implement and fast in computation. However, we can still improve these algorithm for making dynamic texture performed better in video coding.

The organization of the rest of the paper is given as follows : Section Ⅱ briefly describes a brief background covering the encoding part in HEVC. Section Ⅲ gives the proposed methods for adaptive Lagrange multiplier in HEVC. Section Ⅳ presents global view of my method for the predicting adaptive Lagrange multiplier factor and show the result of the experiment. Finally, Section Ⅴ concludes the paper and give some thoughts for the future work.

II. LAGRANGIAN RATE DISTORTION OPTIMIZATION IN HEVC

In the HEVC, rate distortion optimization (RDO) plays an important role in the mode decision process, which is to find a good trade-off between the reconstructed video quality and the required bits. To adapt to various video content, there are various prediction modes in HEVC that can be roughly classified into Intra, SKIP, and Inter Modes. For example, the mode with larger size consumes less bits for head information and is efficient to code the picture block with homogeneous textures. In contrast, the mode with smaller size provides more accurate prediction and thus yields less residual, at the expense of higher head information. The mode decision process is to exhaustively compute the RD cost of all the prediction modes and find the one with the minimum RD cost as the optimal mode. In fact, this process is an optimization problem that minimizes the overall reconstructed video distortion D at a given rate R. The Lagrange RDO is defined as :

min J where J = D + 𝜆 𝐻𝐸𝑉𝐶 * 𝑅 ( 1
)
where J is the Lagrange cost function, R denotes the total number bits for coding the headers, quantized coefficients, etc, measured in terms of bits per pixel and D means the distortion between the original block and its reconstructed block. The is the Lagrange multiplier in HEVC, which is defined as :

𝜆 𝐻𝐸𝑉𝐶 = 𝛼 * 2 ( 𝑄𝑃 -12 3 ) (2)
where QP is the quantization parameter, and is a constant that is empirically-determined from extensive experiments [START_REF] Zeng | Perceptual adaptive Lagrangian multiplier for high efficiency video coding[END_REF].

It is easily observed from equation (1) that HEVC optimizes the RD performance for a given CTU based on a empirically-determined Lagrange multiplier . Therefore, is very important, as it controls HEVC encoder to find the optimal trade-off between the distortion and the bit rate.

However, has one drawback that it is a only function of QP and does not consider the characteristic of the input video and the HVS perception. It means that cannot well adapt to various video contents and is not efficient for perceptual video coding. Therefore, it is very essential to develop a perceptual adaptive Lagrange multiplier for HEVC by incorporating HVS perception to improve the perceptual coding efficiency.

III. PROPOSED LAGRANGE MULTIPLIER DETERMINATION METHOD FOR HEVC

A. Lagrange multiplier factor

As it is well known, texture represented homogeneous area of video scenes with coherent statistics and appear in large areas of video streams while structures represented rather the semantics of the scene [START_REF] Naser | Experimenting texture similarity metric STSIM for intra prediction mode selection and block partitioning in HEVC[END_REF]. Therefore, human visual system usually focus on the structural area rather than textured area. However, textured area would be coded bit by bit as the structural area in the previous methods and the only difference of dealing with them is to give a different weight in Lagrange multiplier. But human visual system only focus on the semantic meaning of the textured area rather than the exact details of each pixel. Therefore, replacing them by an equivalent stochastic signal results in significant bitrate saving [START_REF] Balle | Models for Static and Dynamic Texture Synthesis in Image and Video Compression[END_REF] [START_REF] Zhang | A Parametric Framework for Video Compression Using Region-Based Texture Models[END_REF].

It is also noted that Lagrange multiplier in HEVC mainly depend on QP values as function [START_REF] Zeng | Perceptual adaptive Lagrangian multiplier for high efficiency video coding[END_REF], and are not directly related to the characteristics of the input video signal. Moreover, this model is based on the experiment in [START_REF] Wiegand | Lagrange multiplier selection in hybrid video coder control[END_REF] that used an H.263 codec (without B frames) and four QCIF test sequences. With recent advances in video compression, especially with bi-directional prediction and intra coding in inter frames, the RD characteristic of codec with B frames is likely to be quite different.

In order to investigate the optimum Lagrange multiplier factor for encoding, an Lagrange multiplier selection experiment was applied to HEVC reference codec. The test values used are given in function [START_REF] Jung | Perceptual rate distortion optimization for video coding using free-energy principle[END_REF].

𝜆 𝑡𝑒𝑠𝑡 = 𝑘 𝑓𝑎𝑐𝑡𝑜𝑟 • 𝜆 𝑜𝑟𝑖𝑔 (3)
Where the value of is chosen as, and this parameter was constant during encoding.

Primary coding settings used in this experiment include : HM16.2 for HEVC ; uniform QP used for all frames: QP 22, 27, 32, 37, 42 and 47 tested for HEVC ; Structural Similarity Index (SSIM) and Peak Signal-to-Noise Rate (PSNR) is used as distortion metric for RDO in the codec.

B. Determination of the best factor

For choosing the best value of Lagrange multiplier factor, we use the bjontegaard metric for deciding which value of Lagrange multiplier factor have the best performance in R-D curve. In figure 9, the figure has shown all of the different value of perform in rate distortion map with PSNR. The way to measure the compression quality with the bjontegaard metric, Bjøntegaard delta bit rate(BDBR) and Bjøntegaard delta peak signal-to-noise rate (BD-PSNR).

In BDBR, the basic idea is to measure the bit-rate saving with the same video quality. In our experiment as shown in Fig. 1. We take the and the for all the Lagrange multiplier factor. It is easily to find out that the bit-rate is smallest while in these two figures. Therefore, we could prove that is the best Lagrange multiplier factor in this video.

In BD-PSNR or Bjøntegaard delta structural similarity index (BD-SSIM), the basic idea is to measure the video quality with the same bit-rate. In our experiment, we consider the video quality while bit-rate equal to 20. It can be seen that has the highest SSIM or PSNR value among them. Thus, we can make sure that it is the best Lagrange multiplier factor in this video once again.

C. Extracting the features

In this paper, we extract several features of the dynamic texture sequences: Normal flow, the standard Spatial Information (SI) and Temporal Information (TI), Gray Level Cooccurrence Matrix (GLCM).

The normal flow field is easy to compute and can be directly estimated without any iterative scheme used by regularization methods [START_REF] Horn | Determining optical flow[END_REF]. Moreover, it included both structural and temporal information on dynamic texture : spatial information is linked to edge gradient vectors, while temporal information is related to the moving edges. The drawback of its is the sensitivity to the noise, which can be reduced by smoothing or applying a threshold on the spatial gradients.

The Spatial perceptual Information, SI, is based on the Sobel filter. Each frame of the dynamic texture (luminance plane) at time n 𝐹 𝑛 is firstly filtered with the Sobel filter [Sobel 𝐹 𝑛 ]. The standard deviation over the pixels (𝑠𝑡𝑑 𝑠𝑝𝑎𝑐𝑒 ) in each Sobel-filtered frame is therefore computed. This operation is repeated for each frame in the dynamic texture sequence and results in a time series of spatial information of the scene. The maximum value in the time series (𝑚𝑎𝑥 𝑡𝑖𝑚𝑒 ) is chosen to represent the spatial information content of the scene.

The GLCM descriptor combines 4 features, that are contrast, correlation, energy and homogeneity. Similarly, the following descriptors are defined for normal flow vectors : Divergence, Curl, Peakness and Orientations.

Therefore, we have a list of the best Lagrange multiplier factor for each dynamic texture sequences and each corresponded features. Support Vector Machine (SVM) was used as a classification tool with the previous defined features as the attributes and the Lagrange multiplier factor as the result. To test the learning performance of SVM, we performed leave-one-out, cross-validation and random sampling to test and measured the classification accuracy.

IV. EXPERIMENTAL RESULTS

The proposed predicting the best adaptive Lagrange multiplier factor method has been integrated into the HEVC reference models, and compared with the original codec. Identical test conditions are used here as in the experiment in Section 4.4, uniform test quantization parameters (QP) are used for all I, P and B frames from QP 22 to QP 47 with an interval of 5 for both codec.

The group of progressive format test sequences (YUV 4 :2 :0) are used here including 37 videos at in 30fps. These are all public video sequences from the standard test sequence group in the DynTex database.

Since we have 37 dynamic texture sequences in our dataset, we use the different uniform test quantization parameters (QP) which have been mentioned above for each dynamic texture sequences. Then we sum up all of the sequences in the same quantization parameter and compute the average SSIM and PSNR value. Finally, we also compute the total average SSIM and PSNR value among all the sequences with all test quantization parameters.

The compression performance of the proposed method for HEVC is compared with the corresponding anchor codec. The results are based on the Bjontegaard delta measurements with the two video quality metric SSIM and PSNR are shown in Table2. Besides, the proposed method compared with the original method with measurement of SSIM and PSNR over all frames are shown in Table Ⅰ. It can be observed that the proposed method always performs better than the anchor codec in all test quantization parameters with average more than 0.1 better in SSIM. It should be noted that the proposed method is based on experimental results using uniform QP for all framesone of the most commonly used scenarios. For cases with different GOP structure for different frame types, the optimum Lagrange multiplier factors may vary. In terms of computational complexity, even when including computation for scene cut detection, the increased complexity of our method is negligible in the overall context of HEVC compression.

Although the method presented here are inspired from the adaptive Lagrange multiplier selection method from [START_REF] Zhang | An adaptive Lagrange multiplier determination method for rate-distortion optimization in hybrid video codecs[END_REF], we want to dispel the misconception that our method is trying to predict the better Lagrange multiplier factor based on the features of dynamic texture sequences instead of selecting the best one among a number of values. In particular, we indeed choose the best Lagrange multiplier factor among some values in the training step. However, we use machine learning as solving the linear regression problem instead of the classification. Therefore, the techniques under consideration turn out to be simple predictor that show the predicted best Lagrange multiplier factor while we put in the features of the dynamic texture sequence.

V. CONCLUSION

In this paper, a method for predicting the adaptive perceptual Lagrange multiplier factor is proposed for HEVC to improve its perceptual coding performance. In our approach, it has trained by 37 homogeneous spatio-temporal patches, referred as dynamic texture. For a given test dynamic texture sequence, it was first extracted the features such as spatial information, temporal information and normal flow. Once we know the feature of the given dynamic texture, we can achieve predicting the best Lagrange multiplier factor in HEVC. Experimental results show that the proposed method is able to predict one Lagrange multiplier factor to obtain significant improvement on perceptual RD performance and visual quality of the reconstructed dynamic texture sequences, compared with the original rate distortion optimization in HEVC.

We derive a complete framework for predicting the best Lagrange multiplier factor in video compression standard (HEVC). We provide preliminary results indicating that the method can provide a predicted Lagrange multiplier factor that can improve the visual quality at equal bit-rate and should be further optimized.

The possible future outcome of this work is to improve the computation of the features of dynamic texture sequences. Although we extract a great number of features in this experiment for trying to using these features to describe the whole characteristic of the sequences better, we simply deal with these features with computing the average value of all the pixels. In this case, the average cannot well represent the characteristic of the dynamic texture sequences. Therefore, we will try to compute the features of dynamic texture sequences in a more reasonable way for representing the sequences better.

Besides, we only have 37 dynamic texture sequences in our experiment. However, it is not enough for machine learning to make the precise prediction. Moreover, the 37 dynamic texture has the same format and the same size from the same database. In another word, the dataset we used is not variety enough. Therefore, the prediction cannot be very precise in predicting the best Lagrange multiplier factor. In the future work, we need to collect the dynamic texture sequences from many database as much as possible. Besides, using different length and GOP structure of the dynamic texture sequences may improve the prediction of the Lagrange multiplier factor.

Fig. 1 .

 1 Fig. 1. Different 𝑘 𝑓𝑎𝑐𝑡𝑜𝑟 performed in R-D curve with PSNR

ACKNOWLEDGMENT This work was supported by the Marie Sktodowska-Curie under the PROVISION (PeRceptually Optimised Video CompresSION) project bearing Grant Number 608231 and Call Identifier: FP7-PEOPLE-2013-ITN and the Fundamental Research Funds for the Central Universities in China under Grant 2015ZZ032.


Karam Naser

Vincent Ricordel

Patrick Le Callet
email: patrick.le-callet@univ-nantes.fr

A FOVEATED SHORT TERM DISTORTION MODEL FOR PERCEPTUALLY OPTIMIZED DYNAMIC TEXTURES COMPRESSION IN HEVC

Due to their rapid change over time, dynamic textures represent challenging contents for the video compression standards. While several studies proposed different coding techniques, such as synthesis based coding, they mostly lack the perceptual studies on the perceived distortions.

In this paper, a framework of perceptually optimized dynamic texture compression is presented. It is based on a psychophysically driven distortion model, which is utilized inside the rate distortion loop of HEVC. The model is tested for three compression levels, and showed a significant rate saving for both training and validation sequences set.

I. INTRODUCTION

The demand for high quality video services is continuously expanding. Modern technologies enable the end-user to record, view, stream and share videos with diverse quality and resolution. Due to the limited storage and transmission capacity, these videos are often compressed to match the available rate budget. This compression would necessarily degrade the quality and may introduced undesired decrease in the user quality of experience.

The state of the art video compression standard, known as HEVC [START_REF] Gary J Sullivan | Overview of the high efficiency video coding (hevc) standard[END_REF], has shown significant improvement over the previous (AVC), in which it can provide up to 50% bitrate saving for the same subjective quality [START_REF] Ohm | Comparison of the coding efficiency of video coding standardsincluding high efficiency video coding (HEVC)[END_REF]. This achievement is mainly due to better prediction mechanism as well as flexibility in the block partitioning.

Despite the high performance of HEVC, it shows weaknesses when it deals with dynamic textures. This prediction tools are not suited for this contents. It is especially true for inter prediction, in which high residual, after motion compensation, is to be encoded . In contrast, for ordinary signals, a small residual signal is yielded, and many blocks are skipped.

For this reason, coding dynamic textures represents a challenge. There has been lots of effort put to provide a better coding strategy. In particular, texture synthesis has been the prosperous alternative of the conventional coding. One of the first approaches was introduced by NdjikiNya et. al in [START_REF] Ndjiki-Nya | Improved h. 264/avc coding using texture analysis and synthesis[END_REF]. In this approach the textured areas are synthesized, and only the synthesis parameters are sent to the decoder. more recent approaches, such as [START_REF] Bosch | An overviewof texture and motion based video coding at purdue university[END_REF] and [START_REF] Zhang | A parametric framework for video compression using region-based texture models[END_REF], are also following the same methodology.

The backbone of all of the synthesis based approach is the quality of the synthesized textures. In which, a proper metric is needed to decided precisely whether to switch to synthesis or conventional coding. The metric is also desired to work on block level, which makes it difficult to be designed, and thus, it is still unsolved problem.

On the other hand, the coding efficiency can be improved by utilizing the knowledge about the human visual perception. A large body of research was put into developing several ways to compress the videos into the class of perceptual video compression [START_REF] Hong Ren Wu | Perceptual visual signal compression and transmission[END_REF] [START_REF] Lee | Perceptual video compression: A survey[END_REF]. An example of this, in [START_REF] Sun | Perceptually adaptive lagrange multiplier for rate-distortion optimization in h. 264[END_REF] [START_REF] Liu | An improved rate control algorithm of h. 264/avc based on human visual system[END_REF], is to consider the sensitivity of each region of the scene in distributing the bitrate. Most of these kind of approaches consider the static texture properties, whereas the dynamic texture are still not fully explored.

In the foveal vision, as compared to peripheral one, we are more sensitive to visual distortions. This is because of the high concentration of photo-receptors in the fovea. For this reason, the foveal distortion model considers the lower case of the allowed distortions. In other words, by optimizing the distortion for foveal vision, it is guaranteed that it would not result in negative impact if the stimuli are perceived in the peripheral vision. For this reason, the proposed model is designed as a foveated one.

Our recent investigation on dynamic textures showed that there is a large amount of perceptual redundancies, that can be exploited to provide significant saving in HEVC [START_REF] Naser | Estimation of perceptual redundancies of hevc encoded dynamic textures[END_REF]. On the other hand, the perceived distortion of dynamic texture contents can be modeled to derive the rate-distortion mechanism in HEVC to provide a significant bitrate saving [START_REF] Naser | Modeling the perceptual distortion of dynamic textures and its application in hevc[END_REF]. In this paper, we present a general framework for perceptually optimized dynamic texture compression. The model is parameterized via psychophysical measurement, and used inside the rate distortion loop of HEVC. It showed a significant bitrate saving for different categories of contents. Further, the model parameters were able to be predicted The rest of the paper is organized as follows: Sec. II provides the details of the psychophysical test for estimating the perceived distortion. Sec. III describes the implementation of the model inside HEVC, accompanied by the bitrate saving resutls. In Sec. IV, the generalization test and results are explained. Finally, the concluding remarks as well as the future work is summarized in V.

II. HEVC PERCEPTUAL DISTORTION MODEL ESTIMATION II-A. Method

Subjective Assessment of the perceived distortions is the most accurate way as compared to different available distortion metrics. There exist several standard methods for measuring the perceived distortion/quality which are recommended by ITU-T are listed in [START_REF] Itur Rec | Methodology for the subjective assessment of the quality of television pictures[END_REF]. Beside them, there are also some other methodologies that are base on binary decision, such as pair comparison test. Generally, binary tests are more accurate and require less effort from the observers.

One of the promising methodology is known as the Maximum Likelihood Difference Scaling (MLDS [START_REF] Laurence | Maximum likelihood difference scaling[END_REF]). It is based on comparing supra-threshold distortions by comparing two pairs of stimuli, and selecting the pair that shows a higher difference. The method have shown a good performance in the task of estimating the perceived distortions of compressed images [START_REF] Knoblauch | MLDS: Maximum likelihood difference scaling in R[END_REF], thus, we opted to use it in this work.

Adapting MLDS in this work is straightforward. The observers were presented 4 sequences, that are horizontally 1 degree of visual angle apart, and 3 degrees vertically. The observers were asked to select the pair that shows more visual difference, as compared to the other pair. The selection was done via the keyboard arrows, and by pressing "enter" to validate the selection. A screenshot of the used software is shown in Fig. 1.

The subjective test was conducted in a professional room specifically designed for subjective testing. It complies with the ITU recommendations regarding the room lighting and screen brightness [START_REF] Itur Rec | Methodology for the subjective assessment of the quality of television pictures[END_REF]. The used screen was a TVLogic LVM401 with a resolution of 1920x1080 at 60Hz. The viewing distance was 3H, where H is the screen height.

II-B. Material

The distortion model that we are seeking is to be used for video coding purpose. Knowing that the video coding standards work on small blocks, with limited access to the past and future frames, the optimal model is the one that has a very short spatio-temporal extent. However, we are limited by two factors: first, we can't go below the foveal vision (one degree of visual angle), and second, subjects would need around 100-200 ms to fixate, which is known as the minimum fixation time.

Accordingly, we manually cropped sequences from two dynamic texture datasets, namely DynTex dataset [START_REF] Péteri | DynTex: A comprehensive database of dynamic textures[END_REF] and BVI textures [START_REF] Miltiadis Alexios Papadopoulos | A video texture database for perceptual compression and quality assessment[END_REF]. Overall, we collected homogeneous 43 sequences These sequences have 128x128 spatial extent (4 Coding Tree Units) and 500 ms temporal extent.

For the subjective evaluation, it is inconvenient to use all the 43 sequences, but rather a representative subset that covers the original feature space. This is to reduce the effort required to obtain the subjective results. We considered the rate-distortion behavior of the sequences as a distinguishing feature. Using HEVC reference software (HM 16.2 [START_REF]29/WG[END_REF]), the sequences where encoded to 10 levels of Quantization Parameter (QP), and the Bjontegaard delta PSNR (BD-PSNR [START_REF] Bjontegaard | Calculation of average PSNR differences between RD-curves[END_REF]) was computed between all sequences. The sequence which has the minimum sum of BD-PSNR compared with all the other sequences is considered as the reference one, and the BD-PSNR with respect to this sequence is consider as the sequence feature. Accordingly, 8 sequences were retrieved using k-means clustering algorithm (k = 8).

Finally, in the subjective test, the viewers were shown only the inner circle of 91 pixels diameter. Upon the end of each sequence, it was repeated with time reversal in order to avoid temporal flickering artifacts. The sequences are shown in Fig. 2. For clarity, each video was assigned to a SeqId from 1 to 8, which follows the same order as shown in the figure (from left to right, and top to bottom).

II-C. Results

The binary response of the observers was converted to a perceptual difference scale as described in [START_REF] Laurence | Maximum likelihood difference scaling[END_REF]. It can be interpreted as effect of the change of a physical quantity on the perceived one. In our case, this corresponds to the average MSE and perceived difference. Examples of the results are shown in Fig. 3. The x-axes represents the overall average MSE of all the frames, whereas the y-axes represents the perceived difference. The confidence intervals are computing by learning the observers probability and repeat 10000 simulations using a boot-strapping procedure as explained in [START_REF] Knoblauch | MLDS: Maximum likelihood difference scaling in R[END_REF].

The two curves shown in Fig. 3 represent two different trends in the MSE vs perceptual difference relationship. The first trend, as for SeqId 2, shows that there is a big deviation between the measure distortion (MSE) and the perceived one. On the other hand, the second trend, which is shown for SeqId 7, indicates that MSE is directly proportional to the perceived value of distortion.

The perceptual distortion model is thus a piece-wise linear function that maps the measured distortion in MSE to the perceived distortion. This model is content dependent, but it can be predicted based on feature analysis (Sec. IV-A) and applied in HEVC to enhance the coding efficiency III.

III. MODEL APPLICATION IN VIDEO CODING III-A. Perceptual Rate Distortion Optimization

Looking at the relationship between the measured and perceived distortions in Fig. 3, we can see that the sequences belonging to the first trend are suitable candidates for perceptual optimization. This is because the high deviation between the perceived distortion and the measured distortion can lead to wrong decisions inside the coding loop and thus would not lead to the optimal rate quality compromise.

A straightforward way to utilize the subjective test result in the video compression scenario (HEVC) is to map the distortion measure in HEVC to its perceptual value. This is achieved by using the piece-wise linear mapping functions derived from the subjective test. As HEVC encoder is using the sum of square difference (SSD), the measured M SE is mapped into a perceptual value (SSD p ) as follows:

SSD p = (αM SE + β) × N ( 1
)
Where N is the number of pixels belonging to the given block. Similarly, the new Lagrangian multiplier λ can be mapped to the perceptual one λ p as follows:

λ p = - ∂SSD p ∂r = ( ∂SSD p ∂SSD ) × (- ∂SSD ∂r ) = α × λ ( 2
)
where r is the bit-rate. Thus, the new λ is a scaled version of the old one.

III-B. Estimating the Bitrate Saving

Instead of only testing whether the proposed framework is more preferred, we were interested in measuring the amount of bitrate saving that it can provide. For this purpose, one needs to compare the bitrate at equal subjective quality. However, finding the subjective equality is not straightforward, but rather requires a specific psychophysical test known as threshold estimation.

For this purpose, we designed a specific psychophysical test to estimate the iso-quality points. It is simply a yes/no forced choice test, in which the observers are asked to select one of the two pairs, that is of better quality One of the pairs is the reference one with a fixed compression level, and the other is tested with different bitrates. The responses are then converted to a psychometric function of preference. The threshold of 50% preference is considered as a point of subjective equality, and the corresponding relative rate is considered as the amount of rate saving. The point of subjective equality is considered as the rate at which 50% or preference occurs. This choice of 50% is because that the subjects are not sure which pair is preferred and they simply make a random selection.

Estimating the psychometric function is a classical task in psychophysics. However, we sought an advanced test, that adaptively selects the stimuli level and requires less number of trails to converge, and thus limits the overall test duration and cost. For this reason, we used the recent psychometric estimation toolbox in [START_REF] Shen | A matlab toolbox for the efficient estimation of the psychometric function using the updated maximum-likelihood adaptive procedure[END_REF], known as Updated Maximum Likelihood test.

III-C. Results

The optimization process in Sec. III-A was used for the specific sequences, which showed a large deviation between the measured distortion (in terms of MSE) and perceived one. These sequences, which belong to the first trend as explained in Sec. II-C, are namely defined by their sequence id: SeqId1, SeqId2, SeqId3 and SeqId8 (Fig. 2). The sequences were encoded to three quality levels: high quality (Q1), middle quality (Q2) and low quality (Q3). Using the procedure described in Sec. II, the bitrate saving at the same subjective quality is shown in Table I Table I. Bitrate saving (%) due to perceptual optimization. +-refers to 95% confidence interval that the proposed perceptual optimization algorithm provides a significant bitrate saving, up to 37%.

IV. GENERALIZATION OF THE PROPOSED MODEL IV-A. Model Prediction via Feature Analysis

The results presented so far are based on optimizing sequences utilizing their measured perceived distortion profile. To generalize the perceptual optimization algorithm, the distortion model parameters need to be estimated from the sequences features. In other words, the piece-wise linear function parameters (values of α and β in Sec. II-C), must be learned from each sequence.

We used a set of few, computationally simple, features in the machine learning approach. First, we selected the spatial and temporal information (SI and TI) [START_REF] Recommendation | Subjective video quality assessment methods for multimedia applications[END_REF] and the colorfullness (CF) [START_REF] Winkler | Analysis of public image and video databases for quality assessment[END_REF]. These features are often used to categorize contents in datasets. For image analysis, the gray-level cooccurrence matrix is one of the highly used features for different classification/recognition problems [START_REF] Robert M Haralick | Textural features for image classification[END_REF]. However, we used only its homogeneity property. On the other side, we used also some dynamic texture features, namely the curl and peakness of normal flow as defined in [START_REF] Péteri | Dynamic texture recognition using normal flow and texture regularity[END_REF].

This set of features were used in the form of linear regression. The performance has been evaluated by the mean squared error (normalized) of leave one out cross-validation test, which has a value of 0.087. This indicates that model prediction is reasonably well.

IV-B. Generalization Test

The trained linear regression model has been used to predict the perceptual distortion model parameters of novel sequences. As explained in Sec. II-B, we have an overall of 43 dynamic texture sequences, 8 of them where used in the first experiment. For the rest of sequences (33 sequences), The trained linear regression model was used to predict their perceptual distortion model.

Among these sequences, we selected the top 24 sequences having the highest deviation between the measured and the perceived (predicted) distortion.

Using the same perceptual optimization algorithm described in Sec. III-A, we encoded these sequences also for 3 quality points (Q1,Q2 and Q3). The bitrate saving was measured subjectively, using the same psychophysical procedure in Sec. III-B. The results are shown in Fig. 4, in which the average saving of the three quality point is plotted for each sequence, defined by its sequence id (SeqId). We can clearly see that the model can provide significant bitrate saving for the majority of the sequences. However, some exceptions are also present. For a certain category of dynamic textures, a straightforward perceptual optimization was possible, achieving a bitrate saving up to 37%.

The distortion model parameters were shown to be predictable via a linear regression model using computationally simple features. This leaded to show the applicability of the model on novel sequences.

The advantages of the proposed optimization algorithm are the simplicity and compatibility. That is, no need for a complicated quality metric and only linear mapping of the used distortion measure is needed. In terms of compatibility, there is no change in the reference decoder, so the sequences can be directly decoded by the HEVC standard.

The future work would be to deploy the framework in a complete scene. In this case, a proper segmentation is first to be done base on the content features. For each content, the model parameters will be estimated, and used for perceptual optimization. An overall significant bitrate saving is expected.

Fig. 1 .

 1 Fig. 1. Screen shot of the software used for MLDS

Fig. 2 .

 2 Fig. 2. Sequences used for subjective test

Fig. 3 .

 3 Fig. 3. Subjective test results of 2 sequences representing 2 different trends

Fig. 4 .

 4 Fig. 4. Average bitrate saving for three quality points of the generalization test

  . One can clearly realize

	SeqId	Q1	Q2	Q3	Ave(row)
	1	12.2+-7.4	6.8+-2.2	19.2+-1.4	12.7+-3,7
	2	40.4+-1.3	34.9+-1.0	20.7+-0.9	32.0+-1.1
	3	36.9+-4.6	37.3+-5.5	33.5+-6.02	35.9+-6.0
	8	13.3+-5.9	26.9+-6.3	3.8-7.4	14.6+-6.5
	Ave(col)	25.7+-5.3	26.5+-3.7	19.3+-3.9	23.8+-4.3

ACKNOWLEDGEMENT

This work was supported by the Marie Sklodowska-Curie under the PROVISION (PeRceptually Optimized VIdeo CompresSION) project bearing Grant Number 608231 and Call Identifier: FP7-PEOPLE-2013-ITN.


Uday Singh Thakur

Karam Naser

Mathias Wien
email: wien@ient.rwth-aachen.dekaram.naser@univ.nantes.fr

Dynamic Texture Synthesis using Linear Phase Shift Interpolation

Dynamic texture motions like flowing water, motion of leaves etc. have a complex random character. A sequence containing such a content is challenging to encode even when using state of the art High Efficiency Video Coding (HEVC) especially, if the available bandwidth is limited. It is observed that often when predicting dynamic textures, codec switches to intra prediction. At lower rates, dynamic texture content shows visually annoying blurring and blocking artifacts.

For dynamic textures, both spatial and temporal details are perceptually of less importance. This property of the Human Visual System (HVS) can be exploited when coding dynamic texture content, as suggested in this paper. At the encoder, preprocessing is done by skipping even numbered B pictures. At the decoder side, skipped pictures are synthesized using linear phase shift interpolation of the complex wavelet coefficients, from the adjacent already decoded pictures. Subjective evaluation of proposed approach is done by using a pair wise comparison test between the proposed results and the conventional HEVC decoded bitstream at similar bitrates. The evaluation results show that viewers prefer the proposed result over conventional HEVC.

I. INTRODUCTION

Textures are categorized into two categories based on motion i.e. static or dynamic [START_REF] Ballé | Models for static and dynamic texture synthesis in image and video compression[END_REF]. The former refers to an object in a scene which exhibits spatial homogeneity such as a fabric, surface of a stone and does not have any local motion over time (excluding potential camera motion). The latter are sequences of images of moving scenes that exhibit certain stationarity properties in time; these include flowing water, leaves in motion, fire, etc. We focus primarily on dynamic textures, as such a type of motion is extremely challenging to compress, when using state of the art High Efficiency Video Coding (HEVC) [START_REF] Wien | High Efficiency Video Coding -Coding Tools and Specification[END_REF], [START_REF] Sullivan | Overview of the high efficiency video coding (HEVC) standard[END_REF].

It is mostly observed that when encoding dynamic textures, motion compensation performance of HEVC is not efficient, as a consequence the residual has high energy. One of the reason is rapid change in the signal over time. Often, the codec switches to Intra mode over dynamic textured regions instead of using Inter prediction when predicting B pictures as shown in Fig. 1b. It is also observed that Coding Tree Units (CTU's) are partitioned in to smaller Coding Units (CU's) over such regions as shown in Fig. 1c, this further adds to the bitrate.

Accordingly, such a motion is difficult to predict using standard motion compensation algorithms, due to its complex random character. To solve this problem, several texture coding techniques have been proposed in the past. This can be gen-erally classified into two categories: Top-down and bottom-up approaches. Top-down approaches start from the idea that fine details inside textures are perceptually irrelevant and therefore, they can be replaced with an equivalent content given a set of statistical constraints. On the other hand, the bottom-up approaches takes into the account the perceptual properties of the textured signals and distribute the bitrate adaptively, or allocate the distortions, according to their perceptual sensitivity. A well known example of top-down approaches is texture synthesis. It has been utilized many times in video coding after the inspiring work by Ndjiki-Nya et.al. [START_REF] Ndjiki-Nya | Improved H.264/AVC coding using texture analysis and synthesis[END_REF]. In this approach, the texture is removed at the encoder side and synthesis parameters are sent to the decoder. Similarly, texture synthesis was used for interpolating textures between pictures [START_REF] Zhang | A parametric framework for video compression using region-based texture models[END_REF], or replacing the texture with a simplified version [START_REF] Dumitras | A texture replacement method at the encoder for bit-rate reduction of compressed video[END_REF], [START_REF] Naser | Local texture synthesis: A static texture coding algorithm fully compatible with HEVC[END_REF], [START_REF] Thakur | Texture analysis and synthesis using steerable pyramid decomposition for video coding[END_REF] and [START_REF] Thakur | Image coding using parametric texture synthesis[END_REF].

For bottom-up approaches, there has been a lot of focus put into static textures, while neglecting the dynamic ones. An example of this [START_REF] Sun | Perceptually adaptive lagrange multiplier for rate-distortion optimization in H.264[END_REF], [START_REF] Liu | An improved rate control algorithm of H.264/AVC based on Human Visual System[END_REF], is to consider the sensitivity of each region of the scene in distributing the bitrate. A recent investigation on dynamic textures has shown that there is a large amount of perceptual redundancies, that can be exploited to provide significant bitrate saving in HEVC [START_REF] Naser | Estimation of perceptual redundancies of HEVC encoded dynamic textures[END_REF]. Previously, motion of dynamic texture was predicted using texture synthesis model based on Auto Regressive Moving Average (ARMA) prediction H.264/AVC [START_REF] Ballé | Models for static and dynamic texture synthesis in image and video compression[END_REF]. ARMA is a linear model and its performance is limited to simple motions which are now well handled by HEVC. More complicated motion still needs more advanced modeling.

Recently, phase based methods have shown promising results in video motion processing and interpolation [START_REF] Wadhwa | Phase-based video motion processing[END_REF], [START_REF] Meyer | Phase-based frame interpolation for video[END_REF]. In this paper, we have used phase of complex wavelet coefficients for dynamic texture synthesis coding, for every 3 consecutive B pictures, 1 B picture in the middle is skipped at the encoder and later synthesized at the decoder using wavelet transform. Skipping B pictures for such a content will have minor effects on the motion compensation performance of HEVC, due to Intra prediction being mostly used when predicting B pictures, comprising of dynamic texture content. It is a matter of fact that, intra coded signal takes more bits compared to inter and therefore, by skipping 50% of the B pictures provides 27 -45% saving in bitrate for dynamic texture content as shown in Fig. 2.

Rest of the paper is organized as follows: Section II reviews

II. PHASE SHIFT VIDEO INTERPOLATION

The presented approach in this Section is based on the work [START_REF] Meyer | Phase-based frame interpolation for video[END_REF]. Phase shift between two pictures corresponds to the motion in a video. Interpolating such a phase shift can synthesize another intermediate picture. We have exploited this work for benefiting dynamic texture coding. In this section we will give a brief overview of the algorithm given in [START_REF] Meyer | Phase-based frame interpolation for video[END_REF] as it is important to understand the further work.

A. Steerable Pyramid

In general for two-dimensional functions, one can separate the sinusoids into bands not only according to the frequency ω, but also according to spatial orientation θ, using the complexvalued steerable pyramid [START_REF] Simoncelli | The steerable pyramid: A flexible architecture for multi-scale derivative computation[END_REF]. The steerable pyramid filters resemble Gabor wavelets and, when applied to the discrete Fourier transform of an image, they decompose the input image into a number of oriented frequency bands R ω,θ . The remaining frequency content which has not been captured in the pyramid levels is summarized in (real valued) high and lowpass residuals. It is to be noted that for this work these pyramids have been generalized to arbitrarily scaling factor λ due to better cross-scale phase correlation. Amplitude A ω,θ and phase φ ω,θ of above computed complex coefficients are subsequently calculated.

B. Phase shift interpolation with confidence based shifting

Assuming that motion is encoded in the phase shift, interpolating it requires computation of phase difference φ diff between the phases φ 1 and φ 2 of two adjacent pictures. Due to periodicity of the phase value, resulting angular values are between [-π, π] which correspond to smaller angular differences between the two input phases. Displacement corresponding to a phase difference of more than π leads to a phase ambiguity. To overcome this ambiguity, the method for shift correction is proposed in [START_REF] Meyer | Phase-based frame interpolation for video[END_REF], based on the assumption that the phase difference between two pyramid levels does not differ arbitrarily, i.e. phase differences between levels can be used as a confidence measure that quantifies whether the computed phase shift is reliable. The shift correction helps to interpolate the motion of high frequency content more robustly. The corrected phase shift φ diff is linearly interpolated to synthesize any motion in between phases φ 1 and φ 2 .

III. EXTENSION OF PHASE INTERPOLATION TO DYNAMIC TEXTURE CONTENT

Motion of dynamic textures have a complex random character, as a result they are challenging to encode. Conventional motion compensation algorithms used in state of the art HEVC completely fail when performing inter prediction for B pictures as a result, residual has high energy. Based on the Rate Distorion decision mechanism the codec often switches to Intra, shown in Fig. 1b. This behavior of codec opens up door for novel ways of modeling such a content.

E 1 E 5 E 2 E 3 E 4 S 1 S 2 S 3 S 4
Fig. 3: Dynamic texture synthesis: Every S picture is reconstructed at the decoder from the closest neighbors i.e. decoded E pictures using complex wavelets

A. Skipping B pictures

The goal of the algorithm is to first skip and later synthesize the skipped pictures. This is a pre-processing step, in which we skip even numbered pictures during encoding. In general, if the original picture count is even, the remaining pictures left after preprocessing is given by (count/2) + 1 else, if the original picture count was odd the remaining picture count is given by (count/2) -0.5 .

B. Synthesis of B pictures

At the decoder side, the bitstream is decoded followed by skipped B picture synthesis as shown in Fig. 3, skipped picture e.g S 1 is synthesized from the two adjacent already decoded neighbor pictures E 1 and E 2 using the algorithm mentioned in Section II. The decoded E pictures are decomposed using multiscale oriented linear filters [START_REF] Simoncelli | The steerable pyramid: A flexible architecture for multi-scale derivative computation[END_REF]. The resulting coefficients are complex-valued: The real and imaginary parts correspond to even and odd-symmetric filter impulse responses. Phase difference between between corresponding oriented frequency bands of the two consecutive decoded E pictures is calculated using four quadrant inverse tangent, followed by linear interpolation of the phase shift. This method does not require any side information as it is simple linear interpolation of phases between bands of similar frequency and orientation. The output of interpolation is the phase of picture to be synthesized but, to complete the reconstruction of B picture, we will also need its magnitude, The magnitude of the interpolated B picture cannot be just linearly blended for dynamic textures as given [START_REF] Meyer | Phase-based frame interpolation for video[END_REF]. Doing such blending reduces the luminance of picture and introduces blurriness as shown in Fig. 4b. The reason is that motion in case of dynamic textures is very rapid, with highly varying contrasts over time. As a result, the magnitude widely varies between consecutive frames and averaging such a magnitude makes the reconstruction look blurry. In the proposed solution for the intermediate picture's magnitude, the magnitude is not linearly blended where is it changing beyond a certain threshold ρ.

Algorithm 1 Algorithm for synthesis of magnitude

if |A 1 -A 2 | > ρ then if A 1 > A 2 then A syn = A 1 else if A 1 < A 2 then A syn = A 2 end if else A syn = (A 1 + A 2 )/2 end if
In algorithm 1 A 1 and A 2 are magnitudes of decoded picture E 1 and E 2 . We use the greater of two magnitudes for the intermediate picture S 1 as perceptually it looked better and sharper as shown in Fig. 4c. If the difference in magnitudes is less that ρ we simply blend the magnitudes. Lowband is linearly blended in this case and high frequency of the later picture E 2 is chosen. Final reconstruction is obtained by using inverse transform. The interpolated S picture between two E pictures is perceptually of high quality.

IV. RESULTS AND DISCUSSION

For evaluation purposes a 256 × 256 sequence resolution consisting of dynamic texture is studied. These sequences were cropped from original 4k video sequences [START_REF] Papadopoulos | A video texture database for perceptual compression and quality assessment[END_REF] such that the selected areas only include dynamic texture content. Temporally, the sequences have an extent of 500 ms. The purpose of selecting short term sequences is to have as much homogeneous contents as possible. Both spatial and temporal resolution have been selected subject to perceptual constraints, spatially the sequences are within the foveal vision, whereas temporally they are beyond the minimum fixation time (100-200 ms).

A. Bitrate Saving

In order to show the amount of possible saving in bitrate, we have compared the bitrate between HEVC's random access configuration and the proposed coding scheme at the same QPs. The results are averaged for four QP values (22, 27, 32 and 37) as shown in Fig. 2, the error bar in the figure corresponds to standard deviation of the four QPs.

The bar graph in Fig. 2 clearly shows that 27 -45% of the bitrate is allocated to the skipped B pictures. For our proposed scheme, we have used 120 Hz sequences, after skipping B pictures during encoding it changes to 60 Hz. The skipped B pictures are then synthesized at the decoder using the algorithm mention in Section II and III. The resulting sequences have better spatial quality as shown in Fig. 5 at same bitrate, as it retains more spatial details compared to HEVC. Temporally, the motion is coherent with less blockiness compared to HEVC. Perceptual details inside dynamic texture are of less importance to the human observer and therefore, the approach is considered to be appropriate for such type of contents. Subjective evaluations are performed for quality assessment, to assess the quality of the proposed method in comparison to the HEVC at similar bitrates.

B. Objective Evaluation

Evaluating the proposed model objectively is not appropriate as the target of the proposed scheme is not to approximate the reference. This is because we are highly deviating from pixel fidelity when synthesis is used. However, for odd pictures which are encoded with HEVC, the objective score is always better, as we have saving in bitrate. However, synthesis causes reduction in PSNR for even pictures. This is quite expected as PSNR is not a proper measure of the perceived distortion for synthesis. In contrast, the visual quality of the synthesized picture is better than the reconstructed HEVC image at the same bitrate shown in Fig. 5.

C. Subjective Evaluation

For evaluation of the proposed model, we designed a specific subjective test to verify its usefulness. The test is a pair wise comparison in which the observers saw two sequences side by side as shown in Fig. 7, and were asked two compare and select the one that they preferred. The observers were also allowed to have no preference option, to reduce the amount of random selections. The subjective testing material consisted of five source sequences as shown in Fig. 6. The observers were allowed to repeat and play the sequences at their choice. The sequences were encoded at four compression levels (q1; q2; q3 and q4), QPs ranging in value between 22 to 37. The proposed scheme is compared to conventional HEVC random access configuration at same bitrate. Five subjects participated in the test, their respective responses are given in Table I. In this table, 1 refers to when the proposed model is preferred, -1 when default HEVC is preferred and 0 refers to no preference. Overall, we can see that the average is a positive number, which indicates that the subjects generally preferred the synthesis over the default HEVC.

V. CONCLUSION

The paper presents a novel scheme for B picture synthesis in the context of dynamic texture coding. HEVC switches to intra prediction in B pictures with smaller partitionings eventually, leading to high bitrate. The proposed scheme skips every even B picture during encoding process. The skipped pictures are synthesized using phase shift interpolation from already decoded neighboring pictures. Skipping half of B pictures saves 27 -45% bitrate. The paper has presented a novel idea, about new ways for exploration and modeling dynamic texture content from the perspective of benefitting video coding. In a realistic scenario structure and texture will be segmented, textured blocks in B pictures can be skipped and later synthesized at the decoder. Objective quality Our future work will focus on skipping more than 1 B picture, and then synthesizing. This is currently challenging as dynamic textures have rapid motion and interpolating phase shift in between distant pictures can be ambiguous and produce annoying artifacts in the synthesized pictures.

Fig. 1 :

 1 Fig. 1: HEVC's behavior over dynamic texture content for both small and large QP values. (a) shows the B picture from the sequence, Fountain [13] at QP=22 random access configuration. (b) shows the prediction mode selected by HEVC, Inter predicted regions are shown with color green, Intra in purple (mostly observed over dynamic texture content) and maroon shows region where skip mode is chosen. (c) shows the block partitioning sizes, smaller partitions are observed over dynamic texture content. Similarily, we have also shown the behavior of HEVC at large QP (QP=37) in (d), (e) and (f ). It is clearly evident that HEVC's motion compensation performance when predicting dynamic texture content is not effective.

Fig. 2 :

 2 Fig. 2: Average saving in bitrate for homogeneous dynamic texture sequences, when 1 picture is skipped between 3 consecutive B pictures. The comparison is averaged at QP=22, 27, 32 and 37

Fig. 4 :

 4 Fig. 4: Subjective comparison of results for magnitude interpolation. (a) shows the reference, (b) linear blending of coefficient magnitudes as given in [15], (c) is the proposed result. It is clearly evident that proposed method reconstructs sharper interpolated picture as compared to the linear blending.

Fig. 5 :

 5 Fig. 5: Subjective comparison of HEVC and Synthesis at similar bitrates. (b) shows the conventional HEVC decoded picture, with blockiness and blurriness. (c) shows the synthesized B picture at similar bitrate, with more spatial details compared to the HEVC

Fig. 6 :Fig. 7 :

 67 Fig. 6: Subjective testing material

TABLE I :

 I Subjective test result.

		Subject	1	2	3	4	5	Ave
		Calming Water	-1	0	1	-1	1	0
		Drops on Water	-1	0	0	-1	0	-0.4
	q1	Lamp Leaves-1	0	-1	1	1	1	0.4
		Lamp Leaves-2	0	1	1	1	0	0.6
		Treewills	1	1	1	1	-1	0.6
		Calming Water	0	-1	1	1	1	0.4
		Drops on Water	-1	0	1	1	0	0.2
	q2	Lamp Leaves-1	0	0	0	1	1	0.4
		Lamp Leaves-2	1	1	1	0	-1	0.4
		Treewills	0	0	1	-1	1	0.2
		Calming Water	1	1	1	1	-1	0.6
		Drops on Water	-1	0	1	1	0	0.2
	q3	Lamp Leaves-1	0	0	0	0	-1	-0.2
		Lamp Leaves-2	-1	-1	1	-1	0	-0.4
		Treewills	0	-1	0	0	1	0
		Calming Water	1	0	1	1	0	0.6
		Drops on Water	-1	-1	1	1	-1	-0.2
	q4	Lamp Leaves-1	0	1	1	1	1	0.8
		Lamp Leaves-2	-1	0	0	0	0	-0.2
		Treewills	1	-1	1	-1	1	0.2
		Ave	-0.1	-0.05	0.75	0.3	0.15	0.21

ACKNOWLEDGEMENT This work was carried out within the Marie Sklodowska Curie Training Network PROVISION (PeRceptually Optimized VIdeo CompresSION) and received funding from the European Union's Seventh Framework Program for research, technological developments and demonstration under grant agreement no 608231.