Low-Resolution Object Recognition with Cross-Resolution Relational Contrastive Distillation
Kangkai Zhang Shiming Ge Ruixin Shi Dan Zeng







IEEE Transactions on Circuits and Systems for Video Technology
Shell et al.: A Sample Article Using IEEEtran.cls for IEEE Journals









Low-Resolution Object Recognition with Cross-Resolution Relational Contrastive Distillation
    Kangkai Zhang,
        Shiming Ge, Senior Member, IEEE,
        Ruixin Shi,
        and Dan Zeng, Senior Member, IEEE
Kangkai Zhang is with the Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100084, China, and with Baidu Inc., Beijing 100080, China. Email: zhangkangkai99@gmail.com.
Shiming Ge and Ruixin Shi are with the Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100084, China, and with School of Cyber Security at University of Chinese Academy of Sciences, Beijing 100049, China. Email: {geshiming, shiruixin}@iie.ac.cn.
Dan Zeng is with the Department of Communication Engineering, Shanghai
University, Shanghai 200040, China. E-mail: dzeng@shu.edu.cn.
Shiming Ge is the responding author. Email: geshiming@iie.ac.cn.
    
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§ ABSTRACT 
Recognizing objects in low-resolution images is a challenging task due to the lack of informative details. Recent studies have shown that knowledge distillation approaches can effectively transfer knowledge from a high-resolution teacher model to a low-resolution student model by aligning cross-resolution representations. However, these approaches still face limitations in adapting to the situation where the recognized objects exhibit significant representation discrepancies between training and testing images. In this study, we propose a cross-resolution relational contrastive distillation approach to facilitate low-resolution object recognition. Our approach enables the student model to mimic the behavior of a well-trained teacher model which delivers high accuracy in identifying high-resolution objects. To extract sufficient knowledge, the student learning is supervised with contrastive relational distillation loss, which preserves the similarities in various relational structures in contrastive representation space. In this manner, the capability of recovering missing details of familiar low-resolution objects can be effectively enhanced, leading to a better knowledge transfer. Extensive experiments on low-resolution object classification and low-resolution face recognition clearly demonstrate the effectiveness and adaptability of our approach.



Low-resolution face recognition, low-resolution object classification, knowledge distillation, domain adaptation.




§ INTRODUCTION

With the rapid development of deep learning, deep models have demonstrated remarkable success in various visual recognition applications <cit.>. For example, EfficientNet <cit.> delivers a top-1 classification accuracy of 88.61% on ImageNet <cit.> in large-scale visual recognition, Groupface <cit.> gives an extreme high accuracy of 99.85% on LFW <cit.> in face verification, cross-domain methods deliver impressive performance in gait recognition  <cit.> and micro-expression recognition <cit.>. These achievements can be attributed to the ability of deep models with massive parameters to extract rich knowledge from extensive high-quality datasets. However, it may suffer from a sharp drop in accuracy when directly applying these models in practical scenarios due to domain distribution difference, i.e., the identified objects lack informative details due to occlusion <cit.> or low resolution <cit.>. Meanwhile, it is difficult to correct sufficient low-resolution training data in practical scenarios. Thus, it is necessary to explore a feasible solution that can address a key challenge in low-resolution object recognition: How to effectively transfer knowledge from high-resolution source domain to low-resolution target domain with minimal accuracy loss?



As shown in Fig. <ref>, in spite of the missing of many informative details, low-resolution objects still can be well recognized by subjects when they are familiar with the corresponding high-resolution objects. Recent works <cit.> have shown that it is feasible to improve the recognition capacity of a model by knowledge transfer from high-resolution domain to low-resolution one. According to the level of this cross-resolution knowledge transfer, current approaches can be mainly grouped into sample-level or relation-level approaches.
For sample-level knowledge transfer, Wang  <cit.> first proposed to use the corresponding high-resolution images to facilitate the model to extract features from low-resolution images. Subsequently, by learning low-resolution face representations and mimicking the adapted high-resolution knowledge, a light-weight student model can be constructed with high efficiency and promising accuracy in recognizi ng low-resolution faces <cit.>. However, sample-level knowledge is limited and insufficient to help the model extract sufficiently discriminative features, especially for cross-resolution knowledge transfer. Therefore, the researchers explored the relation-level knowledge transfer. Some recent works have shown that transferring the structural similarity instead of representation is beneficial to student learning <cit.>. Ge  <cit.> proposed a hybrid order relational distillation to distill richer knowledge from pretrained high-resolution models to facilitate low-resolution object recognition. In general, these approaches have achieved impressive performance. However, they all use low-order relation knowledge to model the mutual information, which may ignore complex high-order inter-sample interdependencies, , contrastive relation, and lead to insufficient knowledge transfer for object recognition.

Recently, contrastive learning approaches <cit.> have been widely used to learn feature representations from data samples by comparing the data with the positive and negative samples in the feature space. These approaches only need to learn discrimination in the feature space. Thus, they will not pay too much attention to pixel details, but can focus on more abstract semantic information, leading to simpler processing than pixel-level reconstruction <cit.>. Recent contrastive learning is combined with knowledge distillation, and these contrastive-based distillation approaches <cit.> aim to capture the correlations and higher-order output dependencies for each sample. Typically, contrastive-based distillation approaches can facilitate cross-resolution knowledge transfer, since they essentially preserve the inter-sample relations which usually are more valuable than the sample representations themselves, especially in visual recognition tasks. The key is the relation modeling for effective knowledge transfer. 

To transfer high-order dependency within the representation in both relation estimation and knowledge distillation, we propose a teacher-student learning approach for low-resolution object recognition via cross-resolution relational contrastive knowledge distillation with two streams, as shown in Fig. <ref>. The teacher stream is initialized with a complex pretrained model for high-resolution recognition and the student stream trains a compact model with the help of structural relational knowledge between different resolution samples. By making the high-order relation between low-resolution samples and other high-resolution samples mimic the high-order relation between corresponding high-resolution sample and other high-resolution samples, the student can pay more attention on semantic information instead of pixel details, and then learn the distinction between low-resolution images in the feature space to improve low-resolution object recognition.

Our main contributions are three folds: 1) we propose a cross-resolution relational contrastive distillation approach that is able to distill richer structural knowledge from pretrained high-resolution models to facilitate low-resolution object recognition, 2) we propose a relational contrastive module to extract relational knowledge in contrastive representation space, and 3) we conduct extensive experiments to show the state-of-the-art performance and good adaptability of our approach in low-resolution object recognition.



§ RELATED WORKS



 §.§ Low-Resolution Object Recognition

The recognition of low-resolution visual objects is attracting increasing interest due to its widespread applications in long distance surveillance scenarios <cit.>, blurry image analysis <cit.>. Its major challenge is that the informative identity details of the identified objects are seriously missing. In particular, low-resolution objects have less high variance information and the textures can be visually indistinguishable. Recently, an effective way to address this problem is to utilize high-resolution object information for learning improved recognition models. Existing approaches can be categorized into reconstruction-based and prediction-based category. Reconstruction-based approaches employ super-resolution methods to the low-resolution objects before recognition. Grm  <cit.> proposed a cascaded super-resolution network, along with an ensemble of face recognition models as identity priors. Chan  <cit.> obtained the effective super-resolution by using the rich and diverse prior knowledge in the pretrained GAN. Kong  <cit.> proposed resolution invariant model (RIM) to  recognize low-resolution faces from CCTV cameras at different resolutions. RIM uses a tri-path GAN to jointly learn face hallucination sub-net and heterogeneous recognition sub-net. Unfortunately, such approaches require additional computation and the recovered details may be not always beneficial to recognition.

By contrast, prediction-based approaches directly recognize low-resolution objects by knowledge transfer and it is essential to sufficiently represent the domain knowledge and transfer them effectively. On the one hand, a direct approach is transferring the knowledge from high-resolution objects, in which the feature vector distance matters. Soma  <cit.> proposed to map the low-resolution images to Euclidean space, and then approximate the corresponding high-resolution ones through the distance dimension. Zangeneh  <cit.> proposed a new coupled mapping method consisting of two DCNN branches for mapping high and low-resolution face images to non-linear transformed public space. Zha <cit.> proposed an end-to-end transferable coupling network in high-resolution and low-resolution domains respectively, and introduced a transferable triple loss to narrow cross-resolution positive pairs and separate negative pairs, which improves the recognition performance for low-resolution objects. 

It has been proved feasible using teacher-student learning to transfer knowledge for facilitating visual applications <cit.>. Such knowledge distillation approaches are mainly based on response, feature and relation. Response-based distillation approaches <cit.> aim to directly imitate the neural response of the last output layer of the teacher model. While feature-based distillation approaches <cit.> mimic the intermediate representations of teacher model to improve the learning of student model by matching original or transformed features. Huang  <cit.> proposed to transfer rich privilege information from a wide and complicated teacher network to a thin and simplified student one. Unlike the above two types of approaches using sample-level outputs of specific layers, relation-level approaches <cit.> further explore the relation between data samples, and have shown that transfer structural similarity between instances rather than individual instance representations is beneficial for student learning. Since semantically similar inputs produce similar activations, Tung  <cit.> used pairwise activation similarities in each input mini-batch to supervise the student learning, and Park  <cit.> proposed to transfer explicit sample relations from pretrained teacher. In general, these approaches base on response or low-order relations between samples are often insufficient for cross-resolution knowledge transfer. To address that, we propose a teacher-student learning approach to facilitate low-resolution object recognition via cross-resolution relational contrastive distillation.



 §.§ Contrastive Learning

Contrastive learning is regarded as a very important part of self-supervised learning, which builds representations by learning to encode what makes two things similar or different. Recent works <cit.> have been widely used to learn the feature representations of samples by comparing the data with positive and negative samples in the feature space. Contrastive losses such as NCE <cit.> and infoNCE <cit.> measure the similarities of data samples in a deep representation space, which learn representations by contrasting positive and negative representation pairs. One of the major difficulties in contrastive learning is how to construct the positive and negative samples. Deep InfoMAX <cit.> takes local features of training images and different images as positive and negative samples respectively. Instance Discrimination <cit.> learns to contrast the current embedding with previous embeddings from an online memory bank. The MOCO<cit.> and SimCLR <cit.> apply augmentation to train samples and requires the network to match original image and transformed images through contrastive loss. These methods only need to learn in the feature space, thus avoiding focus too much on pixel details but paying more abstract semantic information instead.

For knowledge distillation, Tian  <cit.> proposed to combine contrastive learning with knowledge distillation, and Xu  <cit.> represented contrastive task as a self-supervised pretext task to facilitate the extraction of richer knowledge from the teacher to the student. They show that incorporating contrastive learning loss into knowledge distillation can help student learn higher-order structural knowledge which can promote cross domain knowledge transfer. They are based on samples and the mutual relations are still insufficient. Thus, it is necessary to explore more effective forms to model the mutual relations of deep representations instead of the representations themselves. Zheng  <cit.> proposed relation knowledge distillation by linking cluster-based and contrastive-based self-supervised learning. However, such methods often suffer from poor generalization. To address that, we take into account higher-order relational information between the samples across different image resolutions.






§ THE APPROACH

The objective of our cross-resolution relational contrastive distillation (CRRCD) is sufficiently distilling high-order relational knowledge from a pretrained teacher for high-resolution recognition and effectively transferring it to learn a compact student for low-resolution recognition. Toward this end, we build the training instances by taking massive pairs of high-resolution images and corresponding low-resolution images in a self-supervised manner, and utilize vectors to define the representation relations. A feature relation module is utilized to estimate the teacher relation vector in teacher space and the student relation vector in cross-resolution space, respectively. The module is a simple learnable network that consists of two linear layers and a nonlinear activation layer. It is employed to estimate the relation vector between sample representations. Additionally, the cross-resolution relation vector is supervised by its corresponding vector in teacher space. In this manner, relation estimation and representation learning is performed in a unified way. In general, the student is trained on the images from source domain but deployed in target domain, and these two domains often exist large representation discrepancy. Therefore, our relation modeling manner needs to address cross-resolution knowledge transfer with good adaptability.



 §.§ Problem Formulation

We denote the training set as D={(x^h_i, x^l_i, y_i)}_i=1^|D|, where x^h_i represents the ith high-resolution sample with class label y_i∈{1,2,...,c} and x^l_i corresponds to the corresponding low-resolution sample. Here c is the number of classes. Given a teacher network ϕ^t with parameters 𝒲^t and a student network ϕ^s with parameters 𝒲^s, we denote the representation of a sample pair (x^h, x^l) produced by the two networks as e^t=ϕ^t(𝒲^t;x^h) and e^s=ϕ^s(𝒲^s;x^l), respectively. Let (x^h_i,x^l_i) and (x^h_j,x^l_j) be two sample pairs randomly chosen from the training set. The relation between x^h_i and x^h_j in teacher space can be modeled as v^t_i,j, where v^t_i is a relation vector produced by the feature relation module 𝔽 that takes e^t_i and e^t_j as inputs. Similarly, we denote v^t,s_i,j as the relation vector across the teacher and student space, the inputs of feature relation module are e^t_i and e^s_j, respectively. The specific form is v^t,s = φ(σ(φ_iϕ^t(x_i)-φ_jϕ^s(x_j))), where φ and τ denote the linear transformation and the ReLU function, respectively. We hope that the cross-space relation v^t,s_i,j can be consistent with v^t_i,j with the help of relational contrastive distillation loss. 



 §.§ Cross-Resolution Relational Contrastive Distillation

Let x represent the input, we denote its empirical data distribution as p(x). For the conditional marginal distributions p(v^t|x), p(v^t,s|x), the sampling procedure is described as:

    x_i^h, x_j^h, x_i^l, x_j^l∼ p(x) 
    v_i, j^t=F^t(ϕ^t(𝒲^t;x_i^h), ϕ^t(𝒲^t;x_j^h)) 
    v_i, j^t, s=F^t, s(ϕ^t(𝒲^t;x_i^h), ϕ^s(𝒲^s;x_j^l)),

where F^t and F^t,s are two learnable networks for computing the relation vectors. v_i, j^t and v_i, j^t, s represent the relationship between the i-th and j-th samples in teacher space and cross-resolution space, respectively. Intuitively, by maximizing Kullback-Leibler (KL) divergence between the joint distribution p(v^t,v^t,s|x) and the product of marginal distributions p(v^t|x)p(v^t,s|x), we can maximize the mutual information (MI) 𝕀 between student and teacher representations <cit.>:

    𝕀(v^t,v^t,s)=𝔼_p(v^t,v^t,s|x)logp(v^t,v^t,s|x)/p(v^t|x) p(v^t,s|x).


MI lower bound. To setup an appropriate loss to maximize the mutual information, we define a distribution q with latent variable b which indicates whether the relation tuple (v_i,j^t, v_i,j^t,s) is drawn from the joint distribution (b=1) or the product of marginal distributions (b=0):


    q(v^t,v^t,s| b=1)=p(v^t,v^t,s) 
       q(v^t,v^t,s| b=0)=p(v^t) p(v^t,s).

Here, b=1 means v_i,j^t and v_i,j^t,s are computed based on the same input pair, and b=0 means v_i,j^t and v_i,j^t,s are independently selected. Now, suppose in our data, we give 1 relevant relation pair (b=1) with n irrelevant relation pairs (b=0). Then the priors on the latent b are q(b=1)=1/(n+1) and q(b=0)=n/(n+1). By combining the priors with the Bayes’ rule, the posterior for b=1 is given by:

    q(b=1 |v^t,v^t,s)=p(v^t,v^t,s)/p(v^t,v^t,s)+n p(v^t) p(v^t,s).

Then the mutual information is defined as: 

    log q(b=1 |v^t,v^t,s) ≤-logn+logp(v^t,v^t,s)/p(v^t) p(v^t,s).

Taking the expectation on both sides, Eq. (<ref>) is rewritten as:

    𝕀(v^t,v^t,s)    ≥logn+
       𝔼_q(v^t,v^t,s| b=1)log q(b=1 |v^t,v^t,s),

where 𝕀(v^t,v^t,s) is the mutual information between the relation distributions of the teacher and student embedding. Thus maximizing 𝔼_q(v^t,v^t,s| b=1)log q(b=1 |v^t,v^t,s) the parameters of the student network will increase a lower bound on mutual information.

Relation contrastive loss. Actually, we maximize the log likelihood of the data under the model to estimate true distribution, which is defined as:


    ℒ_critic(h)    =𝔼_q(v^t,v^t,s| b=1)[log h(v^t,v^t,s)] 
        +n 𝔼_q(v^t,v^t,s| b=0)[log (1-h(v^t,v^t,s))].



    h^*=hmaxℒ_critic (h)   ◃ optimal critic .

We term h the critic since the representations are learned to optimize the critic’s score.
Considering that the bound in Eq. (<ref>) and the 𝔼_q(v^t,v^t,s| b=1)[log h(v^t,v^t,s)] is non-positive, we weaken the bound in Eq. (<ref>),

    𝕀(v^t, v^t,s) ≥logn+ℒ_critic(h).

We may choose to represent h with any family of functions that satisfy h:{v^t,v^t,s}→[0,1]. In practice, 


    h(v^t, v^t, s)=e^h_1(v^t) h_2(v^t, s) / τ/e^h_1(v^t) h_2(v^t, s) / τ + n/m,

where n is the number of negatives, m is the dataset cardinality and τ is a temperature for adjusting concentration level. h_1 and h_2 first perform the linear transformation on relations, then normalize the transformed relations with l_2 norm.

In our approach, the inputs for the function h are teacher-space relation v^t and cross-space relations v^t,s. We aim to maximize the mutual information, which is equivalent to minimizing the relation contrastive loss ℒ_rcd:


    ℒ_rcd   =-∑_q(b=1)log h(v^t, v^t, s) 
       -n∑_q(b=0)log[1-h(v^t, v^t, s)],

where {(v^t, v^t, s) | b=1} acts as positive pairs while {(v^t, v^t, s) | b=0} acts as negative pairs.

To achieve superior performance and conduct fair comparisons, we also incorporate the naive knowledge distillation loss ℒ_kd along with our relation contrastive loss. Given the presoftmax logits z^t for teacher and z^s for student, the naive knowledge distillation loss can be expressed as


    ℒ_k d=ρ^2ℋ(σ(z^t / ρ), σ(z^s / ρ)),

where ρ is the temperature, ℋ refers to the cross-entropy
and σ is softmax function. The complete objective is:

    ℒ=ℒ_c l s+αℒ_kd+βℒ_rcd,

where ℒ_cls represents the arcface loss for face recognition, or cross-entropy loss for object classification. We experimentally determine a best combination of the three loss terms, and set α=0.5 and β=2 in our approach.

Relationships to similar distillation approaches. Like CRD <cit.> and CRCD <cit.>, our CRRCD is also based on contrastive learning and has a certain similarity in analysis such as a lower bound on the mutual information. Different from them, our approach is designed for cross-quality knowledge transfer in low-resolution recognition task, and the modeling granularity of relational knowledge between samples is finer and the order is higher. Specifically, compared with CRD, CRRCD takes into account higher-order information between samples in different resolution data and requires less negative samples for training. The main differences from CRCD include: 1) CRRCD focuses on the relation between sample representations, while CRCD calculates the relation between sample gradients which may affect the performance of student model detrimentally on low-resolution recognition and increase the cost, 2) CRRCD facilitates cross-resolution knowledge transfer by modeling the relation between samples in different resolution data, while CRCD only transfers information from the same data resolution, 3) CRRCD uses a more efficient critic function Eq. (<ref>) to estimate the distribution q(b=1 |v^t,v^t,s), which helps to maximize a lower bound on the mutual information. Therefore, our CRRCD can achieve better performance on low-resolution object recognition.



§ EXPERIMENTS

To validate the effectiveness of our cross-resolution relational contrastive distillation approach (CRRCD), we conduct experiments on two representative types of applications: low-resolution object classification and low-resolution face recognition. For the low-resolution object classification experiments, we utilize four benchmark datasets: CIFAR100 <cit.>, SVHN <cit.>, STL10 <cit.> and TinyImageNet <cit.>. The purpose is to assess the performance and generalizability of our approach. Furthermore, we investigate low-resolution face recognition by training models on CASIA-WebFace <cit.> and evaluating them on three face recognition tasks: verification on LFW <cit.>, identification on UCCS <cit.> and retrieval on TinyFace <cit.>. In these experiments, we employe VGG <cit.>, ResNet <cit.>, wide ResNet <cit.>, ShuffleNetV1 <cit.> and ShuffleNetV2 <cit.> as as our backbone models. In the model learning process, we use a batch size of 96 and initialize the learning rate to 0.05. The learning rate is multiplied by 0.1 at epochs 21, 28, and 32. We maintain a fixed random seed of 5 and set the distillation temperature (T) to 4. All experiments are conducted with PyTorch on a NVIDIA 3090 GPU.



 §.§ Low-resolution Object Classification

Object classification is a general visual recognition task and has very important applications under the low-resolution condition like industrial inspection and medical diagnosis. In the experiments, we first check the effectiveness of our distillation method and then evaluate the effectiveness and transferability of our approach in low-resolution object classification. 





 
The effectiveness of distillation. Our approach distills cross-resolution contrastive relations between different resolution samples that can better mimic the model capacity of the high-resolution teacher model. To verify that, we conduct two low-resolution object classification experiments on CIFAR100 by comparing with other advanced distillation approaches under both peer-architecture and cross-architecture settings. CIFAR100 has 100 classes containing 600 images each.

Peer-architecture distillation uses homogeneous architecture for teacher-student pairs. The results are shown in Tab. <ref>. From the results, we can see that our CRRCD outperforms six sample-level distillation approaches (KD <cit.>, FitNet <cit.>, AT <cit.>, PKT <cit.>, VID <cit.> and Abound <cit.>) as well as six relation-level distillation approaches (SP <cit.>, RKD <cit.>, CC <cit.>, CRD <cit.>, CRCD <cit.> and WCoRD <cit.>), and is comparable with DKD <cit.>. For example, comparing with WCoRD <cit.> that combines contrastive learning and knowledge distillation to help student learn richer sample-wise knowledge in a certain maturity, when taking ResNet56 as teacher and ResNet20 as student, our CRRCD achieves 72.10% accuracy on CIFAR100 which is 0.54% higher than WCoRD, and gains 0.24% improvement when the teacher and student is ResNet110 and ResNet32. The main reason comes from that our CRRCD focuses on higher-order relational contrasting knowledge. It implies the remarkable effectiveness in improving student learning.

To further explore the flexibility of our approach, cross-architecture distillation applies heterogeneous architecture for teacher-student pairs during learning. In this setting, the gap of knowledge transfer will become larger thus put forward higher requirements for knowledge distillation. The results are shown in Tab. <ref>, where our approach achieves the best accuracy and has better competitiveness than peer-architecture setting. For five cross-architecture students, our CRRCD gains 2.54% improvement over CRD and 1.40% improvement over CRCD on average accuracy, respectively. Especially, when taking WRN50-2 as teacher and ShuffleNetV1 as student, CRRCD achieves 5.45% accuracy improvement over CRD and 1.97% accuracy improvement over CRCD, respectively. Moreover, compared to recent evolutionary knowledge distillation approach (EKD) <cit.>, our CRRCD also gives better classification accuracy. These results shows that our approach can provide a flexible way to distill black-box teacher knowledge and learn discriminative student representations for downstream image recognition task. 

Very low-resolution object classification. First, we check the effectiveness of CRRCD on object classification under a very low-resolution of 8 × 8 by evaluating on SVHN dataset. This dataset contains digit images captured from real-world natural scenes, having a resolution of 32×32. We downsample the images by a factor of 4 to create 8×8 data and use them for evaluating very low-resolution digit classification. The teacher model is ResNet56 pretrained with 32×32 images and our student is VGG8 that has very few parameters. We compare our approach to five state-of-the-art very low-resolution image recognition approaches and report the top-1 classification accuracy in Tab. <ref>. Our CRRCD model obtains a classification accuracy of 89.33%, an at least improvement of 1.58%. Compared with other approaches like DeriveNet <cit.> which focuses on learning effective class boundaries by utilizing the class-specific domain knowledge, our CRRCD makes full use of the structural knowledge between different samples and the dark knowledge in the teacher model to obtain stronger feature extraction capability, which greatly improves the recognition performance of model on very low-resolution images.





Representation transferability. After the promising results achieved with the adaptability on low resolution and flexible network architectures, we further verify the cross-dataset transferability of our approach by training on CIFAR100 but testing on STL10 and TinyImageNet. Following CRD <cit.>, we investigate the effectiveness of student representations. A good representation extractor should generate linear separable features. Hence, we use the fixed backbone of student trained on CIFAR100 to extract representations for STL10 and TinyImageNet, and then train a linear classifier to test the classification accuracy. We select WRN-40-2 as teacher and ShuffleNetV1 as student, and compare with three sample-level distillation approaches (KD <cit.>, FitNet <cit.> and AT <cit.>), relation-level distillation approach CRD <cit.> and self-supervised knowledge distillation (SSKD) <cit.>. In the experiment, the input resolution of teacher and student is 32 × 32. As shown in Tab. <ref>, our CRRCD delivers the best accuracy on both STL10 and TinyImageNet. From the results, we find that our approach still has good representation transferability between different objects (e.g., natural objects in CIFAR100 and digits in STL 10). However, all approaches achieve a very low accuracy (e.g., lower than 36%) in recognizing TinyImageNet. The main reason may be insufficient knowledge from 32 × 32 CIFAR100 that is incapable for identifying higher-resolution objects in TinyImageNet. It implies that direct learning from low-resolution images may be ineffective and cross-resolution knowledge transfer can be a more effective way.



 §.§ Low-resolution Face Recognition

Low-resolution face recognition is a specified and challenging object recognition task and has very helpful applications like recognizing surveillance faces in the wild. In practical scenarios, the facial images often have low resolution, uneven light intensity, diverse facial posture and facial expression. These will have a huge impact on the recognition accuracy. In our experiments, we take CASIA-WebFace as training set, which contains 10575 categories and a total of 494414 images collected from the web. The teacher is trained on CASIA-WebFace with ResNet50 under the high-resolution of 112×112, and the students are trained on low-resolution CASIA-WebFace with ResNet18. Then, the trained students are used to evaluate face verification on LFW, face identification on UCCS and face retrieval on TinyFace, respectively. In order to verify the validity of the low-resolution students, we emphatically check the accuracy when the input resolution is 16×16 produced by bilinear downsampling. All approaches use the same experimental settings to ensure fair comparisons. 



Face verification on LFW. We conduct the comparisons with some state-of-the-art face recognition models on LFW, which contains 6000 pairs of face images. We downsample the images to synthesize low-resolution faces. A 512d feature embedding for each image is extracted for similarity comparison. With a pre-set threshold, each face pair is determined to have the same identity if the similarity of the two faces is greater than the threshold and different identity otherwise. The verification accuracy is reported as the percentage of the pairs that are correctly determined. The results are listed in Tab. <ref>, where some conclusions can be found.

Firstly, the state-of-the-art face recognition models usually deliver very high verification accuracy in recognizing faces under normal resolution. For example, ArcFace <cit.> uses ResNet50 and gives a 99.82% accuracy under the input resolution of 112×112. Our CRRCD approach distills the ResNet50 model into a lightweight ResNet18 student, which still achieves a good accuracy of 95.25% under a much low-resolution of 16×16. This is very helpful for practical deployment in resource-limited conditions. Secondly, when these face recognition models are applied to identify low-resolution images, e.g., recognizing 16×16 images after bilinear upsampling, the accuracy will has a great drop. For example, ArcFace gives an accuracy of 92.30% under the low-resolution condition, having a drop of 7.52%. These results reveal that it is necessary to compensate the missing knowledge to facilitate the recognition of low-resolution objects from high-resolution images or models. Finally, we compare our approach with five recent low-resolution face recognition approaches. In comparison to distillation-based methods, our CRRCD achieves higher accuracy. This improvement can be attributed to its ability to extract high-order relation contrastive knowledge, which proves to be more effective than sample-level knowledge (SKD <cit.> and EKD <cit.>) or low-order relation knowledge (HORKD <cit.>). In low-resolution face recognition tasks, our method exhibits significant advantages compared to the non-parametric low-resolution face recognition model (NPM <cit.>). In <cit.>, deep Rival Penalized Competitive Learning (RPCL) is embedded into state-of-the-art face recognition models to learn margin-based discriminative low-resolution face features. Our CRRCD outperforms RPCL-based models since it implicitly encodes margin-based discriminative representation learning by using anchor-based high-order relation preserving distillation. In cross-resolution knowledge transfer, high-order relation can help the model learn better representations from low-resolution domain and contrastive relation can facilitate the learning of representations in visual recognition task.

 


 
Face identification on UCCS. UCCS is collected in real surveillance scenarios and contains 16149 images in 1732 subjects in the wild condition, which is a very challenging benchmark with various levels of challenges. To verify the robustness of our low-resolution student models, we emphatically check the accuracy when the input resolution is 16×16. We follow the setting as <cit.>, randomly select a 180-subject subset, separate the images into 3918 training images and 907 testing images, and report the results with the standard accuracy. In the experiment, we freeze the representation extraction part of each model, modify the final softmax layer into 180-way, and finetune the layer parameters on training set. As shown in Tab. <ref>, our student model achieves an impressive identification accuracy of 97.27%, surpassing the state-of-the-art DirectCapsNet <cit.> by 1.46%. Our approach enhances low-resolution face recognition performance by enabling the student model to acquire discriminative representations. Despite lacking essential information for recognition, our method leverages cross-resolution relational contrastive knowledge from the teacher model and high-resolution data. This allows the student model to learn higher-order feature representations, leading to improved performance.

Face retrieval on TinyFace. TinyFace contains large-scale native low-resolution surveillance face images. In experiment, we finetune basic models on its training set and then evaluate 1:N identification performance on its testing set. Tab. <ref> reports Rank-1, Rank-10 and Rank-20 retrieval results. Different from typical models <cit.> that design margin-based losses to learn discriminative representations, our CRRCD implicitly learns distinct inter-class boundaries under cross-resolution relational constraints with the assistance of a high-resolution teacher and consistently improves retrieval accuracy under various settings. In addition, via high-order knowledge transfer, CRRCD outperforms PeiLi's method <cit.> based on reconstruction and DCR <cit.> that employs two branches to transfer cross-resolution knowledge by feature approximation. There results imply the effectiveness of our approach in learning discriminative and transferable representations.



 §.§ Ablation and Further Analysis




Effect of negative number. An important part of knowledge distillation based on contrastive learning is to construct positive and negative sample pairs, and the negative number has a crucial impact on the final performance. We validate five different negative number (64, 128, 256, 512 and 1024) and show the results in the left of Fig. <ref>. Here, increasing negative number will lead to performance improvement, which means higher-order relation knowledge is built and migrated. Meantime, a larger negative number requires more computations. It suggests that the negative number should be carefully selected to balance the accuracy and computation cost. Thus, we set the negative number to 512 since it only gives a small accuracy gain of 0.05% when increasing negative number to 1024. Our approach can significantly reduce the negative number, which is benefited from modeling the structural relationship that does not pass through the samples with rich knowledge, which reduces the dependence on the number of negative samples.

Effect of sampling policy. We consider two negative sampling policies when giving an anchor x_i: x_j,j ≠ i for the unsupervised case without labels, or x_j, y_j ≠ y_i for supervised case, where y_i represents the label associated with sample x_i. What's more to ensure that negative samples are as up-to-date as possible, we store features and gradients in a queue way which will remove the oldest sample when adding the latest sample. Through experiments, the combination of queue and supervised sampling policy can bring at least 0.25% improvement at accuracy on LFW.

Effect of distillation temperature. The distillation temperature τ in Eq.(<ref>) is used to adjust the concentration level. We report the results when τ varies from 0.02 to 0.30 in the right of Fig. <ref>. A temperature between 0.08 to 0.1 works well and we set τ=0.1 for all our experiments. In general, for different downstream tasks, the value of τ should be carefully set in a task-specified manner.

Effect of projected feature dimension. Our feature relation module builds contrastive relation vectors by projecting the 512d feature embeddings into specific-dimensional features. The projected feature dimension affects model performance and computation cost in training. Increasing dimension boosts performance but also raises computation cost. To balance them, we test various feature dimensions and set it to 128. In addition, our approach employs an efficient critic function h(v^t,v^t,s) to estimate the distribution q(b=1 |v^t,v^t,s), which maximizes a lower bound on the mutual information. It is worth noting that the inference complexity is fixed and not affected by the order of structural relationship.






Representation visualization. To further demonstrate the advantages of our approach visually, we first use the t-SNE <cit.> for visualization. It converts similarities between data points to joint probabilities and tries to minimize the KL divergence between the joint probabilities of the low-dimensional embedding and the high-dimensional data. We randomly select 400 samples each class from SVHN dataset, different numbers indicate different classes in Fig. <ref>. It is obvious that our approach achieves more concentrated clusters than baseline (Same structure as student model, but no distillation strategy) which is trained with softmax loss. And the changes of the distances in classifiers of baseline are more severe than that in classifier of CRRCD. We speculate that transferring high-order relational contrastive knowledge is helpful for student to learn discriminative representations.


Next, we illustrate the estimated similarity distributions of ArcFace and our CRRCD in Fig. <ref>. To quantify their difference, we introduce two statistics for evaluation, the expectation margin and histogram intersection between the two distributions from positive and negative pairs. Typically, smaller histogram
intersection and larger expectation margin indicate better verification performance, since it means that more discriminative deep embeddings are learned. As shown in Fig. <ref>, the deeply learned face features are more discriminative and less overlapped by our CRRCD than by ArcFace, indicating that our approach is effective in enhancing the discriminability and obtains the best performance.



§ CONCLUSION

In this paper, we propose cross-resolution relational contrastive distillation, a novel approach to improve low-resolution object recognition. Our approach successfully transfers high-order relation knowledge from a pretrained high-resolution teacher model to a low-resolution student model. Through extensive experiments on low-resolution object classification and low-resolution face recognition, we validate the effectiveness and adaptability of our approach. Our future work will concentrate on integrating domain generalization and exploring its applicability to a broader spectrum of visual understanding tasks.

Acknowledgements. This work was partially supported by grants from the National Key Research and Development Plan (2020AAA0140001) and Beijing Natural Science Foundation (19L2040).

IEEEtran


[
    < g r a p h i c s >
]Kangkai Zhang received his B.S. degree in Electronical Information Science and Technology from the School of Electronic Information and Optical Engineering in Nankai University, Tianjin, China. He obtained a Master's degree in Communication and Information Systems at the Institute of Information Engineering at Chinese Academy of Sciences, Beijing. Currently, he works as a Computer Vision Algorithm Engineer at Baidu Inc. His major research interests are deep learning and computer vision.


[
    < g r a p h i c s >
]Shiming Ge (M'13-SM'15) is a professor with the Institute of Information Engineering, Chinese Academy of Sciences. Prior to that, he was a senior researcher and project manager in Shanda Innovations, a researcher in Samsung Electronics and Nokia Research Center. He received the B.S. and Ph.D degrees both in Electronic Engineering from the University of Science and Technology of China (USTC) in 2003 and 2008, respectively. His research mainly focuses on computer vision, data analysis, machine learning and AI security, especially efficient and trustworthy solutions towards scalable applications. He is a senior member of IEEE, CSIG and CCF.


[
    < g r a p h i c s >
]Ruixin Shi received her B.S. degree in Information Security from the School of Cyber Security in Beijing Institute of Technology, China. She is now a Ph.D Candidate at the Institute of Information Engineering at Chinese Academy of Sciences and the School of Cyber Security at the University of Chinese Academy of Sciences, Beijing. His major research interests are computer vision and generative modeling.


[
    < g r a p h i c s >
]Dan Zeng (SM'21) received her Ph.D. degree in circuits and systems, and her B.S. degree in electronic science and technology, both from University of Science and Technology of China, Hefei. She is a full professor and the Dean of the Department of Communication Engineering at Shanghai University, directing the Computer Vision and Pattern Recognition Lab. Her main research interests include computer vision, multimedia analysis, and machine learning. She is serving as the Associate Editor of the IEEE Transactions on Multimedia and the IEEE Transactions on Circuits and Systems for Video Technology, the TC Member of IEEE MSA and Associate TC member of IEEE MMSP.




