Introduction
Recently, with the prosperity of multimedia technologies and the popularization of highquality contents, users are becoming increasingly qualityaware moldovan2013user. To catch up with the growing expectation of higher qualityofexperience, robust quality metric that is of higher discriminability, especially for higherquality contents with less visual difference, is in urgent need nandakumar2019accuracy. Due to the ‘range effect’, higher capability of distinguishing pairs in narrow quality range krasula2017quality_highligh is essential. The improvement of objective quality models depends on the accuracy and the discriminability of the subjective data collected utilizing a certain subjective quality protocol or methodology from human observers. According to the standards and recommendations itu1999methods; sector2012recommendation
published for multimedia quality assessment, the subjective quality protocols could be classified into two main categories including the rating and the comparative methodologies. Absolute Category Rating (ACR) is one of the most commonly utilized single stimulus rating protocols, while Pair Comparison (PC) is the most widely employed comparative approach
perez2019pairwise.On one hand, single stimulus rating methods are suitable when the stimuli are easy to be distinguished. Regardless of their simplicity and efficiency, they are prone to objects’ bias and inconsistency li2020simple as observers may have different interpretation of the quality scale li2020gpm, memory ability le2016influence, and the task’s difficulty varies lakshminarayanan2013inferring, etc. On the other hand, pair comparison has its own advantage of discriminability, as the preference of the observer between each pair of stimuli is asked instead of a score of an individual stimulus in a discrete or continuous scale. Although full pair comparison is of advantages in distinguishing stimuli with small visual difference, it is time consuming, since the number of comparisons increases exponentially with the increase of the number of stimuli. Thus, better strategy is required to achieve a better tradeoff between the discriminability and the efficiency of the subjective protocol.
The emergence of crowdsourcing has sparked a lot of interest for the quality assessment community. There is a plethora of pairwise comparison experiments that were conducted via crowdsourcing platforms xu2017hodgerank. Aiming at obtaining crowdsourcing ranking more efficiently and accurately by making better use of the information of past labeled pairs, many active sampling strategies were purposed to boost the accuracy of ranking aggregation pfeiffer2012adaptive; li2018hybrid. Since most of the existing subjective studies were conducted using single stimuli methods, the stateoftheart active sampling strategies are of great potential to be exploited to boost the accuracy and discriminability of subjective data collected with rating protocols.
Recall that after the collection of pair comparison subjective data, models like the BradleyTerry (BT) or the ThurstoneMosteller (TM), i.e., the Thurstone Case V , are commonly adapted to convert the pair comparison results into quality scores or ranking. Thus, they are also the fundamental cornerstones of the subjective data collection procedure. However, most of the existing standardized conversion models neglect the variance of subjective data, and thus may lose important information including the task difficulties, observers’ biases and inconsistencies, etc.
In this study, a novel framework is presented to boost the pair comparison with ACR data so that the quality assessment accuracy could be further improved. The contributions of this framework are threefold:

A brandnew fusion scheme that combines the ACR and PC data to achieve better tradeoff between the accuracy and efficiency of the subjective data collection procedure.

We adapt the Thurstone Model Case III for pairwise comparison data conversion, where the variance of stimuli could be recovered. By doing so, we narrow the gap between the ACR and PC data and avoid relevant information loss regarding the variance.

A new version of HybridMST, where the active batch sampling strategy is strengthen by the ACR initialization and novel recovering model.
Related work
Pairwise preference aggregation/conversion model:
In the past decades, many models have been proposed to covert or aggregate the pair comparisons responses to rating or ranking scale. The heuristic approach of Emerson
et al. emerson2013original, and the probabilistic permutation based models plackett1975analysis are typical examples. In addition, the ThurstoneMosteller mosteller2006remarks and Bradley Terry bradley1952rankare another two widely used linear models of paired comparisons, where the probabilities of preference between stimuli are converted to scales. Due to the issues of computationcomplexity or parameterestimation, several models were developed to improve the the parameteroptimization procedure
azari2012random; lu2011learning. For instance, a generalized methodofmoments was presented
soufiani2013generalized to speed up existing model with welldesigned generalized moment conditions. In freund2003efficient, the RankBoost was proposed for combining multiple preferences. Shah et al. introduced the minmax bounds on the optimal error shah2016estimation to improve the parametric ordinal models. Other type of conversion models were proposed based on inferring the underlying latent scores dangauthier2008trueskill; wauthier2013efficient. Among the existing models, there are only few of them consider fusing the rating score with the comparison subjective data. The relationship between the rating and pairwise comparison data was studied in watson2001measurement. A unified probabilistic model was presented in ye2014active to aggregate rating scores and pairwise comparisons subjective results. Yet none of these models seek to recover the variance of the stimuli. In one of the most recent study perez2019pairwise a Thurstone Case V based probabilistic model was proposed to combine the rating and comparison subjective data, but no active sampling strategy was considered.Sampling strategy for pair comparison: To infer the ranking from pair comparison data, a significant number of pairs are required to be compared. Since data sampling is one of the simplest way to reduce the cost of pairwise labeling, random sampling strategies, e.g., the model proposed by Dykstra et al. dykstra1960rank, were developed in earlier studies. The HodgeRank on Random Graph (HRRG) lin2012hodgerank was developed based on random graph theory and Hodge decomposition of the graphs paired comparison preferences. An Adaptive Rectangular Design (ARD) was shown in li2013boosting
, to sample novel pairs based on the predicted ranks using current pair comparison results. As active learning has been established as an effective approach for many domains, it is also adopted to improve the performance of pair comparison aggregation. Jamieson
et al. proposed an active ranking recovery model by embedding objects into a dimensional Euclidean space jamieson2011active. In pfeiffer2012adaptive, a Bayesian optimization scheme was proposed based on TM model. Similarly, the CrowdBT chen2013pairwise model was proposed following a similar concept but using BT model instead. The HRRG was improved in xu2017hodgerank by maximizing information gains of pairs. Recently, a Hybrid active sampling strategy was proposed by Li et al. li2018hybrid, where a batch mode was designed using the Minimum Spanning Tree (HybridMST) for the ranking of information gains. It was proven in li2018hybrid that HybridMST achieves best aggregation performance compared to the other stateoftheart models, and is of significant advantages in terms of efficiency when utilizing the batch mode for parallel labeling on the crowd sourcing platforms. However, none of them consider to boost the existing subjective data collected via single stimulus protocols.The Proposed Framework^{1}^{1}1The source code and the table that summarizes all the variables used in this paper are provided in the supplemental material.
Even though the ACR test may fail to accurately rank two stimuli with enough precision or discriminability compared to pair comparisons due to a series of factors introduced in previous sections, it can provide a coarse estimation of the underlying quality. Since the underlying ground truth of ACR and the PC test is consistent, complete pair comparisons become unnecessary once the coarse estimation is available. Therefore, resources could be spent on more informative pairs to obtain finer discrimination on pairs with similar quality and high uncertainty. Our framework is inspired by this idea, details are described below.
0. Problem setup and overview of the framework
Let us assume that we have test stimuli in a pairwise comparison experiment. The underlying quality scores of these objects are . In addition, each test stimulus has its task difficulty, , which determines the participant’s perceptual opinion diversity, i.e., higher indicates people’s opinion are more diverse, lower represents opinion consistency. Thus, the quality character of a test stimulus
can be described by a Gaussian distribution
.The diagram of the proposed framework is summarized in Figure 1. In a nutshell, 1) given the subjective data collected from any single stimuli test/tests (e.g., ACR), the linear scores are first transformed into an initial pair comparison matrix , and the overall pair comparison matrix is initialized by ; 2) Afterwards, the proposed pair comparison data conversion model is applied to approximate prior information on , where is the approximated/recovered underlying quality scores regarding , and
is the recovered underlying standard deviation
w.r.t. ; 3) With the recovered , stateoftheart active sampling strategy, e.g., the HybridMST li2018hybrid, is adapted to select the most informative pairs. Then, the pairs with the highest information gains are selected for pair comparison subjective test to collect an extract set of PC data with pairs. is the number of pairs decided by the total budget of the subjective test. By doing so, the discriminability and reliability of the PC data could be enhanced by considering only the most valuable pairs. Moreover, the complexity/cost of the experiment is reduced when compared to full pair comparison as only the top pairs are compared instead of ; 4) Then the overall is updated by adding the new . Procedure (14) is repeated until reaching the total budget of the subjective test. Let be the number of iteration from step 1 to 4 mentioned above, then the total number of pairs compared in the test equals to .1. PCM initialization: Scale score transformation
The process of transforming the linear scale scores collected from a single stimuli subjective experiments to pair comparison matrix is described in Algorithm 1. denotes the number of total observers, is the individual rating of stimulus from the observer. During the procedure, if the observer rates over , then the corresponding element within the initialized pair comparison matrix accumulates 1, and vice versa. For the remaining pairs, where no preference is given, 0.5 is assigned. The output of this procedure is considered as the initialized pair comparison matrix, i.e., , of the proposed boosting framework, where indicates the first iteration.
2. Bridge ACR and PC: the proposed PC conversion model
In a pairwise comparison experiment, the annotator’s observed score for stimulus is , for stimulus is . If , then we consider that the annotator prefers stimulus over . Otherwise, the preference is opposite. When we observe , there is no significant difference between the two candidates. Then, we consider that the annotator makes a random selection.
The observed value is determined not only by the two Gaussian distribution and , but also by the comparison interaction terms. That is to say, in a typical ACR test, the two observed quality scores for and are independent. However, during the comparison procedure, they are not independent any more. The whole pair comparison procedure can be modeled as follows:
(1) 
where is the covariance term. The probability of selecting over is denoted as , which can be calculated by:
(2) 
where is the cumulative function of a Gaussian distribution with .
A Generalized Pair Comparison Model
Ideally, we should estimate the aforementioned parameters through the pairwise comparison observations. However, in this case, the number of parameters is much larger than the number of observations, which makes the equation to have an infinite number of solutions. To resolve this, we abandon the interaction term under the assumption that the influence of the interaction term is limited when compared with the sum of and . The model is then defined as follows, which is in fact the Thurstone Model Case III thurstone1927law:
(3) 
Maximization Likelihood Estimation (MLE) Procedure ^{2}^{2}2More details of the MLE procedure, e.g., the calculation of relevant derivatives regarding the utility function, could be found in the supplemental material.
To infer the parameters of Thurstone model Case III , the Maximum Likelihood Estimation (MLE) method is adopted in this study. Given the pairwise comparison results arranged in a matrix , where represents the total number of trial outcomes , the likelihood function takes the shape:
(4) 
Replacing by , and maximizing the log likelihood function , we could obtain the MLEs , .
To obtain the confidence intervals of the MLEs, the secondorder derivatives should be calculated and the Hessian matrix
can be constructed. For , we have:(5) 
Following wickelmaier2004matlab, we construct a matrix C, which has the following form by augmenting the negative
a column and a row vector of ones and a zero in the bottom right corner:
(6) 
The first columns and rows of form the estimated covariance matrix of , i.e., . Similar procedure can be implemented for the calculation of covariance matrix of .
3. Boosting Procedure: Expected Information Gain (EIG) based active pair selection
In order to recover the underlying rating of the stimuli from the sparse and noisy pair comparison subjective data, an active sampling strategy for pairwise preference aggregation was proposed by Li et al li2018hybrid. Since this model achieves stateoftheart performance, it is hence adapted in this study to boost the accuracy of nonfull pair comparison subjective test. Similarly, we define the utility function as:
(7) 
Differently, in this study, we have and as defined in previous section.
For simplicity, we replace , with and respectively in the remaining of the paper.
The first term of equation (LABEL:eq:utility_func) could be developed in:
(8) 
By operating the following change of variable:
(9) 
we can then obtain a new expression of the first term (same for other terms) of equation (LABEL:eq:utility_func) as being
(10) 
In this forms, the GaussianHermite quadrature could be applied to approximate each term by
(11) 
4. Information fusion of SS and PC tests:
After conducting the pair comparison with the selected most informative pairs, a sparse pair comparison matrix could be obtained. Therefore the current of the iteration is updated via:
(12) 
Experiment and Analysis ^{3}^{3}3More experimental results and the calculation of the EIG based on TM model are given in the supplemental material.
Experimental Setup
Performance evaluation
The performances of the considered models are estimated by calculating the Spearman’s Rank Correlation Coefficient (SROCC) between the ground truth and obtained estimated scores. Due to limited space, only SROCC are shown in the paper, other results are reported in the supplemental material. Since BT and TM are the most commonly used models, we mainly compared to them during performance evaluation.
Experiments on simulated data
A Monte Carlo simulation is conducted on 60 stimuli whose scores are randomly selected from a uniform distribution on the interval of [1 5] with noise
, which is uniformly distributed between 0 and 0.7 as done in li2018hybrid to simulate the procedure of rating from observers. During the simulation, if the sampled score (from the uniform distribution with noise) , then we consider that is preferred over . For statistically reliable evaluations, the simulation experiment was conducted 100 times and the averaged performance are reported. In each iteration, 50 standard trial numbers are simulated (i.e. 50 simulated annotators to compare all pairs using the active learning scheme for pairs sampling). To compare the performances, SROCC is calculated between the simulated ground truth and the estimated scores.Experiments on realworld datasets
In this study, four datasets equipped with both linear quality scores, e.g. MOS obtained using ACR, and the pair comparison ground truth are considered for the performance evaluation of the proposed model. It has to be emphasized that, for the pair comparisons data from the realworld data, only comparisons among PVS from the same contents are available with few crosscontent comparison pair in certain datasets. Details of the datasets are summarized below. As there is no real underlying ground truth for the realworld datasets, the results obtained by all observers are considered as the ground truth and the SROCC between it and the estimated scores is calculated for performance estimation. Similar to the simulation test, the experiments were repeated 100 times to simulate the procedure of rating within the active sampling framework, with 50 standard trial numbers per iteration.

The DIBR Image dataset: To quantify the impacts of the Depth ImageBased Rendering (DIBR) algorithms on the perceived quality of freeviewpoint videos, Bosc et al. bosc2011towards have conducted a subjective studies using the ACR and the PC protocols. Three freeviewpoint contents were synthesized using seven different DIBR methods to obtain four different virtual videos corresponding to each reference, which ends out to 84 synthesized freeviewpoint videos. 43 observer participated in the subjective their study for both ACR and PC test.

The Kaist dataset: This dataset was released for studying the influence of visual discomfort, especially motion, on visual experience jung2013predicting; li2018exploring. It contains 36 of the video sequences labeled with both ACR scores and PC preferences. There are 4 motions types including the vertical planar motion, horizontal planar motion, indepth motion and the combinations of the three previous motions. During the ACR test, 17 observers were asked to rate the sequence with visual comfort scores (5point scale values). In the PC test, totally 180 pairs were collected with 40 naive observers using the same stimuli.

The IVC image dataset: It is one of the earliest and most famous ninassi2006pseudo image quality assessment. Unlike the other famous LIVE image quality assessment database sheikh2005live, it provides both the MOS and the standard deviation of the raw subjective scores, which makes the development of the variance recovery possible. Within the dataset, 10 original images were used, altogether 235 degraded images were obtained via 4 different distortion processes. The original IVC image dataset contain only linear quality scores. Therefore, we also considered the PC dataset summarized in xu2017hodgerank, which is composed of 43,266 paired comparisons using images from both the IVC and LIVE datasets. There was altogether 328 observers in the subjective test. Similarly, as there are no ground truth standard deviation of the raw subjective data from the LIVE dataset, we kept only the pairs from the IVC dataset.

The streaming video dataset: To evaluate how the proposed model could be used for mainstream streaming platform, we have collected 3 contents, i.e., the Hypothetical Reference Circuits (HRC), from one of the most popular streaming platforms, and the contents were proceed with 4 encoding resolutions (i.e., 4K, 1080P, 540P and 270P), 2 QP values (i.e., 22, 28), and 2 dynamic ranges setting (i.e. high dynamic range and standard dynamic range). Hence, Processed Video Sequences (PVS) were generated. We conducted the subjective tests utilizing both the ACR and PC protocol, where 25 participants were involved. In the PC test, the Adaptive Rectangular Design (ARD) li2013boosting was employed to select the comparison pairs for the subject actively, that means his or her playlist was generated based on all previous participants’ results. As there are 48 PVS per content, which leads to 48 pairs per reference. To align the scores cross contents, several cross content pairwise comparisons were also included in the test. In concrete words, only the lowest versus highest quality between the HRCs are compared, ending out 6 extract pairs. The viewing distance, environment, etc. were set up according to the ITU standards recommendation2004144. An LG OLED TV was used during the test.
Experimental results
Visualization of EIG
To have a better understanding of EIG, a meshgrid of EIG versus different and is plotted in Figure 2 (a). It could be observed that pairs have smaller and higher (i.e., higher uncertainty) are of higher information. This observation is aligned with the study summarized in silverstein1998quantifying.
Results on simulated data
The results of the simulation experiment are depicted in Figure 2 (b). The performance of the proposed models start to outperform the TM and BT models after the trial. The performance of the proposed framework saturate at around 0.97 in terms of SROCC after 15 trials while TM reaches the same performances after 40 trials and the maximum SROCC values of BT is only 0.90. These observations indicate that the proposed framework is of advantage and achieves higher performance with less budgets (i.e., trials). A better tradeoff between the discriminability (performance) and efficiency (budgets) could be achieved.
Agreement test
As emphasized earlier in the paper, the conversion from pair comparison preferences to quality rating/ranking scores is important. In order to compare the proposed conversion model with other commonly used models, the agreement test suggested in li2011study was conducted to evaluate the agreement between the converted data and the original ground truth. More specifically, the ground truth is given as input to the undertest pair comparison data conversion model to obtain the recovered rating scores. A matrix is then formed by comparing all possible pairs using the converted scores. For each element within the matrix, if the converted score of stimulus is larger than the one of then 1 is assigned to , otherwise 0 is assigned instead (i.e., it is a binary matrix without considering the diagonal elements). Before its comparison with the ground truth matrix that aggregates both the ACR and PC data, is normalized into the interval of and transferred to a binary matrix with a threshold 0.5 (i.e., if lager than 0.5 then set as 1, otherwise set as 0). With the transferred ground truth matrix , it is then compared elementwise to to calculate the proportion of elements that has the same values (i.e., the number of same elements divided by the number of total elements). This agreement proportion quantifies to which degree the recovered scores agree with the ground truth.
The agreement test results of the proposed conversions model (with Thurstone Case III), BT and TM models on the four realworld datasets are reported in Table 1. Overall, it is shown that the rating scores recovered by the proposed conversion model are the most consistent with the observers’ subjective perception on four realworld dataset.
Dataset / Model  TM  BT  Proposed 

Kaist  0.9583  0.9614  0.9629 
IVC  0.9584  0.9589  0.9602 
DIBR  0.9823  0.9829  0.9829 
Streaming  0.9839  0.9848  0.9883 
Results on realworld data
Figure 3 presents the results on the realworld datasets. In general, the maximum SROCC values of the proposed model on the four datasets are superior compared to both BT and TM models. Particularly, our framework starts to outpace the other models after around 10 trials on the Kaist dataset and around 5 trials on the IVC image dataset. Moreover, it outperforms the other models along with trials increase on both the DIBR and the streaming video dataset. It is demonstrated that the performance of the active sampling framework could be improved by recovering the variance of stimuli.
To further verify the impact of ACR initialization, we have also conducted experiments without using the ACR initialized PCM matrix. Results are shown in Figure 4. Here, only the results of the previous 15 standard trials (same as done in li2018hybrid) are shown to emphasize the difference of performances in earlier trials without ACR initialization. Compared to Figure 3, it is obvious that the starting performances of all the considered models on the four datasets are significantly worse without considering using the ACR data. For example, the starting SROCC values (i.e., trials) of the models in Figure 4 (a) are between , while the ones in Figure 3 (a) are around 0.908. It is demonstrated that significant amount of budget could be saved if ACR data is fully used for initialization.
Conclusion
In this study, we present a novel active sampling framework to reach a better tradeoff between discriminability and efficiency for subjective quality data collection. Within the framework, ACR data is fully exploited for initialization and combined with active sampled pairs comparisons so that budgets could be saved for distinguishing uncertain or similar pairs. In addition, by taking the variance of the stimuli into account, the underlying ground truth quality could be aggregated more accurately. Throughout experiments, the advantages and effectiveness of the proposed framework has been demonstrated.