Hao Chen
email: hao.chen@inria.fr

Benoit Lagadec
email: benoit.lagadec@esifrance.net

Francois Bremond
email: francois.bremond@inria.fr

ICE: Inter-instance Contrastive Encoding for Unsupervised Person Re-identification

Unsupervised person re-identification (ReID) aims at learning discriminative identity features without annotations. Recently, self-supervised contrastive learning has gained increasing attention for its effectiveness in unsupervised representation learning. The main idea of instance contrastive learning is to match a same instance in different augmented views. However, the relationship between different instances has not been fully explored in previous contrastive methods, especially for instance-level contrastive loss. To address this issue, we propose Interinstance Contrastive Encoding (ICE) that leverages interinstance pairwise similarity scores to boost previous classlevel contrastive ReID methods. We first use pairwise similarity ranking as one-hot hard pseudo labels for hard instance contrast, which aims at reducing intra-class variance. Then, we use similarity scores as soft pseudo labels to enhance the consistency between augmented and original views, which makes our model more robust to augmentation perturbations. Experiments on several largescale person ReID datasets validate the effectiveness of our proposed unsupervised method ICE, which is competitive with even supervised methods. Code is made available at https://github.com/chenhao2345/ICE.

Introduction

Person re-identification (ReID) targets at retrieving an person of interest across non-overlapping cameras by comparing the similarity of appearance representations. Supervised ReID methods [28,[START_REF] Hao Chen | Learning discriminative and generalizable representations by spatial-channel partition for person re-identification[END_REF][START_REF] Hao Luo | Bag of tricks and a strong baseline for deep person re-identification[END_REF] use human-annotated labels to build discriminative appearance representations which are robust to pose, camera property and view-point variation. However, annotating cross-camera identity labels is a cumbersome task, which makes supervised methods less scalable in real-world deployments. Unsupervised methods [START_REF] Lin | A bottom-up clustering approach to unsupervised person re-identification[END_REF][START_REF] Lin | Unsupervised person re-identification via softened similarity learning[END_REF][START_REF] Wang | Unsupervised person reidentification via multi-label classification[END_REF] directly train a model on unlabeled data and thus have a better scalability.

Most of previous unsupervised ReID methods [27,[START_REF] Ge | Mutual meanteaching: Pseudo label refinery for unsupervised domain adaptation on person re-identification[END_REF][START_REF] Zhai | Multiple expert brainstorming for domain adaptive person re-identification[END_REF] are based on unsupervised domain adaptation (UDA).

UDA methods adjust a model from a labeled source domain to an unlabeled target domain. The source domain provides a good starting point that facilitates target domain adaptation. With the help of a large-scale source dataset, state-ofthe-art UDA methods [START_REF] Ge | Mutual meanteaching: Pseudo label refinery for unsupervised domain adaptation on person re-identification[END_REF][START_REF] Zhai | Multiple expert brainstorming for domain adaptive person re-identification[END_REF] significantly enhance the performance of unsupervised ReID. However, the performance of UDA methods is strongly influenced by source dataset's scale and quality. Moreover, a large-scale labeled dataset is not always available in the real world. In this case, fully unsupervised methods [START_REF] Lin | A bottom-up clustering approach to unsupervised person re-identification[END_REF][START_REF] Lin | Unsupervised person re-identification via softened similarity learning[END_REF] own more flexibility, as they do not require any identity annotation and directly learn from unlabeled data in a target domain.

Recently, contrastive learning has shown excellent performance in unsupervised representation learning. State-ofthe-art contrastive methods [START_REF] Wu | Unsupervised feature learning via non-parametric instance discrimination[END_REF][START_REF] Chen | A simple framework for contrastive learning of visual representations[END_REF][START_REF] He | Momentum contrast for unsupervised visual representation learning[END_REF] consider each image instance as a class and learns representations by matching augmented views of a same instance. As a class is usually composed of multiple positive instances, it hurts the performance of fine-grained ReID tasks when different images of a same identity are considered as different classes. Self-paced Contrastive Learning (SpCL) [13] alleviates this problem by matching an instance with the centroid of the multiple positives, where each positive converges to its centroid at a uniform pace. Although SpCL has achieved impressive performance, this method does not consider interinstance affinities, which can be leveraged to reduce intraclass variance and make clusters more compact. In supervised ReID, state-of-the-art methods [START_REF] Hao Chen | Learning discriminative and generalizable representations by spatial-channel partition for person re-identification[END_REF][START_REF] Hao Luo | Bag of tricks and a strong baseline for deep person re-identification[END_REF] usually adopt a hard triplet loss [START_REF] Hermans | In defense of the triplet loss for person re-identification[END_REF] to lay more emphasis on hard samples inside a class, so that hard samples can get closer to normal samples. In this paper, we introduce Inter-instance Contrastive Encoding (ICE), in which we match an instance with its hardest positive in a mini-batch to make clusters more compact and improve pseudo label quality. Matching the hardest positive refers to using one-hot "hard" pseudo labels.

Since no ground truth is available, mining hardest positives within clusters is likely to introduce false positives into the training process. In addition, the one-hot label does not take the complex inter-instance relationship into consideration when multiple pseudo positives and negatives exist in a mini-batch. Contrastive methods usually use data augmentation to mimic real-world distortions, e.g., occlusion, view-point and resolution variance. After data augmentation operations, certain pseudo positives may become less similar to an anchor, while certain pseudo negatives may become more similar. As a robust model should be invariant to distortions from data augmentation, we propose to use the inter-instance pairwise similarity as "soft" pseudo labels to enhance the consistency before and after augmentation.

Our proposed ICE incorporates class-level label (centroid contrast), instance pairwise hard label (hardest positive contrast) and instance pairwise soft label (augmentation consistency) into one fully unsupervised person ReID framework. Without any identity annotation, ICE significantly outperforms state-of-the-art UDA and fully unsupervised methods on main-stream person ReID datasets.

To summarize, our contributions are: [START_REF] Chen | Deep credible metric learning for unsupervised domain adaptation person re-identification[END_REF] We propose to use pairwise similarity ranking to mine hardest samples as one-hot hard pseudo labels for hard instance contrast, which reduces intra-class variance. [START_REF] Hao Chen | Learning discriminative and generalizable representations by spatial-channel partition for person re-identification[END_REF] We propose to use pairwise similarity scores as soft pseudo labels to enhance the consistency between augmented and original instances, which alleviates label noise and makes our model more robust to augmentation perturbation. (3) Extensive experiments highlight the importance of inter-instance pairwise similarity in contrastive learning. Our proposed method ICE outperforms state-of-the-art methods by a considerable margin, significantly pushing unsupervised ReID to real-world deployment.

Related Work

Unsupervised person ReID. Recent unsupervised person ReID methods can be roughly categorized into unsupervised domain adaptation (UDA) and fully unsupervised methods. Among UDA-based methods, several works [START_REF] Wang | Transferable joint attribute-identity deep learning for unsupervised person re-identification[END_REF][START_REF] Lin | Multi-task mid-level feature alignment network for unsupervised cross-dataset person re-identification[END_REF] leverage semantic attributes to reduce the domain gap between source and target domains. Several works [START_REF] Wei | Person transfer gan to bridge domain gap for person reidentification[END_REF][START_REF] Zhong | Generalizing a person retrieval model hetero-and homogeneously[END_REF]8,[START_REF] Zhong | Invariance matters: Exemplar memory for domain adaptive person re-identification[END_REF][START_REF] Zou | Joint disentangling and adaptation for cross-domain person re-identification[END_REF][START_REF] Hao Chen | Joint generative and contrastive learning for unsupervised person re-identification[END_REF] use generative networks to transfer labeled source domain images into the style of target domain. Another possibility is to assign pseudo labels to unlabeled images, where pseudo labels are obtained from clustering [27,[START_REF] Fu | Self-similarity grouping: A simple unsupervised cross domain adaptation approach for person re-identification[END_REF][START_REF] Zhang | Self-training with progressive augmentation for unsupervised cross-domain person re-identification[END_REF]3] or reference data [START_REF] Yu | Unsupervised person re-identification by soft multilabel learning[END_REF]. Pseudo label noise can be reduced by selecting credible samples [START_REF] Chen | Deep credible metric learning for unsupervised domain adaptation person re-identification[END_REF] or using a teacher network to assign soft labels [START_REF] Ge | Mutual meanteaching: Pseudo label refinery for unsupervised domain adaptation on person re-identification[END_REF]. All these UDA-based methods require a labeled source dataset. Fully unsupervised methods have a better flexibility for deployment. BUC [START_REF] Lin | A bottom-up clustering approach to unsupervised person re-identification[END_REF] first treats each image as a cluster and progressively merge clusters. Lin et al. [START_REF] Lin | Unsupervised person re-identification via softened similarity learning[END_REF] replace clustering-based pseudo labels with similarity-based softened labels. Hierarchical Clustering is proposed in [START_REF] Zeng | Hierarchical clustering with hard-batch triplet loss for person re-identification[END_REF] to improve the quality of pseudo labels. Since each identity usually has multiple positive instances, MMCL [START_REF] Wang | Unsupervised person reidentification via multi-label classification[END_REF] introduces a memory-based multi-label classification loss into unsupervised ReID. JVTC [START_REF] Li | Joint visual and temporal consistency for unsupervised domain adaptive person reidentification[END_REF] and CycAs [START_REF] Wang | Cycas: Selfsupervised cycle association for learning re-identifiable descriptions[END_REF] explore temporal information to refine visual similarity. SpCL [13] considers each cluster and outlier as a single class and then conduct instance-to-centroid contrastive learning. CAP [START_REF] Wang | Camera-aware proxies for unsupervised person re-identification[END_REF] calculates identity centroids for each camera and conducts intra-and inter-camera centroid contrastive learning. Both SpCL and CAP focus on instance-to-centroid contrast, but neglect inter-instance affinities.

Contrastive Learning. Recent contrastive learning methods [START_REF] Wu | Unsupervised feature learning via non-parametric instance discrimination[END_REF][START_REF] He | Momentum contrast for unsupervised visual representation learning[END_REF][START_REF] Chen | A simple framework for contrastive learning of visual representations[END_REF] consider unsupervised representation learning as a dictionary look-up problem. Wu et al. [START_REF] Wu | Unsupervised feature learning via non-parametric instance discrimination[END_REF] retrieve a target representation from a memory bank that stores representations of all the images in a dataset. MoCo [START_REF] He | Momentum contrast for unsupervised visual representation learning[END_REF] introduces a momentum encoder and a queue-like memory bank to dynamically update negatives for contrastive learning. In SimCLR [START_REF] Chen | A simple framework for contrastive learning of visual representations[END_REF], authors directly retrieve representations within a large batch. However, all these methods consider different instances of a same class as different classes, which is not suitable in a fine-grained ReID task. These methods learn invariance from augmented views, which can be regarded as a form of consistency regularization.

Consistency regularization. Consistency regularization refers to an assumption that model predictions should be consistent when fed perturbed versions of the same image, which is widely considered in recent semi-supervised learning [START_REF] Tarvainen | Mean teachers are better role models: Weight-averaged consistency targets improve semi-supervised deep learning results[END_REF][START_REF] Sohn | Fixmatch: Simplifying semisupervised learning with consistency and confidence[END_REF][START_REF] Chen | Big self-supervised models are strong semi-supervised learners[END_REF]. The perturbation can come from data augmentation [START_REF] Sohn | Fixmatch: Simplifying semisupervised learning with consistency and confidence[END_REF], temporal ensembling [START_REF] Tarvainen | Mean teachers are better role models: Weight-averaged consistency targets improve semi-supervised deep learning results[END_REF][START_REF] Laine | Temporal ensembling for semisupervised learning[END_REF][START_REF] Ge | Self-supervising fine-grained region similarities for large-scale image localization[END_REF] and shallow-deep features [START_REF] Zheng | Rectifying pseudo label learning via uncertainty estimation for domain adaptive semantic segmentation[END_REF][START_REF] Chen | Big self-supervised models are strong semi-supervised learners[END_REF]. Artificial perturbations are applied in contrastive learning as strong augmentation [7,[START_REF] Wei | Co2: Consistent contrast for unsupervised visual representation learning[END_REF] and momentum encoder [START_REF] He | Momentum contrast for unsupervised visual representation learning[END_REF] to make a model robust to data variance. Based on temporal ensembling, Ge et al. [START_REF] Ge | Self-supervising fine-grained region similarities for large-scale image localization[END_REF] use inter-instance similarity to mitigate pseudo label noise between different training epochs for image localization. Wei et al. [START_REF] Wei | Co2: Consistent contrast for unsupervised visual representation learning[END_REF] propose to regularize inter-instance consistency between two sets of augmented views, which neglects intra-class variance problem. We simultaneously reduce intra-class variance and regularize consistency between augmented and original views, which is more suitable for fine-grained ReID tasks.

Proposed Method

Overview

Given a person ReID dataset X = {x 1 , x 2 , ..., x N }, our objective is to train a robust model on X without annotation. For inference, representations of a same person are supposed to be as close as possible. State-of-the-art contrastive methods [START_REF] He | Momentum contrast for unsupervised visual representation learning[END_REF][START_REF] Chen | A simple framework for contrastive learning of visual representations[END_REF] consider each image as an individual class and maximize similarities between augmented views of a same instance with InfoNCE loss [START_REF] Van Den Oord | Representation learning with contrastive predictive coding[END_REF]:

L Inf oN CE = E[-log exp (q • k + /τ ) K i=0 exp (q • k i /τ ) ] (1)
where q and k + are two augmented views of a same instance in a set of candidates k i . τ is a temperature hyper-parameter that controls the scale of similarities.

Following MoCo [START_REF] He | Momentum contrast for unsupervised visual representation learning[END_REF], we design our proposed ICE with an online encoder and a momentum encoder as shown in Fig. 1. The online encoder is a regular network, e.g., ResNet50 [START_REF] He | Deep residual learning for image recognition[END_REF], which is updated by back-propagation. The momentum encoder (weights noted as θ m ) has the same structure as the online encoder, but updated by accumulated weights of the online encoder (weights noted as θ o ):

θ t m = αθ t-1 m + (1 -α)θ t o ( 2
)
where α is a momentum coefficient that controls the update speed of the momentum encoder. t and t -1 refer respectively to the current and last iteration. The momentum encoder builds momentum representations with the moving averaged weights, which are more stable to label noise. At the beginning of each training epoch, we use the momentum encoder to extract appearance representations M = {m 1 , m 2 , ..., m N } of all the samples in the training set X . We use a clustering algorithm DBSCAN [START_REF] Ester | A density-based algorithm for discovering clusters in large spatial databases with noise[END_REF] on these appearance representations to generate pseudo identity labels Y = {y 1 , y 2 , ..., y N }. We only consider clustered inliers for contrastive learning, while un-clustered outliers are discarded. We calculate proxy centroids p 1 , p 2 , ... and store them in a memory for a proxy contrastive loss L proxy (see Sec. 3.2). Note that this proxy memory can be cameraagnostic [13] or camera-aware [START_REF] Wang | Camera-aware proxies for unsupervised person re-identification[END_REF].

Then, we use a random identity sampler to split the training set into mini-batches where each mini-batch contains N P pseudo identities and each identity has N K instances. We train the whole network by combining the L proxy (with class-level labels), a hard instance contrastive loss L h ins (with hard instance pairwise labels, see Sec. 3.3) and a soft instance consistency loss L s ins (with soft instance pairwise labels, see Sec. 3.4):

L total = L proxy + λ h L h ins + λ s L s ins (3)
To increase the consistency before and after data augmentation, we use different augmentation settings for prediction and target representations in the three losses (see Tab. 1).

Loss

Predictions (augmentation) Targets (augmentation)

L proxy f (Strong) p (None) L h ins f (Strong) m (Strong) L s ins P (Strong) Q (None)
Table 1: Augmentation settings for 3 losses.

Proxy Centroid Contrastive Baseline

For a camera-agnostic memory, the proxy of cluster a is defined as the averaged momentum representations of all the instances belonging to this cluster:

p a = 1 N a mi∈ya m i (4)
where N a is the number of instances belonging to the cluster a.

We apply a set of data augmentation on X and feed them to the online encoder. For an online representation f a belonging to the cluster a, the camera-agnostic proxy contrastive loss is a softmax log loss with one positive proxy p a and all the negatives in the memory:

L agnostic = E[-log exp (f a • p a /τ a ) |p| i=1 exp (f a • p i /τ a ) ] ( 5
)
where |p| is the number of clusters in a training epoch and τ a is a temperature hyper-parameter. Different from unified contrastive loss [START_REF] Ge | Mutual meanteaching: Pseudo label refinery for unsupervised domain adaptation on person re-identification[END_REF], outliers are not considered as single instance clusters. In such way, outliers are not pushed away from clustered instances, which allows us to mine more hard samples for our proposed hard instance contrast. As shown in Fig. 2, all the clustered instances converge to a common cluster proxy centroid. However, images inside a cluster are prone to be affected by camera styles, leading to high intra-class variance. This problem can be alleviated by adding a cross-camera proxy contrastive loss [START_REF] Wang | Camera-aware proxies for unsupervised person re-identification[END_REF].

For a camera-aware memory, if we have C = {c 1 , c 2 , ...} cameras, a camera proxy p ab is defined as the averaged momentum representations of all the instances belonging to the cluster a in camera c b :

p ab = 1 N ab mi∈ya∩mi∈c b m i (6)
where N ab is the number of instances belonging to the cluster a captured by camera c b . Given an online representation f ab , the cross-camera proxy contrastive loss is a softmax log loss with one positive cross-camera proxy p ai and N neg nearest negative proxies in the memory:

Lcross = E[- 1 |P| i̸ =b∩i∈C log exp (< f ab • pai > /τc) Nneg +1 j=1 exp (< f ab • pj > /τc) ] (7)
where < • > denotes cosine similarity and τ c is a crosscamera temperature hyper-parameter. |P| is the number of cross-camera positive proxies. Thanks to this cross-camera proxy contrastive loss, instances from one camera are pulled closer to proxies of other cameras, which reduces intra-class camera style variance. We define a proxy contrastive loss by combining cluster and camera proxies with a weighting coefficient 0.5 from [START_REF] Wang | Camera-aware proxies for unsupervised person re-identification[END_REF]:

L proxy = L agnostic + 0.5L cross (8)

Hard Instance Contrastive Loss

Although intra-class variance can be alleviated by crosscamera contrastive loss, it has two drawbacks: 1) more memory space is needed to store camera-aware proxies, 2) impossible to use when camera ids are unavailable. We propose a camera-agnostic alternative by exploring interinstance relationship instead of using camera labels. Along with training, the encoders become more and more strong, which helps outliers progressively enter clusters and become hard inliers. Pulling hard inliers closer to normal inliers effectively increases the compactness of clusters.

A mini-batch is composed of N P identities, where each identity has N K positive instances. Given an anchor instance f i belonging to the ith class, we sample the hardest positive momentum representation m i k that has the lowest cosine similarity with f i , see Fig. 4. For the same anchor, we have J = (N P -1) × N K negative instances that do not belong to the ith class. The hard instance contrastive loss for f i is a softmax log loss of J + 1 (1 positive and J negative) pairs, which is defined as:

L h ins = E[-log exp (< f i • m i k > /τ h ins ) J+1 j=1 exp (< f i • m j > /τ h ins ) ] (9)
where k = arg min k=1,..,N K (< f i • m i k >) and τ h ins is the hard instance temperature hyper-parameter. By minimizing the distance between the anchor and the hardest positive and maximizing the distance between the anchor and all negatives, L h ins increases intra-class compactness and inter-class separability.

Relation with triplet loss. Both L h ins and triplet loss [START_REF] Hermans | In defense of the triplet loss for person re-identification[END_REF] pull an anchor closer to positive instances and away from negative instances. As shown in Fig. 3, the traditional triplet loss pushes away a negative pair from a positive pair by a margin. Differently, the proposed L h ins pushes away all the negative instances as far as it could with a softmax. If we select one negative instance, the L h ins can be transformed into the triplet loss. If we calculate pairwise distance within a mini-batch to select the hardest positive and the hardest negative instances, the L h ins is equivalent to the batch-hard triplet loss [START_REF] Hermans | In defense of the triplet loss for person re-identification[END_REF]. We compare hard triplet loss (hardest negative) with the proposed L h ins (all negatives). in Tab. 2.

Soft Instance Consistency Loss

Both proxy and hard instance contrastive losses are trained with one-hot hard pseudo labels, which can not capture the complex inter-instance similarity relationship between multiple pseudo positives and negatives. Especially, inter-instance similarity may change after data augmentation. As shown in Fig. 4, the anchor A becomes less similar to pseudo positives (P 1 , P 2 , P 3 ), because of the visual distortions. Meanwhile, the anchor A becomes more similar to pseudo negatives (N 1 , N 2 ), since both of them have red shirts. By maintaining the consistency before and after augmentation, a model is supposed to be more invariant to augmentation perturbations. We use the inter-instance similarity scores without augmentation as soft labels to rectify those with augmentation.

For a batch of images after data augmentation, we measure the inter-instance similarity between an anchor f A with all the mini-batch N K × N P instances, as shown in Fig. 4. Then, the inter-instance similarity is turned into a prediction distribution P by a softmax:

P = exp (< f A • m > /τ s ins ) N P ×N K j=1 exp (< f A • m j > /τ s ins ) (10)
where τ s ins is the soft instance temperature hyperparameter. f A is an online representation of the anchor, while m is momentum representation of each instance in a mini-batch.

For the same batch without data augmentation, we measure the inter-instance similarity between momentum representations of the same anchor with all the mini-batch N K × N P instances, because the momentum encoder is more stable. We get a target distribution Q:

Q = exp (< m A • m > /τ s ins ) N P ×N K j=1 exp (< m A • m j > /τ s ins ) (11)
The soft instance consistency loss is Kullback-Leibler Divergence between two distributions:

L s ins = D KL (P ||Q) (12)
In previous methods, consistency is regularized between weakly augmented and strongly augmented images [START_REF] Sohn | Fixmatch: Simplifying semisupervised learning with consistency and confidence[END_REF] or two sets of differently strong augmented images [START_REF] Wei | Co2: Consistent contrast for unsupervised visual representation learning[END_REF]. Some methods [START_REF] Laine | Temporal ensembling for semisupervised learning[END_REF][START_REF] Tarvainen | Mean teachers are better role models: Weight-averaged consistency targets improve semi-supervised deep learning results[END_REF]] also adopted mean square error (MSE) as their consistency loss function. We compare our setting with other possible settings in Tab. 3.

Experiments

Datasets and Evaluation Protocols

Market-1501 [43], DukeMTMC-reID [START_REF] Ristani | Performance measures and a data set for multi-target, multi-camera tracking[END_REF] and MSMT17 [START_REF] Wei | Person transfer gan to bridge domain gap for person reidentification[END_REF]

Implementation details

General training settings. To conduct a fair comparison with state-of-the-art methods, we use an ImageNet [START_REF] Russakovsky | Imagenet large scale visual recognition challenge[END_REF] pretrained ResNet50 [START_REF] He | Deep residual learning for image recognition[END_REF] as our backbone network. We report results of IBN-ResNet50 [START_REF] Pan | Two at once: Enhancing learning and generalization capacities via ibn-net[END_REF] in Appendix. An Adam optimizer with a weight decay rate of 0.0005 is used to optimize our networks. The learning rate is set to 0.00035 with a warm-up scheme in the first 10 epochs. No learning rate decay is used in the training. The momentum encoder is up- Clustering settings. We calculate k-reciprocal Jaccard distance [START_REF] Zhong | Reranking person re-identification with k-reciprocal encoding[END_REF] for clustering, where k is set to 30. We set a minimum cluster samples to 4 and a distance threshold to 0.55 for DBSCAN. We also report results of a smaller threshold 0.5 (more appropriate for the smaller dataset Mar-ket1501) and a larger threshold 0.6 (more appropriate for the larger dataset MSMT17) in Appendix.

Data augmentation. All images are resized to 256×128. The strong data augmentation refers to random horizontal flipping, cropping, Gaussian blurring and erasing [START_REF] Zhong | Random erasing data augmentation[END_REF].

Parameter analysis

Compared to the proxy contrastive baseline, ICE brings in four more hyper-parameters, including λ h ins , τ h ins for hard instance contrastive loss and λ s ins , τ s ins for soft instance consistency loss. We analyze the sensitivity of each hyper-parameter on the Market-1501 dataset. The mAP results are illustrated in Fig. 5. As hardest positives are likely to be false positives, an overlarge λ h ins or undersized τ h ins introduce more noise. λ h ins and λ s ins balance the weight of each loss in Eq. (3). Given the results, we set λ h ins = 1 and λ s ins = 10. τ h ins and τ s ins control the similarity scale in hard instance contrastive loss and soft instance consistency loss. We finally set τ h ins = 0.1 and τ s ins = 0.4. Our hyper-parameters are tuned on Market-1501 and kept same for DukeMTMC-reID and MSMT17. Achieving state-of-the-art results simultaneously on the three datasets can validate the generalizability of these hyper-parameters.

Ablation study

The performance boost of ICE in unsupervised ReID mainly comes from the proposed hard instance contrastive loss and soft instance consistency loss. We conduct ablation experiments to validate the effectiveness of each loss, which is reported in Tab. 4. We illustrate the number of clusters during the training in Fig. 6 and t-SNE [START_REF] Van Der Maaten | Visualizing data using t-SNE[END_REF] after training in Fig. 8 to evaluate the compactness of clusters. We also illustrate the dynamic KL divergence of Eq. ( 12) to measure representation sensitivity to augmentation perturbation in Fig. 7 .

Hard instance contrastive loss. Our proposed L h ins reduces the intra-class variance in a camera-agnostic manner, which increases the quality of pseudo labels. By reducing intra-class variance, a cluster is supposed to be more compact. With a same clustering algorithm, we expect to have less clusters when clusters are more compact. As shown in Fig. 6, DBSCAN generated more clusters during the training without our proposed L h ins . The full ICE framework has less clusters, which are closer to the real number of identities in the training set. On the other hand, as shown in Fig. 8, the full ICE framework has a better intra-class compactness and inter-class separability than the camera-aware Camera-agnostic scenario. Above results are obtained with a camera-aware memory, which strongly relies on ground truth camera ids. We further validate the effectiveness of the two proposed losses with a camera-agnostic memory, whose results are also reported in Tab. 4. Our proposed L h ins significantly improves the performance from the camera-agnostic baseline. However, L s ins should be used under low intra-class variance, which can be achieved by the variance constraints on camera styles L cross and hard samples L h ins . L h ins reduces intraclass variance, so that AA ≈ AP 1 ≈ AP 2 ≈ AP 3 ≈ 1 before augmentation in Fig. 4. L s ins permits that we still have AA ≈ AP 1 ≈ AP 2 ≈ AP 3 ≈ 1 after augmentation. However, when strong variance exists, e.g., AA ̸ ≈ AP 1 ̸ ≈ AP 2 ̸ ≈ AP 3 ̸ ≈ 1, maintaining this relationship equals maintaining intra-class variance, which decreases the ReID performance. On medium datasets (e.g., Market1501 and DukeMTMC-reID) without strong camera variance, our proposed camera-agnostic intra-class variance constraint L h ins is enough to make L s ins beneficial to ReID. On large datasets (e.g., 15 cameras in MSMT17) with strong camera variance, only camera-agnostic variance constraint L h ins is not enough. We provide the dynamic cluster numbers of camera-agnostic ICE in Appendix.

Comparison with state-of-the-art methods

We compare ICE with state-of-the-art ReID methods in Tab. 5. Comparison with unsupervised method. Previous unsupervised methods can be categorized into unsupervised domain adaptation (UDA) and fully unsupervised methods. We first list state-of-the-art UDA methods, including MMCL [START_REF] Wang | Unsupervised person reidentification via multi-label classification[END_REF], JVTC [START_REF] Li | Joint visual and temporal consistency for unsupervised domain adaptive person reidentification[END_REF], DG-Net++ [START_REF] Zou | Joint disentangling and adaptation for cross-domain person re-identification[END_REF], ECN+ [START_REF] Zhong | Learning to adapt invariance in memory for person re-identification[END_REF], MMT [START_REF] Ge | Mutual meanteaching: Pseudo label refinery for unsupervised domain adaptation on person re-identification[END_REF], DCML [START_REF] Chen | Deep credible metric learning for unsupervised domain adaptation person re-identification[END_REF], MEB [START_REF] Zhai | Multiple expert brainstorming for domain adaptive person re-identification[END_REF], SpCL [13] and ABMT [3]. UDA methods usually rely on source domain annotation to reduce the pseudo label noise. Without any identity annotation, our proposed ICE outperforms all of them on the three datasets.

Under the fully unsupervised setting, ICE also achieves better performance than state-of-the-art methods, including BUC [START_REF] Lin | A bottom-up clustering approach to unsupervised person re-identification[END_REF], SSL [START_REF] Lin | Unsupervised person re-identification via softened similarity learning[END_REF], MMCL [START_REF] Wang | Unsupervised person reidentification via multi-label classification[END_REF], JVTC [START_REF] Li | Joint visual and temporal consistency for unsupervised domain adaptive person reidentification[END_REF], HCT [START_REF] Zeng | Hierarchical clustering with hard-batch triplet loss for person re-identification[END_REF], CycAs [START_REF] Wang | Cycas: Selfsupervised cycle association for learning re-identifiable descriptions[END_REF], GCL [START_REF] Hao Chen | Joint generative and contrastive learning for unsupervised person re-identification[END_REF], SpCL [13] and CAP [START_REF] Wang | Camera-aware proxies for unsupervised person re-identification[END_REF]. CycAs leveraged temporal information to assist visual matching, while our method only considers visual similarity. SpCL and CAP are based on proxy contrastive learning, which are considered respectively as camera-agnostic and cameraaware baselines in our method. With a camera-agnostic memory, the performance of ICE(agnostic) remarkably surpasses the camera-agnostic baseline SpCL, especially on Market1501 and MSMT17 datasets. With a camera-aware memory, ICE(aware) outperforms the camera-aware baseline CAP on all the three datasets. By mining hard positives to reduce intra-class variance, ICE is more robust to hard samples. We illustrate some hard examples in Fig. 9, where ICE succeeds to notice important visual clues, e.g., characters in the shirt (1st row), blonde hair (2nd row), brown shoulder bag (3rd row) and badge (4th row). Comparison with supervised method. We further provide two well-known supervised methods for reference, including the Part-based Convolutional Baseline (PCB) [28] and the joint Discriminative and Generative Network (DG-Net) [START_REF] Zheng | Joint discriminative and generative learning for person re-identification[END_REF]. Unsupervised ICE achieves competitive performance with PCB. If we replace the clustering generated pseudo labels with ground truth, our ICE can be transformed into a supervised method. The supervised ICE is competitive with state-of-the-art supervised ReID methods (e.g., DG-Net), which shows that the supervised contrastive learning has a potential to be considered into future supervised ReID.

Conclusion

In this paper, we propose a novel inter-instance contrastive encoding method ICE to address unsupervised ReID. Deviated from previous proxy based contrastive ReID methods, we focus on inter-instance affinities to make a model more robust to data variance. We first mine the hardest positive with mini-batch instance pairwise similarity ranking to form a hard instance contrastive loss, which effectively reduces intra-class variance. Smaller intra-class variance contributes to the compactness of clusters. Then, we use mini-batch instance pairwise similarity scores as soft labels to enhance the consistency before and after data augmentation, which makes a model robust to artificial augmentation variance. By combining the proposed hard instance contrastive loss and soft instance consistency loss,

Figure 1 :

 1 Figure1: General architecture of ICE. We maximize the similarity between anchor and pseudo positives in both inter-class (proxy agreement between an instance representation f1 and its cluster proxy p1) and intra-class (instance agreement between f1 and its pseudo positive m2) manners.

Figure 2 :

 2 Figure 2: Proxy contrastive loss. Inside a cluster, an instance is pulled to a cluster centroid by Lagnostic and to cross-camera centroids by Lcross.

Figure 3 :

 3 Figure 3: Comparison between triplet and hard instance contrastive loss.

Figure 4 :

 4 Figure 4: Based on inter-instance similarity ranking between anchor (A), pseudo positives (P) and pseudo negatives (N), Hard Instance Contrastive Loss matches an anchor with its hardest positive in a mini-batch. Soft Instance Consistency Loss regularizes the interinstance similarity before and after data augmentation.

Figure 5 :

 5 Figure 5: Parameter analysis on Market-1501 dataset.

Figure 6 :

 6 Figure 6: Dynamic cluster numbers during 40 training epochs on DukeMTMC-reID. "hard" and "soft" respectively denote L h ins and Ls ins. A lower number denotes that clusters are more compact.

Figure 7 :

 7 Figure 7: Dynamic KL divergence during 40 training epochs on DukeMTMC-reID. Lower KL divergence denotes that a model is more robust to augmentation perturbation.

Table 4 :

 4 79.5 92.0 97.0 98.1 67.2 81.3 90.1 93.0 29.8 59.0 71.7 77.0 Comparison of different losses. Camera-aware memory occupies up to 6, 8 and 15 times memory space than camera-agnostic memory on Market1501, DukeMTMC-reID and MSMT17 datasets. baseline in the test set. The compactness contributes to better unsupervised ReID performance in Tab. 4.Soft instance consistency loss. Hard instance contrastive loss reduces the intra-class variance between naturally captured views, while soft instance consistency loss mainly reduces the variance from artificially augmented perturbation. If we compare the blue (ICE full) and yellow (w/o soft) curves in Fig.7, we can find that the model trained without L s ins is less robust to augmentation perturbation. The quantitative results in Tab. 4 confirms that the L s ins improves the performance of baseline. The best performance can be obtained by applying L h ins and L s ins on the camera-aware baseline.

Figure 8 :

 8 Figure 8: T-SNE visualization of 10 random classes in DukeMTMC-reID test set between camera-aware baseline (Left) and ICE (Right).

Figure 9 :

 9 Figure 9: Comparison of top 5 retrieved images on Market1501 between CAP [34] and ICE. Green boxes denote correct results, while red boxes denote false results. Important visual clues are marked with red dashes. ICE significantly outperforms previous unsupervised ReID methods on Market1501, DukeMTMC-reID and MSMT17 datasets.

Table 2 :

 2 Comparison between using the hardest negative and all negatives in the denominator of L h ins .

	Negative in L h ins	Market1501 mAP Rank1 mAP DukeMTMC-reID Rank1
	hardest	80.1	92.8	68.2	82.5
	all	82.3	93.8	69.9	83.3

Table 3 :

 3

	Consistency	Market1501 mAP Rank1 mAP DukeMTMC-reID Rank1
	MSE	80.0	92.7	68.4	82.1
	Strong-strong Aug 80.4	92.8	68.2	82.5
	ours	82.3	93.8	69.9	83.3

Comparison of consistency loss. Ours refers to KL divergence between images with and without data augmentation.

  datasets are used to evaluate our proposed method.

	Market-1501 dataset is collected in front of a supermarket
	in Tsinghua University from 6 cameras. It contains 12,936
	images of 751 identities for training and 19,732 images of
	750 identities for test. DukeMTMC-reID is a subset of the
	DukeMTMC dataset. It contains 16,522 images of 702 per-
	sons for training, 2,228 query images and 17,661 gallery
	images of 702 persons for test from 8 cameras. MSMT17
	is a large-scale Re-ID dataset, which contains 32,621 train-
	ing images of 1,041 identities and 93,820 testing images
	of 3,060 identities collected from 15 cameras. Both Cu-
	mulative Matching Characteristics (CMC) Rank1, Rank5,
	Rank10 accuracies and mean Average Precision (mAP) are
	used in our experiments.

  proxy 79.3 91.5 96.8 97.6 67.3 81.4 90.8 92.9 36.4 67.8 78.7 82.5 +L h ins 80.5 92.6 97.3 98.4 68.8 82.4 90.4 93.6 38.0 69.1 79.9 83.4 +L s ins 81.1 93.2 97.5 98.5 68.4 82.0 91.0 93.2 38.1 68.7 79.8 83.7 +L h ins + L s ins 82.3 93.8 97.6 98.4 69.9 83.3 91.5 94.1 38.9 70.2 80.5 84.4

	Camera-aware memory	Market1501 mAP R1 R5	DukeMTMC-reID R10 mAP R1 R5	MSMT17 R10 mAP R1 R5	R10
	Baseline L Camera-agnostic memory	Market1501 mAP R1 R5	DukeMTMC-reID R10 mAP R1 R5	MSMT17 R10 mAP R1 R5	R10
	Baseline L agnostic	65.8 85.3 95.1 96.6 50.9 67.9 81.6 86.6 24.1 52.3 66.2 71.6
	+L h ins	78.2 91.3 96.9 98.0 65.4 79.6 88.9 91.9 30.3 60.8 72.9 77.6
	+L s ins	47.2 66.7 86.0 91.6 36.2 50.4 70.3 76.3 17.8 38.8 54.2 60.9
	+L h ins + L s ins

Table 5 :

 5 .4 92.8 95.0 51.4 72.4 82.9 85.0 16.2 43.6 54.3 58.9 JVTC[START_REF] Li | Joint visual and temporal consistency for unsupervised domain adaptive person reidentification[END_REF] ECCV'20 61.1 83.8 93.0 95.2 56.2 75.0 85.1 88.2 20.3 45.4 58.4 64.3 DG-Net++ [51] ECCV'20 61.7 82.1 90.2 92.7 63.8 78.9 87.8 90.4 22.1 48.8 60.9 65.9 ECN+ [50] TPAMI'20 63.8 84.1 92.8 95.4 54.4 74.0 83.7 87.4 16.0 42.5 55.9 61.5 .3 93.5 95.5 62.8 82.9 87.1 88.5 21.3 45.7 58.6 64.5 SpCL(agnostic) [13] NeurIPS'20 73.1 88.1 95.1 97.0 65.3 81.2 90.3 92.2 19.1 42.3 55.6 61.2 ICE(agnostic) This paper 79.5 92.0 97.0 98.1 67.2 81.3 90.1 93.0 29.8 59.0 71.7 77.0 CAP(aware)[34] AAAI'21 79.2 91.4 96.3 97.7 67.3 81.1 89.3 91.8 36.9 67.4 78.0 81.4 ICE(aware) This paper 82.3 93.8 97.6 98.4 69.9 83.3 91.5 94.1 38.9 70.2 80.5 84.4 Supervised PCB [28] ECCV'18 81.6 93.8 97.5 98.5 69.2 83.3 90.5 92.5 40.4 68.2 ICE (w/ ground truth) This paper 86.6 95.1 98.3 98.9 76.5 88.2 94.1 95.7 50.4 76.4 86.6 90.0 Comparison of ReID methods on Market1501, DukeMTMC-reID and MSMT17 datasets. The best and second best unsupervised results are marked in red and blue.

	Method	Reference	Market1501 mAP R1 R5	DukeMTMC-reID R10 mAP R1 R5	MSMT17 R10 mAP R1 R5	R10
	Unsupervised Domain Adaptation
	MMCL [32] 60.4 84MMT [11] CVPR'20 ICLR'20 71.2 87.7 94.9 96.9 65.1 78.0 88.8 92.5 23.3 50.1 63.9 69.8
	DCML [1]	ECCV'20	72.6 87.9 95.0 96.7 63.3 79.1 87.2 89.4	-	-	-	-
	MEB [41]	ECCV'20	76.0 89.9 96.0 97.5 66.1 79.6 88.3 92.2	-	-	-	-
	SpCL [13]	NeurIPS'20 76.7 90.3 96.2 97.7 68.8 82.9 90.1 92.5 26.8 53.7 65.0 69.8
	ABMT [3]	WACV'21	78.3 92.5	-	-	69.1 82.0	-	-	26.5 54.3	-	-
	Fully Unsupervised
	BUC [20]	AAAI'19	29.6 61.9 73.5 78.2 22.1 40.4 52.5 58.2	-	-	-	-
	SSL [21]	CVPR'20	37.8 71.7 83.8 87.4 28.6 52.5 63.5 68.9	-	-	-	-
	JVTC [18]	ECCV'20	41.8 72.9 84.2 88.7 42.2 67.6 78.0 81.6 15.1 39.0 50.9 56.8
	MMCL [32]	CVPR'20	45.5 80.3 89.4 92.3 40.2 65.2 75.9 80.0 11.2 35.4 44.8 49.8
	HCT [40]	CVPR'20	56.4 80.0 91.6 95.2 50.7 69.6 83.4 87.4	-	-	-	-
	CycAs [35]	ECCV'20	64.8 84.8	-	-	60.1 77.9	-	-	26.7 50.1	-	-
	GCL [4]	CVPR'21	66.8 87-	-
	DG-Net [44]	CVPR'19	86.0 94.8	-	-	74.8 86.6	-	-	52.3 77.2	-	-

Acknowledgements. This work has been supported by the French government, through the 3IA Côte d'Azur Investments in the Future project managed by the National Research Agency (ANR) with the reference number ANR-19-P3IA-0002. The authors are grateful to the OPAL infrastructure from Université Côte d'Azur for providing resources and support.


Claudia Mariana Castillo-Fraire

Sandrine Pottier

Arnaud Bondon

Erika Salas

Stéphane Bernillon

Sylvain Guyot
email: sylvain.guyot@inrae.fr

Pascal Poupard

NMR structural elucidation of dehydrodimers resulting from oxidation of 5-O-caffeoylquinic acid in an apple juice model solution

Keywords: phenolic compounds, CQA dehydrodimers, chlorogenic acid, PPO, caffeicin

During apple juice and cider-making processes, phenolic compounds undergo enzymatic oxidation. 5-O-caffeoylquinic acid (CQA) is one of the major hydroxycinnamic acid derivatives and it is the preferential substrate for polyphenol oxidase (PPO) in apple juices. Consequently, CQA dehydrodimers (MW 706 Da) are among the main products resulting from CQA oxidation. CQA dehydrodimers were previously synthesized in a biomimetic apple juice model solution.

Following their purification and characterization using UV-Visible spectra and mass spectrometry, the structures of seven CQA dehydrodimers were elucidated using 1 H and 13 C oneand two-dimensional NMR spectroscopy. Six of them exhibited dihydrobenzofuran, benzodioxane, or dihydronaphtalene skeletons, which are caffeicin-like structures. Interestingly, a new dehydrodicaffeoyldiquinic acid molecule was also characterised for which two novel structures showing a symmetric dicatechol skeleton were also proposed.

Introduction

Chlorogenic acids (CGA) are a group of phenolic acids that correspond to hydroxycinnamic acids esterified by a quinic acid moiety. These widespread compounds are present in plants, fruits, and vegetables, and are characteristic compounds in coffee beans, tea, maté, blueberries, cherries, plums, pears, apples, spinach, and potato tubers (Clifford, 1999[START_REF] Clifford | Chlorogenic acids and other cinnamates-nature, occurence, dietary burden, absorption and metabolism[END_REF]. CGA are known to have bioactive properties such as antioxidant, free radical-scavenging, antibacterial, and antidiabetic properties, as well as neuroprotective activity [START_REF] Bao | Chlorogenic acid prevents diabetic nephropathy by inhibiting oxidative stress and inflammation through modulation of the Nrf2/HO-1 and NF-ĸB pathways[END_REF][START_REF] Naveed | Chlorogenic acid (CGA): A pharmacological review and call for further research[END_REF]. Regarding apple and applederived products, the major hydroxycinnamic acid derivative is 5-O-caffeoylquinic acid (CQA).

Depending on the apple variety, CQA concentrations range from 200 to 1000 mg/L in apple juices [START_REF] Guyot | Multiplicity of Phenolic Oxidation Products in Apple Juices and Ciders, from Synthetic Medium to Commercial Products[END_REF].

During the first step of apple juice production (crushing, pressing), polyphenols come into contact with polyphenol oxidase (PPO). In this step, CQA, the preferential substrate for PPO, can be oxidised into its corresponding ortho-quinone in presence of oxygen. This highly reactive species can be involved in different reaction pathways leading to the formation of a multiplicity of neoformed molecules [START_REF] Poupard | Characterisation by liquid[END_REF]. However, the detailed structures and properties of these oxidation products are yet little known.

Oxidation products have been explored in synthetic solutions using caffeic acid as a model compound [START_REF] Cilliers | Characterization of the Products of Nonenzymic Autoxidative Phenolic Reactions in a Caffeic Acid Model System[END_REF][START_REF] Fulcrand | Characterization of compounds obtained by chemical oxidation of caffeic acid in acidic conditions[END_REF][START_REF] Pati | Characterization of caffeic acid enzymatic oxidation by-products by liquid chromatography coupled to electrospray ionization tandem mass spectrometry[END_REF]Weber et al., 2019). Some of these oxidised products have been characterised using several techniques: UV-Visible spectra, [START_REF] Cilliers | Characterization of the Products of Nonenzymic Autoxidative Phenolic Reactions in a Caffeic Acid Model System[END_REF][START_REF] Fulcrand | Characterization of compounds obtained by chemical oxidation of caffeic acid in acidic conditions[END_REF][START_REF] Pati | Characterization of caffeic acid enzymatic oxidation by-products by liquid chromatography coupled to electrospray ionization tandem mass spectrometry[END_REF], mass spectrometry [START_REF] Pati | Characterization of caffeic acid enzymatic oxidation by-products by liquid chromatography coupled to electrospray ionization tandem mass spectrometry[END_REF], and NMR [START_REF] Cilliers | Characterization of the Products of Nonenzymic Autoxidative Phenolic Reactions in a Caffeic Acid Model System[END_REF][START_REF] Fulcrand | Characterization of compounds obtained by chemical oxidation of caffeic acid in acidic conditions[END_REF]. Their characterization has highlighted that they are mainly dehydrodimers resulting from oxidative coupling whose linkage could involve the aromatic ring and/or the double bond of the propenoic acid chain. Most of them have been classified as caffeicin and correspond to dihydrobenzofuran, dihydrobenzodioxan, or dihydronaphtalene types [START_REF] Cilliers | Characterization of the Products of Nonenzymic Autoxidative Phenolic Reactions in a Caffeic Acid Model System[END_REF].

In apple juice, caffeoylquinic acid oxidation products were first detected using LC/MS analyses [START_REF] Bernillon | Detection of phenolic oxidation products in cider apple juice by high-performance liquid chromatography electrospray ionisation ion trap mass spectrometry[END_REF]. These compounds were then synthesized in an apple juice model solution.

LC/MS analyses confirmed the molecular weight of 706 Da, suggesting that these compounds correspond to oxidative coupling between two CQA molecules [START_REF] Castillo-Fraire | Preparative fractionation of 5'-O-caffeoylquinic acid oxidation products using centrifugal partition chromatography and their investigation by mass spectrometry[END_REF]Wong-Paz et al., 2015). Their tanning properties have been explored previously, highlighting a specific interaction with certain families of salivary proteins [START_REF] Castillo-Fraire | Interactions between polyphenol oxidation products and salivary proteins : Specific affinity of CQA dehydrodimers with cystatins and P-B peptide[END_REF].

In our previous research, sufficient quantities of CQA oxidation products were synthesized enzymatically for purification on a milligram scale. Centrifugal Partition Chromatography (CPC) was optimised to fractionate these CQA dehydrodimers [START_REF] Castillo-Fraire | Preparative fractionation of 5'-O-caffeoylquinic acid oxidation products using centrifugal partition chromatography and their investigation by mass spectrometry[END_REF]. After preparative/semi-preparative HPLC, ten CQA dehydrodimers with a chromatographic purity higher than 85% were successfully recovered [START_REF] Castillo-Fraire | Preparative fractionation of 5'-O-caffeoylquinic acid oxidation products using centrifugal partition chromatography and their investigation by mass spectrometry[END_REF].

In this work, we present the structure elucidation of seven of these CQA dehydrodimers using Nuclear Magnetic Resonance (NMR).

Material and Methods

Chemicals and enzymes

5-O-caffeoylquinic acid (CQA) was obtained from Sigma-Aldrich (St. Louis, MO, USA) and the crude extract of polyphenol oxidase (PPO) was prepared in our laboratory as described previously (Le [START_REF] Bourvellec | Inhibition of Apple Polyphenol Oxidase Activity by Procyanidins and Polyphenol Oxidation Products[END_REF]. HPLC-grade solvents for the purification of the CQA oxidation products [START_REF] Castillo-Fraire | Preparative fractionation of 5'-O-caffeoylquinic acid oxidation products using centrifugal partition chromatography and their investigation by mass spectrometry[END_REF] and methanol for the NMR analyses were purchased from Eurisotop (Saint-Aubin, France).

Synthesis and purification of CQA oxidation products

The complete procedure has been described in detail in a previous study published recently [START_REF] Castillo-Fraire | Preparative fractionation of 5'-O-caffeoylquinic acid oxidation products using centrifugal partition chromatography and their investigation by mass spectrometry[END_REF]. Briefly, CQA dehydrodimers were synthesized by enzymatic oxidation (PPO) of CQA in a model solution (Figure 1). The remaining CQA was eliminated using Centrifugal Partition Chromatography (CPC) performed in Elution-Extrusion Counter Current Chromatography (EECCC) mode. Finally, purification was sharpened using preparative/semi-preparative HPLC.

The ten CQA dehydrodimers were eluted between 14 min and 46 min (10-33 % ACN), suggesting a wide dispersion of polarity. The polarity of most of the compounds was lower than their precursors, except for 705-1 and 705-1.1 that were eluted before CQA in the LC/MS analysis. The compound number indicates the order of elution.

NMR analyses

To elucidate their structures, seven CQA dehydrodimers (705-1, 705-1.1, 705-2, 705-3, 705-4, 705-5, and 705-6) were analysed using NMR. Samples were dissolved in deuterated methanol (CD 3 OD).

NMR spectra were recorded at 298 K and measurements were carried out on a Bruker AVANCE 500 spectrometer (Bruker, Wissembourg, France) with a Triple Resonance (TCI) 5 mm cryoprobe ( 1 H, 13 C, 15 N). The chemical shifts were attributed using 2D Homo-nuclear and Hetero-nuclear spectra: DQF-COSY, TOCSY, edited 13 C-HSQC, 13 C-HSQC-TOCSY, and 13 C-IMPACT-HMBC. Standard pulse sequences from the Bruker database were used. Chemical shifts were expressed as ppm and the spectra were processed using Topspin software.

Results and discussion

NMR analyses

In a previous study based on UV-Visible spectra and MS n spectrometry, three hypothetical structures were proposed for 9 out of the 10 dehydrodimers purified [START_REF] Castillo-Fraire | Preparative fractionation of 5'-O-caffeoylquinic acid oxidation products using centrifugal partition chromatography and their investigation by mass spectrometry[END_REF]. In the present study, NMR spectrometry confirmed these structural hypotheses. In addition, NMR was successfully used to propose two novel structural hypotheses. Table 1 shows 1 H proton and 13 C carbon chemical shifts for the seven compounds analysed. A dihydronaphtalene-type structure (Figure 4) was proposed for compounds 705-1 and 705-1.1, a dihydrobenzofuran-type structure (Figure 2) for dehydrodimers 705-3 and 705-4, and a dihydrobenzodioxane-type structure (Figure 3) for dehydrodimers 705-5 and 705-6.

As dehydrodimer 705-2 presented a completely different MS n fragmentation and UV-Visible spectrum compared to the other CQA dehydrodimers, no hypothetical structure was proposed for this compound in our previous study [START_REF] Castillo-Fraire | Preparative fractionation of 5'-O-caffeoylquinic acid oxidation products using centrifugal partition chromatography and their investigation by mass spectrometry[END_REF]. NMR spectrometry analyses were necessary to elucidate its structure.

Structure elucidation of the dihydrobenzufuran-type dehydrodimers

These compounds presented UV-vis spectra with a λmax at 327 nm [START_REF] Castillo-Fraire | Preparative fractionation of 5'-O-caffeoylquinic acid oxidation products using centrifugal partition chromatography and their investigation by mass spectrometry[END_REF]. The detailed structure of products 705-3 and 705-4 (Figure 2A) was elucidated from the 1 H and 13 C NMR spectra. The chemical shifts of the carbon and proton atoms are presented in Table 1. The structural analyses of 705-3 and 705-4 have been discussed in a previous paper [START_REF] Castillo-Fraire | Preparative fractionation of 5'-O-caffeoylquinic acid oxidation products using centrifugal partition chromatography and their investigation by mass spectrometry[END_REF].

MS n fragmentation highlighted that they likely correspond to two CQA dehydrodimer isomers with a dihydrobenzofuran moiety. The MS n transitions for 705-3 and 705-4 were 705→513→339→295 [START_REF] Castillo-Fraire | Preparative fractionation of 5'-O-caffeoylquinic acid oxidation products using centrifugal partition chromatography and their investigation by mass spectrometry[END_REF]. These compounds are analogues of caffeic acid oxidation products (caffeicin F) already described by [START_REF] Cilliers | Characterization of the Products of Nonenzymic Autoxidative Phenolic Reactions in a Caffeic Acid Model System[END_REF].

In the following paragraph, all 1 H and 13 C chemical shifts are given for isomer 705-3. The corresponding chemical shifts for isomer 705-4 are listed in Table 1.

The 13 C NMR signal at 167.09 ppm was used as a starting point for the structure elucidation. It corresponds to a strongly deshielded carbon consistent with an ester group. Moreover, the HMBC spectrum showed a clear correlation of this carbon (167.09 ppm) with two adjacent protons showing a large coupling constant 2 J (15.9 Hz) consistent with α-β ethylene protons. This carbon (167.09 ppm) was thus identified as C9 (Figure 2A) and the two protons at 7.62 ppm and 6.35 ppm were attributed to H7 and H8. HMBC correlations allowed H8 (6.35 ppm) to be unambiguously distinguished from H7 (7.62 ppm), as the latter was the only one showing HMBC correlations with 5 carbons (128.45, 116.06, 116.62, 114.78, 167.09 ppm). On the 1 H-13 C HSQC spectrum, carbons C7 and C8 correlated with H7 and H8 were observed at 145.27 ppm and 114.78 ppm, respectively. The signal at 128.45 ppm was attributed to the quaternary carbon C1 (no correlation on 1 H-13 C HSQC spectrum).

On the 1 H-13 C HMBC spectrum, the 13 C signals of carbons C2 and C6 were detected at 116.06 ppm and 116.62 ppm, respectively. The distinction between these two carbons was based on the fact that only carbon C6 (116.62 ppm) was correlated to a moderately deshielded proton (4.37 ppm). From the 1 H-13 C HSQC spectrum, the signals at 7.06 and 7.21 ppm could be attributed to H2 and H6, respectively. Proton H2 (7.06 ppm) was also correlated to 13 C signals at 141.64 ppm and 149.36 ppm corresponding to carbons C3 and C4. The 13 C signal at 149.36 ppm was attributed to carbon C4 as it is the only carbon showing an expected correlation with H6. Then, the 13 C signal at 141.64 ppm was attributed to C3.

Proton H6 (7.21 ppm) on the 1 H-13 C HMBC spectrum was correlated to a weakly deshielded carbon at 55.65 ppm and the 1 H-13 C HSQC spectrum revealed that this carbon at 55.65 ppm was linked to the moderately deshielded proton at 4.37 ppm. The latter proton and carbon were thus temporarily attributed to the 8' position. According to the 1 H-13 C HMBC spectrum, this proton (H8') was correlated to six carbons. The most deshielded one (170.57 ppm) was attributed to C9', which is consistent with an ester group. The latter carbon (C9') was correlated to a 1 H signal at 6.05 ppm, which could be temporarily attributed to H7'. Indeed, this proton (H7') was also correlated to six other carbons (55. 65, 112.58, 117.34, 126.20, 131.78, and 149.36 ppm) (Figure 2B). Among them, three corresponded to quaternary carbons (126.20, 131.78, and 149.36 ppm). Only one carbon (131.78 ppm) was correlated to three aromatic protons (6. 79, 6.79, and 6.86 ppm) allowing its identification as C1'. The signals of the three aromatic protons were consistent with a catechol group. Proton H2' was unambiguously identified at 6.86 ppm and a doublet with a small 3 J coupling constant (1.5 Hz) was observed. Even if the signals of protons H6' and H5' overlapped at 6.79 ppm, they were assigned based on their coupling constants. H6' presented two coupling constants (8.1 Hz and 1.5 Hz) and H5' only one (8.1 Hz). In addition, the whole signal integration of this zone (from 6.76 to 6.80 ppm) was consistent with the signal of two protons. The corresponding carbons C2', C5', and C6' were attributed to chemical shifts at 112.58, 114.97, and 117.34 ppm, respectively, according to the 1 H-13 C HSQC spectrum. The attribution of proton H7' was confirmed thanks to its correlation with both C2' and C6' unambiguously observed on the 1 H-13 C HMBC spectrum. Consequently, the attribution of proton H8' was also confirmed. Indeed, this proton (H8') was correlated to two carbons already identified (C6 at 116.62 ppm and C4 at149.36 ppm) and four other carbons (86.96, 126.20, 131.78, and 170.57 ppm) according to the 1 H-13 C HMBC spectrum.

Structure elucidation of the dihydrobenzodioxane-type dehydrodimers

These compounds presented UV-vis spectra with λmax close to 291 nm and 317 nm [START_REF] Castillo-Fraire | Preparative fractionation of 5'-O-caffeoylquinic acid oxidation products using centrifugal partition chromatography and their investigation by mass spectrometry[END_REF]. These spectra are similar to those of the four caffeicin (A-D) identified by [START_REF] Cilliers | Characterization of the Products of Nonenzymic Autoxidative Phenolic Reactions in a Caffeic Acid Model System[END_REF]. The detailed structures of products 705-5 and 705-6 (Figure 3A) were elucidated from the 1 H and 13 C NMR spectra. The chemical shifts of the 13 C and 1 H atoms are presented in Table 1. The structural analyses of 705-5 and 705-6 have been discussed in a previous paper [START_REF] Castillo-Fraire | Preparative fractionation of 5'-O-caffeoylquinic acid oxidation products using centrifugal partition chromatography and their investigation by mass spectrometry[END_REF]. MS n fragmentation revealed that they likely correspond to two CQA dehydrodimer isomers presenting a dihydrobenzodioxane skeleton. The MS n transitions for compounds 705-5 and 705-9 were 705→513→339→161 [START_REF] Castillo-Fraire | Preparative fractionation of 5'-O-caffeoylquinic acid oxidation products using centrifugal partition chromatography and their investigation by mass spectrometry[END_REF]. These compounds are analogues of caffeic acid oxidation products already described by [START_REF] Cilliers | Characterization of the Products of Nonenzymic Autoxidative Phenolic Reactions in a Caffeic Acid Model System[END_REF].

In the following paragraph, all 1 H and 13 C chemical shifts are given for isomer 705-5. The corresponding chemical shifts for isomer 705-6 are listed in Table 1.

The 13 C NMR signal at 169.1 ppm was used as a starting point for the structure elucidation. It corresponded to a strongly deshielded carbon consistent with an ester group. Moreover, the 1 H-13 C HMBC spectrum showed a clear correlation of this carbon (169.1 ppm) with two adjacent protons presenting a large coupling constant 2 J (15.9 Hz) consistent with α-β ethylene protons. This carbon (169.1 ppm) was thus identified as C9 (Figure 3A) and the two protons at 7.6 ppm and 6.4 ppm were attributed to H7 and H8. HMBC correlations allowed H8 (6.4 ppm) to be unambiguously distinguished from H7 (7.6 ppm). Indeed, the latter was the only one showing HMBC correlations with two carbons (118.8 and 124.5 ppm) that were correlated to aromatic protons on the 1 H-13 C HSQC NMR spectrum assigned as H2 (7.26 ppm, d, 2 Hz) and H6 (7.2 ppm, dd, 8.5 and 2 Hz), respectively.

The corresponding carbons C7 and C8 of protons H7 and H8 were at 146.8 ppm and 118.4 ppm, respectively. The 13 C signal at 130.9 ppm was attributed to the quaternary carbon C1.

Proton H2 (7.26 ppm, d, 2 Hz) was also correlated to 13 C signals at 145.6 ppm and 146.6 ppm that correspond to carbons C3 and C4, respectively. The 13 C NMR signal at 146.6 ppm was attributed to carbon C4 as it was the only carbon showing an expected correlation with H6 (7.2 ppm). The 13 C signal at 145.6 ppm was thus attributed to C3.

The 1 H-13 C HMBC spectrum showed a correlation between carbon C6 (124.5 ppm) and another aromatic proton at 7.03 ppm that was assigned as H5 (d,8.5Hz). This proton H5 was also correlated to two aromatic carbons assigned previously: C3 at 145.6 ppm and C4 at 146.6 ppm.

Conversely, the 13 C NMR signal at 169.5 ppm was used as a starting point for the structure elucidation of the other CQA moiety. It corresponded to a strongly deshielded carbon consistent with an ester group. The 1 H-13 C HMBC spectrum showed a clear correlation of this carbon (169.5 ppm) with three protons (4.9, 5.1, and 5.26 ppm). The proton at 5.26 ppm was assigned as H10', as this proton was correlated to the quinic acid part of the CQA moiety. The carbon at 169.5 ppm was thus assigned as C9'. The 1 H-13 C HMBC spectrum showed correlation of the proton at 5.1 ppm with six carbons (78.9, 116.4, 121.2, 128.7, 145.6, and 169.5 ppm). On the 1 H-13 C HSQC NMR spectrum, two of them (116.4 and 121.2 ppm) were correlated to aromatic protons at 6.79 ppm and 6.88 ppm, corresponding to H2' and H6'. The 13 C signal at 128.7 ppm was attributed to the quaternary carbon C1'. Based on these correlations, the two protons at 5.1 ppm and 4.9 ppm were attributed to H7' and H8', respectively.

Their corresponding carbons C7' and C8' were assigned at 78.4 ppm and 78.8 ppm on the 1 H-13 C HSQC NMR spectrum.

Interestingly, a clear correlation was observed on the HMBC spectrum between H7' (5.1 ppm) and a carbon at 145.6 ppm that was previously assigned as C3. Additionally, a correlation between H8' (4.9 ppm) and a carbon at 146.6 ppm corresponding to C4 was observed. These two correlations constitute proof for the elucidation of the dihydrobenzodioxane structure (Figure 3B).

Structure elucidation of the dihydronaphtalene-type dehydrodimers

This pair of compounds presented UV-vis spectra with λmax around 318 nm and 342 nm [START_REF] Castillo-Fraire | Preparative fractionation of 5'-O-caffeoylquinic acid oxidation products using centrifugal partition chromatography and their investigation by mass spectrometry[END_REF]. The complete NMR analysis of dehydrodicaffeoyldiquinic acid dimers 705-1 and 705-1.1 was used to confirm the structure of dehydrodimers showing a dihydronaphtalene nucleus (Figure 4A) based on the MS n fragmentation, as discussed in a previous paper [START_REF] Castillo-Fraire | Preparative fractionation of 5'-O-caffeoylquinic acid oxidation products using centrifugal partition chromatography and their investigation by mass spectrometry[END_REF]. The proposed structure was an analogue of caffeicin E resulting from caffeic acid oxidative coupling [START_REF] Cilliers | Characterization of the Products of Nonenzymic Autoxidative Phenolic Reactions in a Caffeic Acid Model System[END_REF]. The MS n transitions for 705-1 and 705-1.1 were 705→513→339→229 nm (Castillo-Fraire et al., 2019).

In the following part, the discussion concerns the1 H and 13 C attributions for product 705-1. The same approach can be applied to product 705-1.1 that exhibited the same correlation scheme on the 1 H-13 C HMBC, 1 H-13 C HSQC, and 1 H-1 H COSY spectra. All details of chemical shifts and attribution of coupling constants are provided in Table 1.

Interestingly, in the present case, the 1 H NMR spectrum does not show any deshielded protons that would belong to a free α-β ethylenic system exhibiting a large coupling constant close to 16 Hz. This specific two-proton system was clearly observed and discussed before for products 705-3 and -4 and 705-5 and -6. This suggests that, in the case of 705-1, both ethylene linkages of the caffeoyl moieties have been modified in such a way that they are both involved in oxidative coupling. This observation led us to select as a starting point the only strongly deshielded proton (singlet at 7.65 ppm) that also exhibited a clear HMBC correlation with a strongly deshielded carbon (169.2 ppm) consistent with an ester group. The proton was thus assigned as H7 and this deshielded carbon was attributed to C9. Then, carbon C9 clearly showed an HMBC correlation with another much more shielded proton at 3.95 ppm (doublet with J=3.4 Hz) that was attributed to H8'. Consequently, this coupling constant (3.4 Hz) allowed us to assign proton H7' at 7.47 ppm (doublet, J=3.4 Hz) and its corresponding carbon C7' located at 47.52 ppm using the 1 H-13 C HSQC spectrum. Noticeably, the Only one of them corresponded to a strongly deshielded carbon (174.8 ppm) that was thus attributed to C9'. Another weakly deshielded carbon (50.1 ppm) was attributed to C8', as its corresponding proton H8' was located at 3.94 ppm on the 1 H-13 C HSQC spectrum. The 13 C signals of the other seven carbons were located between 116 ppm and 136 ppm, consistent with aromatic or ethylene carbons.

Among them, C1', C8, and C6 could be distinguished from the others as they showed HMBC correlations with both H7' and H8'. C1' was easily distinguished as it presented typical correlations of an aromatic ABX system in a catechol group. C6 could be distinguished from C8 as only C6 exhibited HMBC correlations with three aromatic or ethylene protons, namely H5 (singlet 6.56 ppm), H2 (singlet, 6.88 ppm), and H7 (7.65 ppm). In contrast, C8 only showed correlation with one ethylene proton, namely H7 (7.65 ppm). H5 was distinguished from H2 as H5 showed HMBC correlation with C7'.

In contrast to the dihydrobenzofuran and the dihydrobenzodioxane structures, proton H8' in the dihydronaphtalene structure showed HMBC correlation with both C9 and C9' (ester group).

The complete NMR signal attributions of the protons and carbons belonging to the two catechol groups are not discussed here due to similarities with the structures of products 705-3 and -4, and 705-5 and -6 that have already discussed. All these attributions are given in Table 1.

Structure elucidation of the dehydrodimer presenting a symmetric structure

Although its molecular weight (MW 706 Da) and the presence of two quinic acid moieties were confirmed by mass spectrometry [START_REF] Castillo-Fraire | Preparative fractionation of 5'-O-caffeoylquinic acid oxidation products using centrifugal partition chromatography and their investigation by mass spectrometry[END_REF], compound 705-2 exhibited very different physicochemical features compared to the other CQA dehydrodimers. For instance, it was the only one showing a specific UV-Visible spectrum with a λmax at 282 nm and no more absorbance in the 300-340 nm region [START_REF] Castillo-Fraire | Preparative fractionation of 5'-O-caffeoylquinic acid oxidation products using centrifugal partition chromatography and their investigation by mass spectrometry[END_REF]. This lack of absorbance at 320 nm for 705-2 indicated that the conjugated double bonds of the propenoic chains of the two CQA moieties were no longer present in the dehydrodimer structure. Interestingly, this particular feature has already been observed for a dehydrodicaffeic acid oxidation product [START_REF] Fulcrand | Characterization of compounds obtained by chemical oxidation of caffeic acid in acidic conditions[END_REF].

In addition, the 1 H NMR spectrum was also original and differed from the other CQA dehydrodimers as it revealed a symmetric structure containing 24 non-hydroxyl protons. The 1 H and 13 C attributions and chemical shifts are given in Table 1. The complete 1D and 2D 1 H and 13 C NMR analyses allowed two hypothetical structures A and B to be proposed (Figure 5).

Except for some crucial NMR correlations, the following discussion mainly concerns the "non-prime" numbered moiety of the molecule. Considering the symmetry of the molecule, the argumentation is the same regarding the attribution of the "prime" numbered moiety.

The detailed structure of product 705-2 was elucidated from the 1 H and 13 C NMR spectra. The 1 H NMR spectrum revealed the presence of two aromatic protons at 6.77 ppm and one at 6.83 ppm. Their corresponding carbons were observed at 116.9, 117.3, and 121.9 ppm, respectively, on the 1 H-13 C HSQC NMR spectrum. HMBC correlations allowed C6 to be assigned at 116.9 ppm as this carbon was correlated with the two aromatic protons at 6.77 ppm (H2 and H5). The 1 H-13 C HMBC and 1 H-13 C HSQC NMR spectra permitted their corresponding carbons C2 and C5 to be assigned at 121.9 ppm and 117.3 ppm, respectively. Carbon C6 (116.9 ppm) was also correlated with a deshielded proton at 6.27 ppm. The 1 H-13 C HMBC NMR spectrum showed that this proton has the particularity of being correlated with 7 carbons (55.3, 73.5, 116.9, 121.9, 131.4, 171.4, and 172.7 ppm). Among them, three corresponded to aromatic carbons that were attributed to C6 at 116.9 ppm, C2 at 121.9 ppm, and the quaternary carbon C1 at 131.4 ppm. The proton at 6.27 ppm was thus attributed to H7 (dd, 11 Hz and 1.7 Hz). The 1 H-13 C HSQC NMR spectrum allowed the chemical shift of its corresponding carbon C7 at 73.5 ppm to be determined.

Noticeably, proton H7 was correlated with two strongly deshielded carbons that have a 13 C NMR signal at 171.4 ppm and 172.7 ppm consistent with the carbon of ester groups. The 13 C signal at 171.4 ppm was attributed to C9 based on its clear HMBC correlation with proton H10 (4.72 ppm) of the quinic acid moiety through the oxygen atom. In contrast, the carbon at 172.7 ppm showed clear HMBC correlations with four shielded protons (at 1.75, 1.77, 2.53, and 2.57 ppm) attributed to the two CH2 groups (H11 and H13 protons) of the quinic acid moiety. This carbon at 172.7 ppm was attributed to C16 or C16' for hypothesis A or B, respectively.

In addition, proton H7 (6.27 ppm) was correlated to a moderately deshielded carbon at 55.3 ppm. The 1 H-13 C HSQC NMR spectrum permitted the chemical shift of its corresponding proton (3.89 ppm) to be determined. The 1 H-13 C HMBC NMR spectrum showed correlations between this proton (3.89 ppm) and four carbons (55.3, 73.5, 131.4, and 171.4 ppm). Among them, the NMR results highlighted the correlation with carbon C7 at 73.5 ppm, the quaternary carbon C1 at 131.4 ppm, and carbon C9 at 171.4 ppm. The proton at 3.89 ppm was thus attributed to H8. The H-H coupling constants of 11 Hz and 1.7 Hz measured for proton H8 (or H8') were the same as those measured for proton H7 (or H7') (Table 1). These coupling constants correspond to 2 J coupling (between H7 and H8 or H7' and H8') and 4 J coupling (between H7 and H8' or H8 and H7'). This can be considered as proof of the C8-C8'covalent bonding between both CQA moieties.

Another spot also confirmed the symmetric character of the molecule when the 1 H-13 C HMBC and HSQC NMR spectra were overlapped. Indeed, the 1 H-13 C HMBC spectrum revealed that the proton H8 (3.89 ppm) was correlated with a carbon presenting the same chemical shift at 55.3 ppm, proving that H8 was correlated with carbon C8' of the other CQA moiety.

Based on the NMR analysis, two "hypothetical" symmetric structures were proposed (Figure 5). Both structures showed two free catechol groups and both carboxylic groups of the quinic acid moieties are here included in two additional ester linkages. Neither the NMR analyses nor the MS n fragmentation pattern enabled one of the two proposed "hypothetical" symmetric structures to be discarded or favoured.

The hypotheses of both structures are based on the fact that the 1 H-13 C HMBC spectrum revealed a correlation between H7 and C16 or C16' and these two carbons cannot be distinguished due to the symmetry of the molecule.

A mechanism was proposed for these structures (Figure 5), starting with the PPO-catalysed oxidation of CQA leading to the formation of CQA ortho-quinone. This CQA ortho-quinone and another CQA molecule can generate two semiquinone radicals by a reverse disproportionation. Then, radical coupling can take place between carbons C8 and C8' of these semiquinones generating a covalent bond between these two molecules. Finally, a nucleophilic addition step occurs between the C16 (or C16') hydroxyl group and the C7 (or C7') position, followed by re-aromatization to yield the symmetric structure.

The particular presence of two catechol groups in this symmetric structure could confer tanning properties to this compound. Indeed, complexation between polyphenols and proteins is dominated mainly by hydrogen bonds and hydrophobic interactions involving the catechol groups of phenolic compounds (de Freitas & Mateus, 2012). These likely tanning properties could lead to specific interactions regarding salivary proteins and might have an impact on mouthfeel/sensations more or less related to astringency perception [START_REF] Castillo-Fraire | Interactions between polyphenol oxidation products and salivary proteins : Specific affinity of CQA dehydrodimers with cystatins and P-B peptide[END_REF].

Conclusion

In a previous study, CQA dehydrodimers were synthesized in a biomimetic apple juice model solution [START_REF] Castillo-Fraire | Preparative fractionation of 5'-O-caffeoylquinic acid oxidation products using centrifugal partition chromatography and their investigation by mass spectrometry[END_REF]. After purification and characterization using UV-Visible spectra and MS n fragmentation, three hypothetical structures were proposed for nine of the ten dehydrodicaffeoyldiquinic acids [START_REF] Castillo-Fraire | Preparative fractionation of 5'-O-caffeoylquinic acid oxidation products using centrifugal partition chromatography and their investigation by mass spectrometry[END_REF].

In this study, we presented the structural confirmation of these hypotheses using 1D and 2D NMR spectroscopy. Four different structures were elucidated for dehydrodicaffeoyldiquinic acid compounds. Six of these CQA dehydrodimers corresponded to three different caffeicin-like skeletons: the dihydronaphtalene type for 705-1 and 705-1.1, the dihydrobenzofuran type for 705-3 and 705-4, and the dihydrobenzodioxane type for 705-5 and 705-6. Although our NMR data did not completely elucidate the stereochemistry of these molecules, the pairs of CQA oxidation products with the same skeleton are very likely stereoisomers resulting from the asymmetric C7' and C8' carbon centres. In addition, a phenolic structure corresponding to a symmetric dicatechol skeleton was highlighted for the first time as one of the dehydrodicaffeoyldiquinic acids resulting from CQA oxidative coupling.

Further studies are needed to better understand the relationships between structure and functional properties, regarding their contribution to organoleptic and nutritional qualities in apple-based beverages. chromatography coupled to electrospray ionisation ion trap mass spectrometry of phloroglucinol and 4-methylcatechol oxidation products to study the reactivity of epicatechin in an apple juice model system.

Journal

Figure 1 .

 1 Figure1

Figure 2 .

 2 Figure 2. A: Structure of products 705-3 and 705-4 corresponding to dehydrodicaffeoylquinic acids showing a dihydrobenzofuran-type structure; B: HMBC correlations of proton H7' where Q is quinic acid moiety.

Figure 3 .

 3 Figure 3. A: Structure of products 705-5 and 705-6 corresponding to dehydrodicaffeoylquinic acids showing a dihydrobenzodioxan-type structure; B: HMBC correlations of proton H7' where Q is a quinic acid moiety.

Figure 4 .

 4 Figure 4. A: Structure of products 705-1 and 705-1.1 corresponding to dehydrodicaffeoylquinic acids showing a dihydronaphthalene-type structure; B: HMBC correlations of proton H7' where Q is a quinic acid moiety.

Figure 5 .

 5 Figure 5. Proposed mechanisms for the formation of two hypothetical structures corresponding to product 705-2.

  Paz, J. E.,Muñiz-Márquez, D. B., Aguilar, C. N., Sotin, H., & Guyot, S. (2015). Enzymatic synthesis, purification and in vitro antioxidant capacity of polyphenolic oxidation products from apple juice. LWT -Food Science and Technology, 64(2), 1091-1098. https://doi.org/10.1016/j.lwt.2015.07.007

	of	Chromatography	A,	1179(2),	168-181.
	https://doi.org/10.1016/j.chroma.2007.11.083
	Weber, F., Engelke, G. H., & Schieber, A. (2019). Structure elucidation and tentative formation
	pathway of a red colored enzymatic oxidation product of caffeic acid. Food Chemistry,
	297(124932). https://doi.org/10.1016/j.foodchem.2019.05.206
	Wong-

Table 1 .

 1 Chemical shifts of protons ( 1 H) and carbon ( 13 C) for the seven CQA dehydrodimers analysed.

	osition	δC	705-1 δH M Hz	δC	705-1.1 δH M Hz	δC	705-2 δH M	Hz	δC	705-3 δH	M	Hz	δC	705-4 δH M	Hz
	1	125,81	-	-	-	125,8	-	-	-	131,4	-	-	-	128,45	-	-	-	128,52	-	-	-
	2	118,06 6,88 s	-	118,17 6,87 s	-	121,9 6,77	-	-	116,06 7,06	d	1,5	116,16 7,05 d	1,3
	3	146,48	-	-	-	146,42	-	-	-	147,2	-	-	-	141,64	-	-	-	141,5	-	-	-
	4	150,05	-	-	-	150,06	-	-	-	148,1	-	-	-	149,36	-	-	-	149,24	-	-	-

H-13 C HMBC spectrum showed that proton H7' was also correlated with nine carbons (Figure4B).

118,16

6,56 s -117,85 6,5 s -117,3 6,77 --126,2 ---126,33 ---

Acknowledgments

We are grateful to the P2M2 platform from the GIS Biogenouest (Le Rheu, France) for providing equipment and technical support for the chromatographic analyses.

Part of this work was performed using the PRISM core facility (Biogenouest©, UMS Biosit, Université de Rennes 1-Campus de Villejean-35043 RENNES Cedex, FRANCE).

Funding sources

The authors wish to thank the Mexican Council for Science and Technology (CONACYT) (556831) for their financial support of a student via a graduate scholarship.


Nwigbo Kenule Tuador

Pham Duong Hung

Varray François

Basarab Adrian

Kouame Denis

BLOCK-WISE 3D ULTRASOUND IMAGE SUPER-RESOLUTION

Keywords: 3D ultrasound image super-resolution, homomorphic filtering, ADMM

This paper addresses the problem of 3D ultrasound (US) single image super-resolution (SR), i.e., recover a high-resolution volume from its blurred, decimated, and noisy version. A new 3D US SR technique based on a linear forward model is studied by taking into account the axial variability of the point spread function (PSF) within a block-wise recovery process. The PSF is estimated using a recent algorithm along the axial direction with the assumption that it is isotropic in the other two spatial directions. By exploiting the linear image formation model, a cost function is constructed from a data fidelity term penalized by an l1-norm regularization function imposing the sparsity of the solution. Numerical results show the efficiency of the proposed method when compared to the observed image.

INTRODUCTION

3D single image super-resolution (SR) has attained increasing interest from the medical imaging community in the last few years. It can indeed be encountered in a wide range of applications e.g., brain magnetic resonance imaging analysis [START_REF] Pham | Multiscale brain MRI super-resolution using deep 3D convolutional networks[END_REF], cardiac applications [START_REF] Oktay | Multi-input cardiac image super-resolution using convolutional neural networks[END_REF] or dental cone beam computed tomography [START_REF] Hatvani | Deep learning-based super-resolution applied to dental computed tomography[END_REF]. The main goal of 3D-SR methods is to recover a 3D high-resolution (HR) image from its acquired low-resolution (LR) counterpart, enabling a better image visualization and content analysis [START_REF] Park | Super-resolution image reconstruction: a technical overview[END_REF]. Many related works have been proposed in the literature, among which learning-based approaches and those based on linear image formation models are the most common. The former typically rely on convolutional neural networks whose parameters are obtained by a training process that makes a connection between LR images and corresponding HR images [START_REF] Pham | Multiscale brain MRI super-resolution using deep 3D convolutional networks[END_REF][START_REF] Oktay | Multi-input cardiac image super-resolution using convolutional neural networks[END_REF][START_REF] Hatvani | Deep learning-based super-resolution applied to dental computed tomography[END_REF]. Unfortunately, these learning-based approaches have a very high computational complexity while the training process generally requires a large dataset which is not always available in many practical situations. Instead, the latter formulate the SR image as an inverse image restoration problem. It consists in minimizing a cost function including regularizations such as total variation (TV) [START_REF] Toma | Total variation super-resolution for 3D trabecular bone micro-structure segmentation[END_REF], low-rank [START_REF] Shi | Lrtv: Mr image super-resolution with low-rank and total variation regularizations[END_REF] or wavelet domain-based sparsity [START_REF] Zhang | Image interpolation by adaptive 2-D autoregressive modeling and soft-decision estimation[END_REF]. In spite of their interest, these methods have many significant drawbacks such as an unsuitability to spatial variability of the point spread function (PSF), a high computational burden, and the fact that 3D volumes are unfolded into either 2D matrices or 1D vectors resulting in information loss on adjacent voxels.

To mitigate these limitations, inspired by our recent modelbased work for 3D SR problem developed in [START_REF] Tuador | A novel fast 3D single image super-resolution algorithm[END_REF], we introduce, in this paper, a novel fast 3D ultrasound (US) SR method based on a non-unfolding technique and a block-wise approach, leading to an HR block-wise (BW) super-resolved image. More precisely, the non-unfolding technique consists in handling simultaneously the associated decimation and blurring operators. It is based on studying their intrinsic properties in the frequency domain that enables a computational cost reduction, while the BW approach takes into account the variation of the PSF in the axial dimension. This proposed method is denoted by 3D BW-SR in the sequel.

The remaining part of this paper is structured as follows. In Section 2, we introduce a US image formation model and its associated 3D SR technique. Then, Section 3 outlines the 3D BW-SR method. Section 4 presents the numerical results on experimental data. Finally, conclusions and future works are given in Section 5.

BACKGROUND

Ultrasound image degradation model

This paper investigates an SR problem applied to 3D US imaging. Assuming linear US wave propagation, under the first Born approximation, post-beamformed radiofrequency (RF) images are expressed as a convolution between a spatially variant PSF and the tissue reflectivity function (TRF) to be recovered [START_REF] Ng | Modeling ultrasound imaging as a linear, shiftvariant system[END_REF][START_REF] Jensen | Field: A program for simulating ultrasound systems[END_REF][START_REF] Jensen | Calculation of pressure fields from arbitrarily shaped, apodized, and excited ultrasound transducers[END_REF]. In order to deal with the low-resolution nature of the acquired images, we introduce a decimation operator D. In the following, we simplify this model by assuming an invariant PSF within an image block, which locally leads to the US image formation model [START_REF] Tuador | A novel fast 3D single image super-resolution algorithm[END_REF]:

y = DHx + n, (1)
where

y ∈ R N l (N l = m l × n l × s l ) is an observed block extracted from the 3D RF volume, x ∈ R N h (N h = m h × n h × s h )
is the TRF to be estimated and n is an additive white Gaussian noise with variance σ 2 , all arranged in lexicographical order with N h and N l being the number of image samples in x and y respectively. H is assumed to be block circulant with circulant blocks which accounts for the 3D convolution with the PSF and together with its conjugate transpose H H can be decomposed as [START_REF] Hansen | Deblurring Images[END_REF]:

H = F H ΛF and H H = F H Λ H F. (2)
In ( 1), Hx is decimated by the operator D with an integer rate of d = dr × dc × ds, i.e., N h = N l × d. The pixel resolution loss in each spatial direction between the observed RF volume and the TRF are dr, dc and ds which satisfies m h = m l × dr, n h = n l × dc and s h = s l × ds.

Super-resolution problem formation

The main purpose of this work is to estimate the TRF from RF image as established in the model [START_REF] Pham | Multiscale brain MRI super-resolution using deep 3D convolutional networks[END_REF]. From a Bayesian viewpoint, one can estimate the TRF by using the standard maximum a posteriori (MAP) estimator by maximizing the posterior distribution

p(x|y) ∝ p(y|x)p(x), (3)
where p(x) is the prior probability density function of x and the like- lihood function p(y|x) is given by:

p(y|x) ∼ N (DHx, σ 2 IN l ), (4)
where N stands for the Gaussian distribution and IN l is the identity matrix of size N l × N l . The negative log-posterior of x is given by:

-log p(x|y) ∝ 1 2 ||y -DHx|| 2 2 data fidelity term + log(p(x)) regularization term . ( 5
)
Considering a sparse assumption on the TRF, which is in consistency with a Laplace prior resulting into an l1 regularization term, x can be estimated by solving the following optimization problem:

x = argmin x 1 2 ||y -DHx|| 2 2 + λ||x||1, (6)
where λ > 0 is a hyper-parameter that weights the compromise between data fidelity term and the sparse regularization term. In what follows, we present an efficient algorithm to solve [START_REF] Shi | Lrtv: Mr image super-resolution with low-rank and total variation regularizations[END_REF], whose numerical implementation is referred to as a 3D-fast SR (3D-FSR) algorithm and denoted by 3D-FSR-l2-l1.

PROPOSED 3D BLOCK-WISE SUPER-RESOLUTION

In this section, we formally present the technique used in handling the SR problem presented in Section 2.2. The method used in this study accounts for a stationary PSF in each image block. Firstly, the beamformed 3D RF image is split into n overlapping axial blocks, having n 3D PSFs to be estimated at n different depths from the RF image (see Fig. 1). Secondly, we obtain the solution of (6) (3D-FSR-l2-l1) for each block. Finally, we present the proposed 3D BW-SR algorithm after which the super-resolved images from each block are merged to obtain the desired TRF as highlighted in Fig. 2.

3D PSF estimation

H operator is formed based on a 3D PSF estimated as follows. First, a 2D PSF is estimated from the central 2D slice extracted from the current block, using the method in [START_REF] Michailovich | Iterative reconstruction of medical ultrasound images using spectrally constrained phase updates[END_REF][START_REF] Pham | Joint blind deconvolution and robust principal component analysis for blood flow estimation in medical ultrasound imaging[END_REF]. Second, this resulting 2D PSF is extended to a 3D PSF based on the assumption that it is isotropic in the azimuthal and lateral directions, which is a reasonable hypothesis for images acquired with a 2D matrix probe.

3D Fast SR with l1-norm regularization

To efficiently solve ( 6), we propose to use an algorithm based on an alternating direction method of multipliers (ADMM) scheme [START_REF] Boyd | Distributed optimization and statistical learning via the alternating direction method of multipliers[END_REF]:

(x, û) = argmin x,u 1 2 ||y -DHx|| 2 2 + λ||u||1 subject to x = u. (7)
The associated augmented Lagrangian function is

L(x, u, d) = 1 2 y -DHx 2 2 + λ u 1 + µ 2 x -(u -d) 2 2 . ( 8
)
For the linear constraints, µ is the penalty parameter and d is the Lagrangian multiplier. ADMM minimizes (8) by iteratively solving subproblems over the variable x using our recent approach for fast 3D SR based on handling concurrently the decimation and blurring operators in the Fourier domain [START_REF] Tuador | A novel fast 3D single image super-resolution algorithm[END_REF], then u using vector soft thresholding and updating the scaled dual variable d:

For i = 0, . . .       x i+1 = argmin x 1 2 ||y -DHx|| 2 2 + µ 2 ||x -(u i -d i )|| 2 2 u i+1 = argmin u λ||u||1 + µ 2 ||x i+1 -(u -d i )|| 2 2 d i+1 = d i + (x i+1 -u i+1 ) (9)

Proposed 3D BW-SR algorithm

The resulting algorithm able to solve efficiently the SR problem for each image block in the RF image is given in Algorithm 1.

As a result, n RF restored images are estimated using the SR algorithm above applied to blocks extracted from the RF volume, with the n estimated PSFs (see Fig. 1). Ideally, these restored images should be merged to produce the final restored TRF but this might incur some sewing effect. In order to avoid this issue, we defined for each PSF a corresponding weighting function wj which reaches its maximum at the depth where the jth PSF is estimated [START_REF] Varray | Hybrid strategy to simulate 3-D nonlinear radio-frequency ultrasound using a variant spatial psf[END_REF]. As Algorithm 1: 3D-FSR-l2-l1

Input: Observed image y, blurring operator H, decimation operator D and factor R, λ Initialize:

Set i = 0, choose λ > 0, µ > 0, d 0 , u 0 1. Compute Λ: Λ = (1 T ds ⊗ Is l ) ⊗ (1 T dc ⊗ In l ) ⊗ (1 T dr ⊗ Im l ) Λ ⊗:
Kronecker product and 1 * : matrices of ones.

2. while stopping criterion is not satisfied do a.

Update x as in [START_REF] Tuador | A novel fast 3D single image super-resolution algorithm[END_REF]:

Determine k: k = F H Λ H FD H y + µ(u i -d i ) Entrywise product: x f = Λ H (µrIN l + ΛΛ H ) -1 ΛFk x i+1 = 1 µ (k -F H x f ) b.
Update u using the soft-thresholding operator (denoted as soft [START_REF] Chen | Reconstruction of enhanced ultrasound images from compressed measurements us-ing simultaneous direction method of multipliers[END_REF]):

u i+1 = soft λ||u|| 1 µ (x i+1 + d i ) c. Update d: d i+1 = d i + (x i+1 -u i+1 ); Output: x = x i .
illustrated in Fig. 2, continuous windows along the z-axis are used to define the amplitudes of the different weights which are normalised. Finally, the restored TRF T is obtained by merging the n restored images following linear combinations:

T = n j wjxj, (10)
where xj is the result in the region of the jth PSF [START_REF] Varray | Hybrid strategy to simulate 3-D nonlinear radio-frequency ultrasound using a variant spatial psf[END_REF].

NUMERICAL RESULTS

The performance of the proposed method is evaluated on a real dataset, acquired using 4 synchronized Verasonics Vantage systems and a 3D 1024 elements probe [START_REF] Petrusca | Fast volumetric ultrasound b-mode and doppler imaging with a new high-channels density platform for advanced 4d cardiac imaging/therapy[END_REF]. 81 titled plane waves were transmitted on a commercial phantom containing three wires with a 3 MHz sinusoidal excitation. The proposed method was tested on the post-beamforming resulting RF volume as described hereafter.

In this experiment, the RF image was divided into three blocks for both PSF estimation and block-wise image recovery process. The solution of the proposed 3D BW-SR method was compared to the observed image. As a metric of spatial resolution, the full width at half maximum (FWHM) computed around the wire locations was calculated. The results of this experiment are all shown in Fig. 3. Visually judging these plots, the SR result in Fig. 3 (b) obtained by 3D BW-SR shows a superior improved spatial resolution over the observed image in Fig. 3 (a). Quantitatively, we computed FWHM values at different depths of the three wires in both the observed image and the 3D BW-SR solution, respectively, and their gains (gains FWHM = FWHMobserved/FWHM3D BW-SR). The quantitative results are reported in Fig. 3 (c). They demonstrate the advantage of the proposed algorithm, which is consistent with the above qualitative observation about the SR performance of the studied techniques.

CONCLUSIONS

The main goal of this paper was to study the role of a non-stationary PSF in the restoration of TRF from the RF image. The problem was formulated as an SR problem in which a PSF estimation step was implemented in a preprocessing step. In this work, allowing the spatial variability of the PSF to be considered, an efficient blockwise restoration approach was presented. The 3D BW-SR herein does not present sewing artifacts, and is easy to implement. Further work can be devoted to jointly estimate the PSF and the TRF as a generalization of the method and to the case of non-isotropic PSF.

FWHM measures

Positions in depth FWHMobserved FWHM3D

Fig. 1 .

 1 Fig. 1. Example of PSF estimation and image super-resolution using three estimated PSFs.

Fig. 2 .

 2 Fig. 2. The block weight principle and the weight functions wj corresponding to various PSFs as a function of depth.

Fig. 3 .

 3 Fig.3. Real data experiment: (a) observed image, (b) SR result using the proposed 3D BW-SR algorithm, (c) the FWHM measures for each wire at each depth in both observed image and the 3D BW-SR solution, and their gains. Note that these are slices from the central axial direction of each resolution.

ACKNOWLEDGMENTS

This work has been supported by the PTDF overseas scholarship under the government of Nigeria. It was also performed within the framework of the LABEX PRIMES (ANR-11-LABX-0063) of the Université de Lyon, within the programme 'Investissements d'Avenir' (ANR-11-IDEX-0007), operated by the French National Research Agency (ANR). This material is based upon work done on the PILoT facility (PILoT, INSA-Lyon).