Images are everywhere in our life. Unfortunately, they are often distorted by the processes of acquisition, transmission, storage, and external conditions like camera motion. Image Quality Assessment (IQA)  is a technique developed to automatically predict the perceptual quality of images. IQA estimates should be highly correlated with quality assessments made by a range of very many human evaluators (commonly referred to as the Mean Opinion Score (MOS) [27, 22]). IQA has been widely applied to problems where image quality is essential, like image restoration 
, image super-resolution
, and image retrieval.
IQA approaches are generally divided into three categories based on whether the undistorted image (called reference image) or information about it is available: full-reference IQA (FR-IQA), reduced-reference IQA (RR-IQA), and no-reference IQA (NR-IQA). Research has mostly focussed on the more realist scenario of NR-IQA where the image quality of an image without any reference image has to be estimated. In NR-IQA, many methods focus on a specific distortion [38, 7], which limits the applicability of these methods. Other methods consider a range of distortions [20, 23, 18, 19].
Convolutional Neural Networks (CNNs) are having an enormous impact on computer vision research and practice. Though they have been around for decades , it wasn’t until 2012, when Krizhevsky et al. 
achieved spectacular results with a CNN in the ImageNet competition, that they achieved wide attention and adoption in the broader computer vision community. The architectures of networks are getting deeper and deeper with respect to the original AlexNet, with ResNet being an example of very deep network architecture. The result of this trend is that state-of-the-art CNNs like AlexNet and ResNet have hundred of millions of parameters and require massive amounts of data to train from scratch (without overfitting).
The success of CNNs encouraged research exploring their potential application to the NR-IQA problem. This research resulted in significant improvements compared to previous hand-crafted approaches [17, 11, 12]. The main problems these papers had to address is the absence of large datasets for IQA . Especially as networks grow deeper and wider, the number of parameters increases dramatically. As a consequence, larger and larger annotated datasets are required for training. However, the annotation process for IQA image datasets requires multiple human annotations for every image, and thus the collection process is extremely labor-intensive and costly. As a results, most available IQA datasets are too small to be effective for training CNNs.
We propose an approach to address the absence of large datasets. The main idea (see Fig. 1) is that while human-annotated IQA data is difficult to obtain, it is easy to generate images that are ranked according to their image quality. That is, we can generate image sets in which, though we do not have an absolute quality measure for each generated image, for any pair of images we know which is of higher quality. We call this learning from rankings approach RankIQA, and with it we learn to rank image in terms of quality using Siamese Networks, and then we transfer knowledge learned from ranked images to a traditional CNN fine-tuned on IQA data in order to improve the accuracy of IQA. The idea to learn IQA features from distorted reference images was proposed by Zhang et al. in a patent . In this paper we go beyond this patent in that we provide a detailed description of our method and experimentally verify the usefulness of pre-training networks using ranked datasets.
As a second contribution we propose a method for efficient backpropagation in Siamese networks. The method forwards a batch of images through a single network and then backpropagates gradients derived from all pairs in the batch. In extensive experiments on established IQA datasets we show that learning from rankings significantly improves results, and that our efficient backpropagation algorithm allows to train these networks better and faster than other training protocols, like hard-negative mining. The supplementary material and project page are available at https://github.com/xialeiliu/RankIQA.
2 Related work
We briefly review the literature related to our approach. We focus on distortion-generic NR-IQA since it is more generally applicable than the other IQA research lines.
Traditional NR-IQA approaches.
Most traditional NR-IQA can be classified into Natural Scene Statistics (NSS) methods and learning-based methods. In NSS methods, the assumption is that images of different quality vary in the statistics of responses to specific filters. Wavelets, DCT  and Curvelets 
are commonly used to extract the features in different sub-bands. These feature distributions are parametrized, for example with the Generalized Gaussian Distribution. The aim of these methods is to estimate the distributional parameters, from which a quality assessment can be inferred. The authors of  propose to extract NSS features in the spatial domain to obtain significant speed-ups. In learning-based methods, local features are extracted and mapped to the MOS using, for example, Support Machine Regression or Neural Networks . The codebook method [40, 39]
combines different features instead of using local features directly. Datasets without MOS can be exploited to construct the codebook by means of unsupervised learning, which is particularly important due to of the small size of existing datasets. Saliency maps can be used to model human vision system and improve precision in these methods.
Deep learning for NR-IQA.
In recent years several works have used deep learning for NR-IQA[1, 11, 12]. One of the main drawbacks of deep networks is the need for large labeled datasets, which are currently not available for NR-IQA research. To address this problem Kang et al.  consider small patches rather than images, thereby greatly augmenting the number of training examples. The authors of [2, 12] follow the same pipeline. In  the authors design a multi-task CNN to learn the type of distortions and image quality simultaneously. Bianco at al.  propose to use a pre-trained network to mitigate the lack of training data. They extract features from a pre-trained model fine-tuned on an IQA dataset. These features are then used to train an SVR model to map features to IQA scores.
In our paper, we propose a radically different approach to address the lack of training data: we use a large number of automatically generated rankings of image quality to train a deep network. This allows us to train much deeper and wider networks than other methods in NR-IQA which train directly on absolute IQA data.
adapt the Stochastic Gradient Descent method to perform pairwise learning to rank. This has been successfully applied to large datasets. Combining ideas from ranking and CNNs, the Siamese network architecture achieves great success on the face verification problem, and in comparing image patches . The only other work which applies rankings in the context of NR-IQA is  in which they combine different hand-crafted features to represent image pairs from the IQA dataset.
Our approach is different in that primarily we are not aiming to learn rankings. Instead we use learning from rankings as a data augmentation technique: we use easily obtainable datasets of ranked images to train a large network, which is then fine-tuned for the task of NR-IQA.
Hard-negative mining for Siamese network training. It is well known that a naive approach to sampling pairs to training Siamese networks is suboptimal. To address this problem several approaches to hard-negative mining have been proposed. In , they propose a hard positive and hard-negative mining strategy to forward-propagate a set of pairs and sample the highest loss pairs with back-propagation. However, hard mining comes with a high computational cost (they report an increase of up to 80% of total computation cost). In  they propose semi-hard pair selection, arguing that selecting hardest pairs can lead to bad local minima. The batch size used is around 1800 examples, which again leads to a considerable increase in computational cost. In  the authors take a batch of pairs as input and choose the four hardest negative samples within the mini-batch. To solve for a bad local optimum, 
optimize a smooth upper bound loss function to take advantage of all possible pairs in the mini-batch.
In contrast with these works, we propose a method for efficient Siamese backpropagation which does not depend on hard-negative selection. Instead, it considers all possible pairs in the mini-batch. This has the advantage that the main computational bottleneck in training deep networks, namely the forward-propagation of images through the network, is optimally exploited.
3 Learning from rankings for NR-IQA
In this section we describe our approach to exploiting synthetically generated rankings for NR-IQA. We first lay out a general framework for our approach, then describe how we use a Siamese network architecture to learn from rankings. Finally, in section 3.3 we show how backpropagation for training Siamese networks from ranked samples can be made significantly more efficient.
3.1 Overview of our approach
The lack of large IQA datasets motivates us to propose a new strategy to take advantage of large, unlabelled databases from which we can generate images ranked by image quality. Our approach is based on the observation that, given a set of arbitrary reference images, it is very easy to apply image distortions to generate a ranking image dataset. As an example, given a reference image we can apply various levels of Gaussian blur. The set of images which is thus generated can be easily ranked because we do know that adding Gaussian blur (or any other distortion) always deteriorates the quality score. Note that in such set of ranked images we do not have any absolute IQA scores for any images – but we do know for any pair of images which is of higher quality.
After learning on these ranked images, we can use fine-tuning on small image quality datasets in order to address the IQA problem. The difference between our approach and the straightforward, classical approach  is shown in Fig. 1. The standard approach trains a shallow network directly on the IQA dataset to estimate IQA score from images. Due to the limited data only few layers can be used, which limits accuracy. Since we have access to much larger datasets with ranked images, we can now train deeper and wider networks to learn a distance embedding. Next we follow this by fine-tuning for domain adaptation to the absolute IQA problem. The overall pipeline of our approach is:
Synthesize ranked images. Using an arbitrary set of images, we synthetically generate deformations of these images over a range of distortion intensities. The absolute distortion amount for each image is not used in subsequent steps, but within each deformation type we know, for any pair of images, which is of higher quality. See section 4.1 for a description of the datasets used for generating ranked images and the distortions applied.
Train Siamese network for ranking. Using the set of ranked images, we train a Siamese network described in the next section using the efficient Siamese backpropagation technique proposed in section 3.3. The result is a Siamese network that ranks images by image quality.
Fine-tune on IQA data. Finally, we extract a single branch of the Siamese network (we are interested at this point in the representation learned in the network, and not in the ranking itself), and fine-tune it on available IQA data. This effectively calibrates the network to output IQA measurements.
3.2 Siamese networks for ranking
Here we introduce the Siamese network  to learn from image rankings, which is a network with two identical network branches and a loss module. The two branches share weights during training. Pairs of images and labels are the input of the network, yielding two outputs which are passed to the loss module. The gradients of the loss function with respect to all model parameters are computed by backpropagation and updated with the stochastic gradient method.
Specifically, given an image as the input of the network, the output feature representation of , denoted by , is obtained by capturing the activation in the last layer. Here are the network parameters, and we will use to denote the ground truth value for the image which for image quality assessment is its quality score. Consequently, in our Siamese networks the output of the final layer is always a single scalar which we want to be indicative of the image quality. Since our aim is to rank the images, we apply the pairwise ranking hinge loss:
where is the margin. Here we assume without loss of generality that the rank of is higher than . The gradient of the loss in Eq. 1 is given by:
In other words, when the outcome of the network is in accordance with the ranking, the gradient is zero. When the outcome of the network is not in accordance we decrease the gradient of the higher and add the gradient of the lower score. Given this gradient of with respect to model parameters , we can train the Siamese network using Stochastic Gradient Descent (SGD).
3.3 Efficient Siamese backpropagation
One drawback of Siamese networks is the redundant computation. Consider all possible image pairs constructed from three images. In a standard implementation all three images are passed twice through the network, because they each appear in two pairs. Since both branches of the Siamese network are identical, we are essentially doing twice the work necessary since any image need only be passed once through the network. It is exactly this idea that we exploit to render backpropagation more efficient. In fact, nothing prevents us from considering all possible pairs in the mini-batch, without hardly any additional computation. We add a new layer to the network that generates all possible pairs in a mini-batch at the end of the network right before computing the loss. This eliminates the problem of pair selection and boosts efficiency.
To approximate the speed-up of efficient Siamese backpropagation consider the following. If we have one reference image distorted by levels of distortions in our training set, then for a traditional implementation of the Siamese network we would have to pass a total of images through the network – which is twice the number of pairs you can generate with images. Instead we propose to pass all images only a single time and consider all possible pairs only in the loss computation layer. This reduces computation to just passes through the network. Therefore, the speed-up is equal to: . In the best scenario , where is equal to the number of images in the mini-batch, and hence the speed-up of this method would be in the order of the mini-batch size. Due to the high correlation among the set of all pairs in a mini-batch, we expect the final speedup in convergence to be lower.
To simplify notation in the following, we let , where is the output of a single branch of the Siamese network on input . Now, for one pair of inputs the loss is:
where is a label indicating the relationship between image and (for example, for ranking it indicates whether is of higher rank than ), and are all model parameters in the Siamese network. We omit the dependency in for simplicity. The gradient of this loss function with respect to the model parameter is:
This gradient of above is a sum since the model parameters are shared between both branches of the Siamese network and and are computed using exactly the same parameters.
Considering all pairs in a mini-batch, the loss is:
The gradient of the mini-batch loss with respect to parameter can then be written as:
We can now express the gradient of the loss function of the mini-batch in matrix form as:
is the vector of all ones of length. For a standard single-branch network, we would average the gradients for all batch samples to obtain the gradient of the mini-batch. This is equivalent to setting
to the identity matrix in Eq.7 above. For Siamese networks where we consider all pairs in the mini-batch we obtain Eq. 6 by setting to:
and where (-1) indicates that (), and that or that they cannot be compared as is the case with images corrupted with different distortions.
The above case considered a single distortion. Suppose instead we have types of distortions in the training set. We can then compute the gradient of the loss using a block diagonal matrix as:
where refers to the network output of the image with the distortion, , and where is the number of images with distortion in the mini-batch. In the definition of above, the are the gradient coefficients as in Eq. 10.
3.4 Fine-tuning for NR-IQA
After training a Siamese network to rank distorted images, we then extract a single branch from the network for fine-tuning. Given images in mini-batch with human IQA measurements, we denote the ground truth quality score of the -th image as , and the predicted score from the network is , as above. We fine-tune the network using squared Euclidean distance as the loss function in place of the ranking loss used for the Siamese network:
4 Experimental results
In this section we report on a number of experiments designed to evaluate the performance of our approach with respect to baselines and the state-of-the-art in IQA.
We use two types of datasets in our experiments: generic, non-IQA datasets for generating ranked images to train the Siamese network, and IQA datasets for fine-tuning and evaluation.
IQA datasets. We perform experiments on two standard IQA benchmark datasets. The LIVE  consists of 808 images generated from 29 original images by distorting them with five types of distortion: Gaussian blur (GB), Gaussian noise (GN), JPEG compression (JPEG), JPEG2000 compression (JP2K) and fast fading (FF). The ground-truth Mean Opinion Score for each image is in the range [0, 100] and is estimated using annotations by 161 human annotators.The TID2013  dataset consists of 25 reference images with 3000 distorted images from 24 different distortion types at 5 degradation levels. Mean Opinion Scores are in the range [0, 9]. Distortion types include a range of noise, compression, and transmission artifacts. See the original publication for the list of specific distortion types.
Datasets for generating ranked pairs. To test on the LIVE database, we generate four types of distortions which are widely used and common : GB, GN, JPEG, and JP2K. To test on TID2013, we generate 17 out of a total of 24 distortions (apart from #3, #4,#12, #13, #20, #21, #24). For the distortions which we could not generate, we apply fine-tuning from the network trained from the other distortions. This was found to yield satisfactory results. We use two datasets for generating ranked image pairs.
The Waterloo dataset consists of 4,744 high quality natural images carefully chosen from the Internet. Additionally, we use the validation set of the Places2  dataset of 356 scene categories. There are 100 images per category in the validation set, for a total 36500 images. After distortion, we have many more distorted images for learning an image quality ranking embedding. The aim of using this dataset is to demonstrate that high-quality ranking embeddings can be learned using datasets not specifically designed for the IQA problem.
4.2 Experimental protocols
We investigate a number of network architectures and use standard IQA metrics to evaluate performance.
Network architectures. We evaluate three typical network architectures varying from shallow to deep. We refer to them as: Shallow, AlexNet , and VGG-16 . The shallow network has four convolutional layers and one fully connected layer. For AlexNet and VGG-16 we only change the number of outputs since our objective is to assign one score for each distorted image.
Strategy for training and testing.
We randomly sample sub-images from the original high resolution images. We do this instead of scaling to avoid introducing distortions caused by interpolation or filtering. The size of sampled images is determined by each network. However, the large size of the input images is important since input sub-images should be at least 1/3 of the original images in order to capture context information. This is a serious limitation of the patch sampling approach that samples very smallpatches from the original images. In our experiments, we sample and
pixel images, depending on the network. We use the Caffe framework and train using mini-batch Stochastic Gradient Descent (SGD) with an initial learning rate of 1e-4 for efficient Siamese network training and 1e-6 for fine-tuning. Training rates are decreased by a factor of 0.1 every 10K iterations for a total of 50K iterations. For both training phases we use
weight decay (weight 5e-4). During training we sample a single subimage from each training image per epoch.
When testing, we randomly sample 30 sub-images from the original images as suggested in . The average of the outputs of the sub-regions is the final score for each image.
Two evaluation metrics are traditionally used to evaluate the performance of IQA algorithms: the Linear Correlation Coefficient (LCC) and the Spearman Rank Order Correlation Coefficient (SROCC). LCC is a measure of the linear correlation between the ground truth and the predicted quality scores. Givendistorted images, the ground truth of -th image is denoted by , and the predicted score from the network is . The LCC is computed as:
where and are the means of the ground truth and predicted quality scores, respectively.
Given distorted images, the SROCC is computed as:
where is the rank of the ground-truth IQA score in the ground-truth scores, and is the rank of in the output scores for all images. The SROCC measures the monotonic relationship between ground-truth and estimated IQA.
4.3 Learning NR-IQA from rankings
We performed a number of experiments to evaluate the ability of Siamese networks to learn to capture image distortions from a large dataset of image quality rankings. In addition, we measure the impact of the efficient Siamese backpropagation approach described in section 3.3.
Siamese networks and IQA discrimination. To demonstrate the ability of our ranking networks to discriminate image quality, we trained our Siamese network on the Places2 validation set (without applying fine-tuning on IQA data) corrupted with five levels of a single distortion. We then used that network to predict image quality for synthetically-distorted images from the Waterloo dataset corrupted using the same five levels of the same distortion. The network outputs are plotted as histograms in Fig. 2 for the JPEG distortion111Graphs for the other distortions are in the supplementary material.. In the plot, we divide the observations according to the true distortion level (indicated by the color of the histogram). The model discriminates different levels of distortions on Waterloo, even though the acquisition process and the scenes of the two datasets are totally different.
Efficient Siamese backpropagation. The objective of this experiment is to evaluate the efficiency of our Siamese backpropagation method. We compare our method to both standard random pair sampling, and a hard-negative mining method similar to .222We experimented with several hard-negative mining methods and found this to work best. For standard random pair sampling we randomly choose 36 pairs for each mini-batch from the training sets. For the hard negative mining strategy we start from 36 pairs in a mini-batch, and gradually increase the number of hard pairs every 5000 iterations. For our method we pass 72 images in each mini-batch. With these settings the computational costs of all three methods is equal, since at each iteration 72 images are passed through the network. We use AlexNet for this experiment. The comparison of convergence rates on JPEG333Results for the other distortions are in the supplementary material. is shown in Fig. 3. The efficient Siamese backpropagation not only converges much faster, but also converges to a considerably lower loss.
Network performance analysis. Here we evaluate whether we can learn a useful image representation from large image ranking datasets. We randomly split on the original, high-quality images before distortion from the LIVE dataset into 80% training and 20% testing samples and compute the average LCC and SROCC scores on the testing set after training to convergence. This process is repeated ten times and the results are averaged. In Table 1 we compare results for three different networks: Shallow, AlexNet and VGG-16. We obtain the best results with the VGG-16 network, which is also the deepest network. This indicates learning from ranking makes it possible to train very deep networks efficiently without overfitting. These results are obtained by training from scratch, however we found that initializing the weights with a network pre-trained on ImageNet further improved the results. In the remainder of the experiments we thus use the VGG-16 network initialized with a pre-trained weights to train the ranking network in the following experiments.
Baseline performance analysis. In this experiment, we evaluate the effectiveness of using rankings to estimate image quality. We compare tree methods: fine-tuning the VGG-16 network initialized from ImageNet to obtain the mapping from images to their predicted scores (called Baseline), our method to train VGG-16 (initialized from ImageNet) on ranking database using all ranking dataset we generate (called RankIQA), and finally our RankIQA approach fine-tuned on the TID2013 database after training using ranked pairs of images (called RankIQA+FT).
We follow the experimental protocol used in HOSA . The entire TID2013 database including all types of distortions is divided into 80% training images and 20% testing images according to the reference images. Thus, the same image can never appear in both training and test sets. The results are shown in Table 2, where ALL means testing all distortions together. All the experiments are performed 10 times and the average SROCC is reported444LCC results are provided in supplementary material.. From Table 2, we can draw several conclusions. First, it is hard to obtain good results by training a deep network directly on IQA data. This is seen in the Baseline results and is due to the scarcity of training data. Second, our RankIQA method achieves superior results on almost all individual distortions even without ever using the TID2013 dataset – which strongly demonstrates the effectiveness of training on ranking data. Slightly better results are obtained on ALL without comparing among different distortions during training the ranking network. The RankIQA-trained network alone does not provide accurate IQA scores (since it has never seen any) but does provide high correlation with the IQA scores as measured by SROCC. After fine-tuning on the TID2013 database (RankIQA+FT), we considerably improve the ALL score, and improve the baseline by 16%. However, in the fine-tuning process to optimize the ALL score the network balances the various distortions, and results decrease for several distortions.
4.4 Comparison with the state-of-the-art
We compare the performance of our method using the VGG-16 network with state-of-the-art methods. We perform experiments on the TID2013 and LIVE dataset.555Results on CSIQ  and MLIVE  are in supplementary material.
Evaluation on TID2013. Table 2 also includes results of state-of-the-art methods. We see that for several very challenging distortions (14 to 18), where all other methods fail, we obtain satisfactory results. For individual distortions, there is a huge gap between our RankIQA method and other IQA methods on most distortions. The state-of-the-art method HOSA performs slightly better than our methods on 6 out of 24 distortions. For all distortions, our method RankIQA+FT achieves about 5% higher than HOSA. Our methods perform well on distortions which are not included when training the ranking network, which indicates that different distortions share some common representation and training the network jointly on all distortions.
Evaluation on LIVE. As done in [11, 43], we randomly split the reference images on LIVE dataset into 80% training samples and 20% testing, and compute the average LCC and SROCC scores on the testing set after training to convergence. This process is repeated ten times and the results are averaged. These results are shown in Table 3. The best method for each dataset is indicated in bold. The column indicated with ALL means we combine all five distortions together on LIVE dataset to train and test the model. For fair comparison with the state-of-the-art, we train our ranking model on four distortions except FF, but we fine-tune our model on all five distortions in the LIVE dataset to compute ALL. Our approach achieves about 1% better than the best results reported on ALL distortions for LCC. Similar conclusions are obtained for SROCC. This indicates that our method outperforms existing work including the current state-of-the-art NR-IQA method SOM  and DNN , and also state-of-the-art FR-IQA method DCNN . To the best of our knowledge this is the first time that an NR-IQA method surpasses the performance of FR-IQA methods (which have access to the undistorted reference image) on all LIVE distortions using the LCC and SROCC evaluation method.
4.5 Independence from IQA training data
This final experiment is to demonstrate that our framework can be also trained on non-IQA datasets. In the previous experiment the network is trained from high-quality images of the Waterloo dataset. Instead here we use the validation set of the Places2 dataset to generate ranked images in place of the Waterloo dataset. The Places2 dataset is of lower quality than Waterloo and is not designed for IQA research. As in the previous experiment, the final image quality scores are predicted by fine-tuning on the LIVE dataset. The performance of this model is compared with the results trained on Waterloo in Table 4. The SROCC and LCC values are very similar, demonstrating that our approach can be learnt from arbitrary, non-IQA data.
To address the scarcity of IQA data we have proposed a method which learns from ranked image datasets. Since this data can be generated in abundance we can train deeper and wider networks than previous work. In addition, we have proposed a method for efficient backpropagation in Siamese networks which circumvents the need for hard-negative mining. Comparison with standard pair sampling and hard-negative sampling shows that our method converges faster and to a lower loss. Results on LIVE and TID2013 datasets show that our NR-IQA approach obtains superior results compared to existing NR-IQA techniques and even FR-IQA methods.
Acknowledgements We acknowledge the Spanish project TIN2016-79717-R, the CHISTERA project M2CR (PCIN-2015-251) and the CERCA Programme / Generalitat de Catalunya. Xialei Liu acknowledges the Chinese Scholarship Council (CSC) grant No.201506290018. We also acknowledge the generous GPU donation from NVIDIA.
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