Hernan Carrillo
email: hernan.carrillo-lindado@labri.fr

Michaël Clément
email: michael.clement@labri.fr

Aurélie Bugeau
email: aurelie.bugeau@labri.fr

Non-local matching of superpixel-based deep features for color transfer

Keywords: Superpixels, Attention mechanism, Color transfer, High-resolution features, Non-local matching

In this article, we propose a new method for matching high-resolution feature maps from CNNs using attention mechanisms. To avoid the quadratic scaling problem of all-to-all attention, this method relies on a superpixel-based pooling dimensionality reduction strategy. From this pooling, we efficiently compute nonlocal similarities between pairs of images. To illustrate the interest of these new methodological blocks, we apply them to the problem of color transfer between a target image and a reference image. While previous methods for this application can suffer from poor spatial and color coherence, our approach tackles these problems by leveraging on a robust non-local matching between high-resolution low-level features. Finally, we highlight the interest in this approach by showing promising results in comparison with state-of-the-art methods.

INTRODUCTION

Non-local operators were introduced in image processing in [START_REF] Buades | A nonlocal algorithm for image denoising[END_REF] with the so-called Non-local means framework, initially used to filter out image noise by computing a weighted mean of all pixels in an image. Non-local means allow remote pixels to contribute to the filtered response, achieving less loss of details. It was then extended to nonlocal features matching for super-resolution [START_REF] Glasner | Superresolution from a single image[END_REF], inpainting [START_REF] Wexler | Spacetime video completion[END_REF], or color transfer [START_REF] Giraud | Superpixelbased color transfer[END_REF] proving to achieve robust global features similarities.

Non-local ideas have recently been introduced within neural networks architectures [START_REF] Wang | Nonlocal neural networks[END_REF] [START_REF] Yu | Generative image inpainting with contextual attention[END_REF]. The computation of nonlocal similarities in neural networks is related to socalled attention mechanisms [START_REF] Bahdanau | Neural machine translation by jointly learning to align and translate[END_REF]. This attention block learns to compute similarities between input embeddings or data sequences. Lately, attention mechanisms have been popularised with the rise of transformers [START_REF] Vaswani | Attention is all you need[END_REF], i.e., endto-end neural network architectures that include only (self-)attention layers. Transformers compute nonlocal similarities between multi-level feature maps. This type of architecture succeeds as a state-of-theart method due to the capacity and flexibility of these attention blocks. The recent work [START_REF] Wang | Nonlocal neural networks[END_REF] has bridged the gap between the self-attention mechanism and non-local means. They stated that the selfattention mechanism captures long-range dependencies between deep learning features by considering all features into the calculation.

Recently, the authors of [START_REF] Zhang | Deep exemplar-based video colorization[END_REF] presented similarity calculation between different feature maps (target and reference images) based on attention mechanism for image colorization. The principal drawback of such mechanism is the complexity of the non-local operation, which has to be done on features with low dimensions due to computational burden. This is known as the quadratic scaling problem. However, low-resolution features usually do not carry sufficient information for calculating precise pixelwise similarities. For instance, deep features mainly carry high-level semantic information related to a specific application (i.e., classification) that can be less relevant for high-resolution similarity calculation or matching purposes.

In this paper, we compute similarities between high-resolution deep features obtained from pretrained convolutional neural networks, as this retains rich low-level characteristics. Due to the dimensionality issue, we exploit existing superpixels extractor in order to match these high-resolution features. To illustrate the interest of this super-features matching operation, we apply it to the problem of color transfer. Color transfer aims at changing the color charac-teristics of a target image by copying the ones from a reference image. Ideally, the result must reach a visually pleasant image, avoiding possible artifacts or improper colors. It covers various applications in areas such as photo enhancement, films post-production, and artistic design. Transferring the right colors requires computing meaningful similarities between the reference and the target images. These similarities must preserve important textures and structures of the target image. Therefore, we will show that highresolution features are essential.

The contributions are: 1) we propose the superfeatures encoding block, which extracts deep feature maps using superpixel decomposition; 2) we propose a robust non-local similarity between superfeatures using an attention mechanism; and 3) we build upon [START_REF] Giraud | Superpixelbased color transfer[END_REF] and include these similarities in a non-local color fusion framework, achieving promising results on several target and reference image pairs.

RELATED WORK

Superpixels

Exploiting superpixel representation allows finding interesting region's characteristics in images, such as color and texture consistency [START_REF] Achanta | SLIC superpixels compared to state-of-the-art superpixel methods[END_REF]. Many advantages can be derived using this type of decomposition, for instance, dimensionality reduction by grouping pixels with similar characteristics [START_REF] Van Den Bergh | SEEDS: Superpixels extracted via energydriven sampling[END_REF]. Additionally, this compact representation helps to overcome high computational costs on computer vision tasks such as object segmentation [START_REF] Tighe | Superparsing: Scalable nonparametric image parsing with superpixels[END_REF] or object localization [START_REF] Fulkerson | Class segmentation and object localization with superpixel neighborhoods[END_REF]. However, the irregular form of the representation makes its usage difficult in computer vision tasks, especially the ones using deep learning approaches. Nevertheless, some works have proposed some representation to cope with this issue. For instance, [START_REF] Ihsan | Superpixels features extractor network (SP-FEN) for clothing parsing enhancement[END_REF] uses a superpixel label map as an input image to a neural network to extract meaningful information for clothing parsing application. [START_REF] He | SuperCNN: A superpixelwise convolutional neural network for salient object detection[END_REF] presents the SuperCNN as a deep neural network approach for salient object detection. It uses superpixels to describe two 1-D sequences of colors in order to reduce the computational burden. Nonetheless, neither of the existing approaches effectively encodes deep learning features for each superpixel.

Color transfer

Transferring the right colors requires computing meaningful similarities between the reference and the target images. These similarities must preserve important textures and structures of the target image. Most works on color transfer have focused on choosing the characteristics on which to compute similarities. These characteristics can be hand-crafted or learned using deep learning methods. The first one extracts image features by relying on manually predefined descriptors (i.e., HOG [START_REF] Dalal | Histograms of oriented gradients for human detection[END_REF], SIFT [START_REF] Lowe | Distinctive image features from scaleinvariant keypoints[END_REF])); however there is no guarantee that the descriptors are well suited for the task. The second solves this issue by learning the features from image dataset and leveraging on a training procedure, nonetheless feature dimensionality increases enforcing the usage on low-resolution images. Features similarities can be matched using global information of the images (i.e., color histograms); or local information such as matching small regions on the images (i.e., cluster segmentation, superpixel decomposition). In the literature, color transfer techniques can be classified into three classes: classic global-based methods, classic local-based methods, and deep learning methods.

Global methods consider global color statistics without any spatial information. It was initially introduced in [START_REF] Reinhard | Color transfer between images[END_REF] which uses basics statistical tools (i.e., mean, standard deviation) to match target and reference color information. (Pitié and Kokaram, 2007) [START_REF] Xiao | Color transfer in correlated color space[END_REF] extend color matching on different color spaces to find an optimal color mapping between the images. [START_REF] Frigo | Optimal transportation for example-guided color transfer[END_REF] [START_REF] Ferradans | Regularized discrete optimal transport[END_REF] propose a global illuminant matching based on optimal transport color transfer for enforcing artifacts-free results. More complex methods such as [START_REF] Murray | Toward automatic and flexible concept transfer[END_REF] rely on Gaussian Mixture Models to create compressed signatures that ensure a compact representation of color characteristics between images. Nevertheless, as mentioned in [START_REF] Pitié | Advances in colour transfer[END_REF], these methods fail to ensure spatial consistency on resulting colors when content change (i.e., transferring day and night images).

Local methods relies on spatial color mappings (i.e., segmentation, clustering) to match local regions of the target image and the reference image. [START_REF] Liu | Photo stylistic brush: Robust style transfer via superpixelbased bipartite graph[END_REF] uses superpixel level style-related and style-independent feature correspondences. [START_REF] Arbelot | Local texture-based color transfer and colorization[END_REF] implement a texture-based framework for matching local correspondence. Alternatively, [START_REF] Tai | Local color transfer via probabilistic segmentation by expectationmaximization[END_REF] uses a probabilistic segmentation in order to impose spatial and color smoothness among local regions. Still, the method does not provide control over the matched superpixel. [START_REF] Giraud | Superpixelbased color transfer[END_REF] overcomes this limitation by proposing a constrained approximate nearest neighbor (ANN) patches and a color fusion framework on superpixels. However, in this type of local methods target and reference images requires to share strong similarities.

Deep learning methods brings to the matching semantic-related characteristics from the target image and reference image. Recently [START_REF] Lee | Deep color transfer using histogram analogy[END_REF] propose a deep neural network architecture that leverages on color histogram analogy for color transfer. The latter uses target and reference histograms as input to exploit global histogram information over a target input image. [START_REF] He | Progressive color transfer with dense semantic correspondences[END_REF] relies on semantically meaningful dense correspondence between images. Nonetheless, this type of methods relies on pure semantic features (low-level features), which leads to imprecise results if images from a different scene or instances are used.

METHOD

In this section, we present our superpixel based framework to match high-resolution features between two RGB images I T and I R of size R H×W ×3 . In the following, we will refer to I T as the target image and I R as the reference image to be consistent with the color fusion application.

Super-features encoding

Let f T and f R be feature maps from a convolutional neural network at layer of I T and I R respectively. In the following, we will consider features coming from pre-trained deep convolutional networks (see Figure 3), but our method could be applied to other types of hand-crafted features. More precisely, we focus on features extracted at the first three layers of a deep network, as they provide a long range of lowlevel features that suit diverse types of images. These feature maps then have high dimensions, typically the same size as the input image, times C channels with H ×W ×C where C = 64, 128 or 256 for example.

A critical drawback of using high-resolution features for matching operations is the high computational complexity. Let the number of features in a feature map be D = H × W × C, then the complexity of the pixel-wise similarity computation is O D 2 . To solve this quadratic complexity problem, we implement an encoding layer based on superpixel representation. We first generate a superpixel map using a superpixel decomposition algorithm on the initial color images. Let us denote the target superpixel map by This layer takes a reference feature map f R and a target feature map f T as an input, and outputs an attention map at superpixel level by means of a non-local operation.

Super-features matching

Our super-features provide a compact encoding to compute the correlation between high-resolution deep learning features. Here, we take inspiration from the attention mechanism [START_REF] Zhang | Deep exemplar-based video colorization[END_REF] to achieve a robust matching between target and reference superfeatures. The process is illustrated in Figure 2. Mainly, we exploit non-local similarities between the target and the reference super-features by computing the attention map at layer as:

A = softmax R (M T R /τ).
(1) The softmax R operation normalizes row-wise the input into probability distributions, proportionally to the number of target superpixels N R . Then, the final attention map A is the weighted sum of the attention maps at each layer :

A = ∑ 3 =1 ω A ∑ 3 =1 ω . (2)
The matrix M T R is a correlation matrix between the target and reference super-features and is computed as:

M T R (i, j) = (F T (i) -µ T ) • (F R ( j) -µ R ) F T (i) -µ T 2 F R ( j) -µ R 2 , (3)
where µ T and µ R are the mean of each super-feature. We found that this normalization keeps correlation values less sensitive to changes on τ for different images. The attention map (1) is the same nonlocal operator as the one proposed by [START_REF] Zhang | Deep exemplar-based video colorization[END_REF]. However, their computation requires lowresolution features due to the inherent quadratic complexity problem (as mentioned in Section 3.1). We solve this complexity problem thanks to our super-features encoding approach. Let n = H ×W be the number of pixels in an image. Then, the number of features in a deep learning feature map is D = n×C which translate into a computational complexity of O(D 2 ) = O(n 2 C 2 ). In contrast, with our novel superfeatures encoding, if we set the number of superpixels in the order of √ n, then instead we rewrite with

D s = √ n × C, resulting in O(D 2 s ) = O(n × C 2 ).

Application to color transfer

We now present our color transfer method. It consists of three blocks: 1) super-features encoding (SFE), 2) super-features matching (SFM), and 3) color fusion framework. The process is illustrated in Figure 3. Our objective is to transfer colors from a reference I R to a target image I T . Concretely, this will be done by passing colors from I R to I T based on pairwise feature-related similarities.

To match colors at superpixel level, we rely on the attention map A and the average of each superpixel color. Specifically, we apply our attention map as a soft-weight on the average colors, resulting in a smooth correspondence.

Figure 4 shows a direct super-features matching between the target and reference images from We can see that the probability distribution is over-smoothed (i.e., gray average colors) for larger values of τ (i.e., τ = 0.1), meaning that several reference super-features match one target super-feature. Otherwise, a small τ value results in a hard one-to-one matching between a target and reference super-features (i.e., τ = 1 × 10 -4 ).

Color fusion framework

Direct superpixel matching by averaging colors is not sufficient to obtain visually satisfying results. Image details are indeed lost at superpixel level (i.e., door, windows, etc., in Figure 4). Therefore we need to transfer color at pixel level from our superpixel matching.

For clarity in further equations, we denote the position and color centroids of a superpixel j in an image I as: X( j) = ∑ p∈S( j) p P j and Ī( j) = ∑ p∈S( j) I(p) P j respectively, where P j is the number of pixels in superpixel j.

Inspired by the formulation of [START_REF] Giraud | Superpixelbased color transfer[END_REF], we compute the new value ÎT (p) of each pixel p of the target as a weighted average of reference superpixel representative colors:

ÎT (p) = ∑ N R j=1 W (p, j) ĪR ( j) ∑ N R j=1 W (p, j) . ( 4
)
The weight matrix W depends firstly on the distance between pixel p and all target superpixel as in [START_REF] Giraud | Superpixelbased color transfer[END_REF], and secondly, on our attention map:

W (p, j) = N T ∑ i=1 d(p, i)A(i, j). (5)
The intuition behind the attention map is the addition of more relevant information about reference superfeatures into the transfer process. The distance between pixel p and superpixel centroids is computed over both positions and colors with a Mahalanobislike formulation: with position and color vectors being V (p) = [p, I(p)] and VT ( j) = [ XT ( j), ĪT ( j)], and the spatial and colorimetric covariances of pixels in superpixel i:

d(p, i) = e - (V T (p)-VT (i)) T Σ -1 i (V T (p)-VT (i)) σg , (6)
Σ i = δ 2 s Cov (p) 0 0 δ 2 c Cov (I(p)) . (7)
Parameters δ s and δ c weight the influence of color and spatial information, respectively. Finally, as in [START_REF] Giraud | Superpixelbased color transfer[END_REF], after color fusion we apply a post-processing step using a color regrain algorithm [START_REF] Pitié | Towards automated colour grading[END_REF], which eventually matches the color distribution of I R and the gradient of I T . Figure 5 presents an example of our color transfer framework compared to the result of [START_REF] Giraud | Superpixelbased color transfer[END_REF]. Visually, our results present better spatial consistency of colors. For instance, the sky on our results has more natural smooth color transitions compared to non-natural ones with [START_REF] Giraud | Superpixelbased color transfer[END_REF] (i.e., yellow to blue).

RESULTS

In this section, we first present the implementation details used to validate our method and then provide a detailed qualitative comparison between our results and three state-of-the-art color transfer approaches.

Implementation details

Superpixel segmentation is done using the SLIC algorithm [START_REF] Achanta | SLIC superpixels compared to state-of-the-art superpixel methods[END_REF], in which the number of superpixel depends on the actual size of the image. Experimentally, we set the number of superpixel as 6: Effect on direct super-features matching (i.e., before color fusion) using high-resolution feature maps (w/o downsampling) and using low-resolution feature maps (with downsampling). Target and reference images are presented in Figure 7.

×

√ n where n is the number of pixels in the current image.

To build feature maps, we rely on a modified pretrained VGG-19 [START_REF] Simonyan | Very deep convolutional networks for large-scale image recognition[END_REF] as our texture and color characteristics extractor, due to its simplicity and its 95.24% classification accuracy on the ImageNet Top-5 classes. The main modification was the removal of max-pooling layers from the first three levels (see Figure 3) as it highly improves matching results compared to using upsampling on max-pooled feature maps at Conv2 2 and Conv3 4 from the baseline VGG-19. Figure 6 exemplifies that matching low-resolution features does not preserve details nor retains color coherence, especially when going deeper into the architecture. Also, note that our approach can work with other types of CNN architectures regardless of their features dimensions.

In order to choose an optimal temperature τ value, we experimented on different images at distinct temperatures. Empirically, we obtain satisfying results using τ = 0.015 and ω = 1. In addition, all experiments have been run with δ s = 10 and δ c = 0.1, as recommended by [START_REF] Giraud | Superpixelbased color transfer[END_REF] to favor spatial consistency.

Analysis on different layers

Our SFE and SFM blocks support any CNN features map dimensions, so choosing to work with one or coupling many of these features maps depends mostly on the application. In this experiment, we analyze the Target

Reference

Layer 1 Layer 2 Layer 3

Figure 7: Results of our method using each of the three layers separately with τ = 0.015.

effects of using separately each of the first three feature map outputs for the color transfer application.

From the different columns of Figure 7 we can retain that each layer focuses on different aspects of the image, resulting in color variations of the same target image. Specifically, in the first row (house image), we can see that the deeper layer (layer 3) focuses on the grass color while the second layer focuses on the mountain color. In the second and third rows, layers 2 and 3 bring stronger colors from the reference image, but the results are still unrealistic. In the first layer, the recovered image seems more natural; however, most of the colors transferred from the reference image are opaque or not transferred.

Finally, we decided to combine all three layers as each of them brings important feature information to achieve pleasant and realistic images for this color transfer application.

Comparison

We compare our method against three approaches: (Pitié et al., 2007) which proposes an automated color transfer based on color distributions; [START_REF] Lee | Deep color transfer using histogram analogy[END_REF] which implements a color transfer approach based on color histogram analogy using a deep neural network; and [START_REF] Giraud | Superpixelbased color transfer[END_REF] which implements the color fusion framework by leveraging on its proper superpixel decomposition. All three mentioned approaches have been considered state-of-the-art in color transfer, and have open-source codes for a fair comparison. Each method has been run with its default parameters.

Results comparing the three methods are shown in Figures 8,9 and 10. Overall, our results (last column) have more visually pleasant colors and consistency in image texture, providing more realistic color transfers with respect to the other methods. Figure 8 shows that our approach correctly matches and transfers natural colors from indoor images, avoiding color bleeding (blue color on the wall) as shown in [START_REF] Giraud | Superpixelbased color transfer[END_REF], [START_REF] Lee | Deep color transfer using histogram analogy[END_REF] and partially in (Pitié and Kokaram, 2007) results. For outdoor images shown in Figure 9, we observe that (Pitié et al., 2007) and [START_REF] Lee | Deep color transfer using histogram analogy[END_REF] can suffer from oversaturation of the illumination on some of their results (first, fourth, sixth images). Although this problem does not appear in [START_REF] Giraud | Superpixelbased color transfer[END_REF]) some of its results present visible unnatural effects on sky colors such as a halo effect (first image) and yellowish marks (fifth, sixth images). Our results for outdoor images overcome these issues thanks to the robust matching on high-resolution superpixel deep features, which ensures color consistency and spatially coherent colors across the resulting images. Figure 10 presents images with no background (studio shooting like images). In this case, results by (Pitié et al., 2007) and [START_REF] Lee | Deep color transfer using histogram analogy[END_REF] show unnatural color effects around the bottle and background. On the other hand, [START_REF] Giraud | Superpixelbased color transfer[END_REF] approach and ours achieve pleasant color results without over-saturation nor artifacts on the resulting image. Lastly, our method correctly transfers colors to the statue image resulting in the most visually satisfying and realistic results with regards to all compared methods. Target Reference (Pitié et al., 2007) [START_REF] Giraud | Superpixelbased color transfer[END_REF] [START_REF] Lee | Deep color transfer using histogram analogy[END_REF] Ours

CONCLUSION

This paper proposed the novel super-features encoding block (SFE) and the super-features matching (SFM) block that successfully encodes and matches high-resolution deep learning features from different images using superpixel decomposition. We validate these two blocks on the problem of color transfer; for doing that, we update the color fusion framework initially proposed by [START_REF] Giraud | Superpixelbased color transfer[END_REF] to consider our attention map, which provides texture and color knowledge from the reference image onto the final color transfer step. Finally, our method achieves more visually consistent and realistic results in compari-

Target

Reference (Pitié et al., 2007) [START_REF] Giraud | Superpixelbased color transfer[END_REF]) [START_REF] Lee | Deep color transfer using histogram analogy[END_REF]) Ours

Figure 1 :Figure 2 :

 12 Figure 1: Diagram of our super-features encoding proposal (SFE). This proposal takes as input a feature map of size H × W × C, in which each superpixel is extracted and encoded in vectors of size C ×P i pixels. Afterward, the vectors are pooled channel-wise and, finally, stacked in the superfeatures matrix F with size C × N number of superpixels.S T , and the reference one by S R . Each of these maps contains N T and N R superpixel respectively with P i pixels each, where i is the superpixel index. Next, we extract features of size C × P i for each superpixel. These extracted features are then pooled spatially by averaging channel-wise and stacked as a matrix of size C ×N called super-features F. Figure1illustrates this process. To sum up, the initial feature maps ( f T and f R ) pass from size H × W × C to super-features encoding (F T l and F R l ) of size N T × C and, N R × C, making feasible operations such as correlation calculation between large deep neural networks features.

Figure 3 :

 3 Figure3: Diagram of our method using the first three levels of a modified VGG-19 architecture as our feature extractor. In our method, we remove max-pooling layers from the baseline VGG-19 architecture to capture similarities between high-resolution feature maps (H ×W ×C ). Also, the diagram presents our two new blocks, the super-features encoding block (SFE) and the super-features matching block (SFM).

Figure 4 :

 4 Figure4: Direct super-features matching using different τ values. Each of the rows depicts our results for direct matching using super-features from the first, second, and third layers. The use of the first-level features helps to preserve fine details and ensures color consistency. However, the second and third layers bring a more colorful and diverse matching between target and reference super-features.

Figure 5 :

 5 Figure 5: Color fusion framework results. (a) (Giraud et al., 2017) color fusion result. (b) Our color fusion result. (c) (Giraud et al., 2017) result + regrain. (d) Our result + regrain. The regrain algorithm is from[START_REF] Pitié | Towards automated colour grading[END_REF].

Figure

  Figure6: Effect on direct super-features matching (i.e., before color fusion) using high-resolution feature maps (w/o downsampling) and using low-resolution feature maps (with downsampling). Target and reference images are presented in Figure7.

Figure 8 :

 8 Figure8: Comparison of color transfer results on indoor images. We compare our method with three different state-of-the-art approaches:(Pitié et al., 2007) color distribution grading,[START_REF] Giraud | Superpixelbased color transfer[END_REF] color fusion based on superpixel representation and,[START_REF] Lee | Deep color transfer using histogram analogy[END_REF] deep learning-based color histogram analogy.

Figure 9 :

 9 Figure 9: Comparison of color transfer results on outdoor images.

Figure 10 :

 10 Figure 10: Comparison of color transfer results on images with no background.

Convolution + ReLU + BN VGG-19 pre-trained weights SFE Color Fusion Reference image Target image Output image Conv 1_1 Conv 1_2 Conv 2_1 Conv 2_2 Conv 3_1 Conv 3_2 Conv 3_3 Conv 3_4 H x W x 64 H x W x 128 H x W x 3 H x W x 3 H x W x 64 H x W x 128 SFM SFM SFM H x W x 256 H x W x 256

ACKNOWLEDGEMENTS

This study has been carried out with financial support from the French Research Agency through the Post-ProdLEAP project (ANR-19-CE23-0027-01).

APPENDIX

Figure 11 shows additional resulting images from the three state-of-the-art methods and our method.


Laurent Bollinger
email: laurent.bollinger@cea.fr

Kristel Le Dortz

Clara Duverger

Amaury Vallage

Sylvie Marin

Yves M Leroy

Seismic swarms in Tricastin, lower

The Tricastin region, in the lower Rhône Valley (France), is affected by an atypical seismic activity characterised by the development of long-lasting and recurrent seismic swarms. Indeed, since the 16th century, hundreds of seismic events sometime associated with underground noises of explosion have been reported by local inhabitants. However, to date, none of the many scenarios of earthquake generation proposed for the area, involving either tectonics and/or hydrological forcings, appears consensual. To overcome that lack of comprehension, we compile and analyse a 880 seismic-events catalogue derived from both historical macroseismicity and instrumental records (Figure 1 to 6). The earthquakes appear occurring at shallow depths (Figure 6) possibly similar to those determined below a local network in 2002-2003(Thouvenot et al., 2007)). We confront to this catalogue models involving hydrological mechanisms, including aquifers elastic loading and karst-drains responses, as well as tectonic mechanisms, including transient aseismic processes and their related effects on the fold hinges or on the local fault planes (Figure 7-8 and Table 1). Most of the earthquakes are located at short distances from karst drains and fractured fold hinges, possibly affected by transient hydrological changes. 1783) and Rothé, 1936Rothé, , 1939a)). The double arrows correspond to the period of operation of the temporary Mainka-SOM seismographs installed by the BCSF in Les Granges-Gontardes (Figure 4). The thin lines represent the most important events for which an epicentral intensity has been determined or interpreted from archives. b-Cumulated number of seismic events (black curve) in FCAT17 catalogue [START_REF] Manchuel | The French seismic CATalogue (FCAT-17)[END_REF] complemented by the LDG catalogue from 2010 (Duverger et al., 2021). The plot starts in 1750 for a better visual appreciation of recent years, but 6 events are reported before, starting in 1173. The right-axis presents the moment magnitude (Mw) of events (orange circles) and the number of events per decade in the catalogues (grey bars). The inset is the depth histogram of events.

Figure 1 :

 1 Figure 1: Simplified geological and seismicity map of the Tricastin region. Historical and instrumental seismicity (circles, coloured according to their date of occurrence) from FCAT17 catalogue (Manchuel et al., 2018) co m p l e m e nte d w i t h t h e L D G catalogue (Duverger et al., 2021). Many other historical events were felt by the population but they are not recorded in the database because no epicentre were determined. See Figure 2 for further information about the location of every swarm compared to the geological structures, as well as the paleocourse of the Rhône River and tributaries. Geology and faults in black are from the BRGM 1:1000000 geological map and field observations. Faults in red and orange are from the B a s e d e D o n n é e de F a i l l e s potentiellement Active (BDFA), the Database of Potentially Active Faults (Jomard et al. 2017). Cross sections AA' and BB' are reported on figure 6 .Ye l l o w sta r a n d t h i c k l i n e respectively for Le Teil earthquake epicentre (from seismological records and InSAR) and fault surface rupture. Red arrows represent the orientation of the Maximum horizontal stress (SHMax) from Heidbach et al., 2018.

Figure 2 :

 2 Figure 2 : Close up view on the geology of the north-eastern part of the Tricastin region showing up: two major anticlinal structures in red arrows (the Donzère fold to the North, and the Echavarelles fold to the South); the position of the Messinian paleocanyons in thick blue dashed lines; the depth of the roof of the Urgonian in drill hole in red hexagons. Thick red dashed ellipses represent the approximate location of the seismic swarms derived from the macroseismic documentations. The black stars correspond to the locations where the local inhabitants though the noises were coming from.

  Figure 3 : Maximum intensities observed in the Tricastin villages for a) 1772-1773 b) 1873-1875 or 1876 c) 1907-1910 and d) 1934-1936 crises. Intensities are from the SisFrance database and interpreted in MSK64 scale. The Yellow circles for intensity I correspond to events that were felt b u t f o r w h i c h n o intensities were assessed. W h i t e c i r c l e s fo r intensities 0 correspond to non-felt events and are only available for the 1933-1936 crises for which macroseismic forms were s e n t t o t h e l o c a l administrations by the B u r e a u C e n t r a l Sismologique Francais (BCSF).

Figure 4 :

 4 Figure 4 :Left: Mainka-Som seismograph at Les Granges-Gontardes. Right: example of seismic signals recorded at the station in 1934

Figure 5

 5 Figure5: a)-Cumulated number of seismic events for the 1772-1773 (red curve) and 1934-1936 (blue curve) crises, starting from the first event of each crisis (sources: SisFrance, 2021; Faujas de St Fond (1783) andRothé, 1936Rothé, , 1939a)). The double arrows correspond to the period of operation of the temporary Mainka-SOM seismographs installed by the BCSF in Les Granges-Gontardes (Figure4). The thin lines represent the most important events for which an epicentral intensity has been determined or interpreted from archives. b-Cumulated number of seismic events (black curve) in FCAT17 catalogue[START_REF] Manchuel | The French seismic CATalogue (FCAT-17)[END_REF] complemented by the LDG catalogue from 2010(Duverger et al., 2021). The plot starts in 1750 for a better visual appreciation of recent years, but 6 events are reported before, starting in 1173. The right-axis presents the moment magnitude (Mw) of events (orange circles) and the number of events per decade in the catalogues (grey bars). The inset is the depth histogram of events.

Figure 6 :

 6 Figure 6 :Comparison of observed and predicted intensities for the 08/08/1873 -Châteauneuf -du -Rhône, 12/05/1934 and 16/05/1934 -Valaurie earthquakes. Observed MSK1964 intensities are from SisFrance (2021) and predicted MSK1964 intensities for different magnitudes (colored curves) are obtained using Marin et al. (2004) attenuation lawand Baumont et al. (2018) IPEs, respectively in ML and in Mw. An empty circle with arrow means that the event was felt but no intensity determined. The observed intensity I might thus be equal to II or greater. The intensity distribution is consistent with shallow hypocentral depths, according to the predicted intensity attenuation deduced from the attenuation law. The grey band corresponds to a range of distances outside the domain of validity of Marinet al., 2004.

Figure 7

 7 Figure 7 :a) Schematic North-South cross-section of the Donzère anticline, interpreted as a fault-propagation fold. b) Schematic East-West cross-section of the Tricastin,through Clansayes and the Echavarelles anticline modified from Gratier et al. (2013). c) Distribution of the scalar of the distance to the Coulomb criteria varying from 0 (dark blue) to 1 (dark red). The right plots show the definition of the distance to the Coulomb criterion (e) and of the scaled distance to the criterion (d). When d=1, e is more than 1% of the cohesion, far from the failure criterion, while when d=0, the Coulomb criterion is satisfied.

Figure 8 :

 8 Figure 8: Schematic West-East cross-section of the Tricastin region (vertical exaggeration of 5). a) A schematic karstic network is drawn in dark blue. Orange dots correspond to the depth distributions of relocated earthquakes from the 2002-2003 crisis at (from Thouvenot et al., 2009). The Rhônes paleocanyon is represented in brown and the present Rhône River and canal in blue. b) and c) illustrate the input parameters of the models.

Table 1. Calculations of the Coulomb stress variations (ΔS) resulting from the changes in water thickness. These calculations have been done 1/ on fault planes similar to the post-Oligocene fault planes observed in the field, and 2/ on the preferential rupture planes deduced from the examination of the regional stress field from focal mechanisms, taking a friction coefficient of 0.6.


Sami Yangui

Andrzej Goscinski

Khalil Drira

Zahir Tari

Djamal Benslimane

Samiyangui

Future generation of service-oriented computing systems

Keywords:

published or not. The documents may come   L'archive ouverte pluridisciplinaire

Introduction

Distributed Computing has arrived when two processes executing on two different platforms started to communicate using Message Passing or Remote Procedure Calls. A need for innovation followed the initial major step in Computing by problems of heterogeneity and low level of communication abstraction, that of the Internet. An initial response was provided by service-oriented architecture, which basic framework exploits the concept of a service, an abstraction that could be invoked to provide a requested computation, storage, and return or pass on a result to another service or even human being. Shortly after, Service-Oriented Computing (SOC) has started to be a subject of intensive research, development, and deployment. Since more and more private users, research institutions, businesses, hospitals, cities, and industry companies wish to benefit from interconnectivity provided by wireless networks, the interest in services study and development is exponentially growing. These days, SOC is in use in all areas of human endeavor, which are heterogeneous, deal with huge data volumes, and subject to security attacks. SOC systems must satisfy high-performance, reliability, and trustworthiness requirements of users. From the first concepts of services that are linked to the abstractions of infrastructure, platforms, and software, we have moved to services created for and exploited in networks, data storage and management, clouds, fogs, edges, huge data, security, trust, workflow, modeling, etc. This move implies a need for new knowledge and enhancement of the existing knowledge of services cloud, enhancing existing knowledge of in the area of services, exploiting new knowledge created for dealing with wireless networks, communication between clouds and edge devices, using Artificial Intelligence (AI) to deal with huge data, and generate new applications that would benefit other researchers, developers of service computing systems, and create a basis for other users to consider making their areas of interest better, faster, more secure, and trustworthy.

Thus, the question is: "what is Future Generation of SOC Systems?". To get even a partial answer to this question this special issue was seeking outstanding, original contributions, including theoretical and empirical evaluations, as well as, practical and industrial experiences, with emphasis on advanced results that solve open research problems and have significant impact in the field of SOC.

Special issue topics of interest

Our study shows that there are some areas that define the research leading toward Future Generation of SOC Systems. They are as follows:

Research outcomes of the special issue papers

All papers submitted to the special issue sit in the area defined by the listed topics.

The main content and contributions of the selected papers are as follows.

Embedding reactive behavior into artifact-centric business process models:

Business processes are an important piece of service modeling and computing. A business process represents a set of activities and tasks that aims at accomplishing an organizational objective. The process must involve clearly defined inputs and a single output. These inputs are made up of all the factors that contribute (either directly or indirectly) to the added value of a service or product. These factors can be categorized into artifact-centric processes, management processes, operational processes and supporting business processes. Artifact-centric business processes are characterized by the changes and evolution of business data, or business entities. These changes are considered the main driver of the processes. Modeling artifact-centric processes focuses on describing how business data is changed/updated, by a particular action or task, throughout the process. This advocates somehow a sort of middle ground between a conceptual formalization of dynamic systems and their actual implementation.

In paper [START_REF] Oriol | Embedding reactive behaviour into artifact-centric business process models[END_REF], the authors introduce novel approach to generate repairs for the activities in artifact-centric business process models. The proposed approach generates extensions to the activities to ensure that the integrity constraints in the data model are fulfilled considering a given a data model, a process model, and the specification of the activities in the process. The authors show that the approach supports the evolution of the data model independently from the business process model and the specification of the activities. The approach relies on service modeling languages such as Unified Modeling Languages and Business Process Management Notation (BPMN).

Topic-based crossing-workflow fragment discovery

Workflows enable making business processes more productive and efficient. Business processes allow modeling services compositions to deliver a result. Workflows provide technology or tool that can help to do achieve this result. The discovery of workflow fragments is significant to promote the reuse or repurposing of best practices evidenced in legacy workflows, when novel scientific experiments are to be conducted. The discovery of workflow fragments is closely related to service discovery, which exploits: Web Service Decription Language-based keyword search, semantic matching based on domain knowledge or ontologies, context awareness, or Quality of Service (QoS)-based discovery, and machine learning techniques adopted to examine service relevance. ZhangBing Zhou et al. proposed in paper [START_REF] Zhou | Topic-based crossing-workflow fragment discovery[END_REF] "a novel crossing workflow fragment discovery mechanism, where an activity knowledge graph is constructed to capture flat invocation relations between activities, and hierarchical parent-child relations specified upon sub-workflows and their corresponding activities". Semantic relevance of activities and sub-workflows is calculated based on their representative topics. Individual candidate activities or sub-workflows are discovered when considering their semantic relevance and short-document descriptions. The fragments are evaluated by balancing their structural and semantic similarities. The authors made four major contributions; (i) demonstrated that their approach is as accurate in discovering appropriate crossing-workflow fragments as the state of art's techniques; (ii) constructed an activity knowledge graph, whose edges capture (a) invocation relations between activities in scientific workflows, and (b) hierarchical parent-child relations specified upon sub-workflows and their corresponding activities; (iii) calculated the semantic relevance of activities and sub-workflows leveraging their representative topics, where these topics are generated by applying the biterm topic model based on the description in short texts for activities and subworkflows, (iv) designed a novel and efficient crossing-workflow fragments discovery algorithm when the requirement is specified in terms of a workflow fragment.

Understanding complex process models by abstracting infrequent behavior

Process mining has become very popular in the last years to analyze the behavior of an organization by offering techniques to discover, monitor and enhance real processes. A key point in process mining is to discover understandable process models. To achieve this goal in complex processes, several simplification techniques have been proposed, from the structural simplification of the model to the simplification of the log to discover simpler process models. However, obtaining a comprehensible model explaining the behavior of unstructured large processesfor instance containing hundreds of activitiesis still an open challenge.

The authors of paper [START_REF] Chapela-Campa | Understanding complex process models by abstracting infrequent behavior[END_REF] introduced the importance of a behavioral simplification in complex processes to understand what is happening in them. They have presented UBeA, a novel algorithm which, given an event log, a process model, and the events considered as core behavior, abstracts the remaining non-core behavior from the process model. They have also presented IBeA, a specific implementation of this algorithm to simplify process models by abstracting infrequent behavior. IBeA can detect the infrequent behavior which obfuscates a process, abstracting it to produce simpler process models with a trade-off between completeness and precision, allowing to obtain an overall view of the process. The proposal also simplifies the event log, allowing to analyze and enhance the process with other process mining techniques. The contribution of this paper is related to Business Process Management research field which falls into service computing. Specifically, this work aims to simplify process models by detecting and abstracting infrequent behavior. Such processes are typically used when provisioning applications and services over mobile and highly dynamic environments like cloud and fog. They use business processes and workflow to describe the management procedures that we need to apply during the cloud/fog applications life cycle (migration, SLA management, service orchestration, load balancing and so on). They compared IBeA with other simplification approaches, using 11 logs from real scenarios, showing that IBeA can obtain, or allow to discover, a simpler and better model in complex processes.

Graph-based data caching optimization in edge computing

Currently, data collection, storage and processing are provided in many organizations, business, cities, hospitals, etc. by cloud computing systems. However, since they deal with huge volumes of data, their use is associated with high costs of transmission and major communication latency. Edge computing has emerged as a new computing paradigm that allows computation and storage resources and associated services in the cloud to be distributed to edge devices and servers. Those edge devices and servers are deployed at base stations close to users; they offer high-quality services. One of them is data caching because it ensures low latency for service delivery, minimizes the data caching cost, and maximizes the reduction in service latency. To achieve these outcomes, the authors formulated in paper [START_REF] Xia | Graph-based data caching optimization in edge computing[END_REF] the Edge Data Caching (EDC) problem as a constrained optimization problem. They proved the NP-completeness of this EDC problem and provided an optimal solution named IPEDC to solve this problem based on Integer Programming. The authors carried out intensive experiments on a real-world data set and a synthesized data set to evaluate representative approaches. They demonstrated that IPEDC and AEDC significantly outperform the three representative baseline approaches. Major contributions of this paper are as follows: (i) the EDC problem from the app vendors' perspective was formulated, and then proved that it is NP-complete; (ii) an optimal approach named IPEDC was developed for finding optimal solutions to EDC problems with the Integer Programming technique; (iii) an approximation approach named AEDC was developed for finding near optimal solutions to EDC problems in large-scale scenarios efficiently, and analyzed its theoretical approximation ratio; (iv) carried out extensive experiments on both a real-world data set and a synthesized data set were carried out to evaluate the proposed approaches against four representative approaches. This research has established the foundation for the EDC problem and opened several research directions.

QoE-aware user allocation in edge computing systems with dynamic QoS

As online services and applications are moving toward a more human-centered design, many app vendors are taking the Quality of Experience (QoE) increasingly seriously. End-to-end latency is a key factor that determines the QoE experienced by users, especially for latency-sensitive applications such as online gaming, autonomous vehicles, critical warning systems and so on. Edge computing has then been introduced as an effort to reduce network latency. In a mobile edge computing system, edge servers are usually deployed at, or near cellular base stations, offering processing power and low network latency to users within their proximity. In paper [START_REF] Lai | QoE-aware user allocation in edge computing systems with dynamic QoS[END_REF], the authors tackle the Edge User Allocation (EUA) problem from the perspective of an application vendor, who needs to decide which edge servers to be used to serve which users in a specific area. Furthermore, the vendor must consider the various levels of QoS for its users. Each QoS level leads to a different QoE level. Thus, the application vendor also needs to decide the QoS level for each user so that the overall user experience is maximized. The authors first optimally solve this problem using Integer Linear Programming (ILP) technique. Being an NP-hard problem, it is intractable to solve it optimally in large-scale scenarios. Thus, the authors propose a heuristic approach that can effectively and efficiently find sub-optimal solutions to the QoE-aware EUA problem. They conduct a series of experiments on a real-world data set to evaluate the performance of their approach against several state-of-the-art and baseline approaches.

The authors made the following main contributions: (i) formally defined the QoEaware EUA problem and show that it is an NP-hard problem; (ii) proposed an optimal approach based on ILP for solving this problem exactly; (iii) introduced QoEUAa new heuristic that performs better than their previous heuristic under resource-scarce circumstances; and (iv) carried out experiments based on a realworld data set to demonstrate the effectiveness and efficiency of QoEUA against several baseline and state-of-the-art approaches.

Lightweight self-organizing distributed monitoring of Fog infrastructures

The authors of paper [6] stated "Monitoring will play an enabling role in the orchestration of next-gen Fog applications. Particularly, monitoring of Fog computing infrastructures should deal with platform heterogeneity, scarce resource availability at the edge, and high dynamicity all along the Cloud-IoT continuum". As a follow up, the authors presented extended, with an automated network overlay restructuring mechanisms, their lightweight, scalable, non-intrusive and robust methodology, and prototype for monitoring Fog computing infrastructures, namely FogMon. FogMon monitors hardware resources at different Fog nodes, end-to-end network QoS between such nodes, and connected IoT devices. Furthermore, FogMon features a self-organizing Peer-to-Peer (P2P) topology with self-restructuring mechanisms, and differential monitoring updates. These extensions ensure scalability, fault tolerance and low communication overhead.

The authors proposed in their paper an extension of their previous methodology and open-source prototype for edge resources monitoring. To that end, they invented and presented a new mechanism for (re-)structuring the P2P overlay network. They also carried out experiments on a real testbed to demonstrate how the footprint of FogMon is limited and how its self-restructuring topology makes it resilient to infrastructure dynamicity.

Toward a correct and optimal time-aware cloud resource allocation to business processes

Cloud computing is an increasingly popular computing paradigm because it provides on-demand services to organizations for deploying their business processes over the Internet that reduces their needs to plan for provisioning resources. Despite providing competitive pricing strategies using them can lead to violating time constraints and exceeding budget constraints due to inappropriate decisions when allocating cloud resources to business processes. The authors of paper [7] present an approach to guarantee a correct (because time constraints on these processes are not violated) and optimal time-aware allocation (because the deployment cost of these processes is minimized) of cloud resources to business processes. The authors' approach uses timed automata to formally verify the matching between business processes' temporal constraints and cloud resources' time availabilities, and linear programming to optimize deployment costs. The authors presented an approach for allocating cloud resources to the activities of business processes that are subject to time constraints. To achieve verification, they developed rules that transform 840 million BPMN-based business process models into a network of time-automata so that proper matching of activities' needs of resources to cloud resources is ensured despite the time constraints. To achieve optimization that the number of a business processes' activities could impact, the authors developed a linear programming model that considered the deployment cost of these activities over cloud resources. Experiments demonstrate the technical do-ability of the proposed approach. The contributions of this work are (i) the development of a set of rules to transform business processes into timedautomata as a step toward a correct time-aware cloud resource allocation in business processes; (ii) formalization of the optimization problem as a math-45ematical model to minimize the deployment cost of time-constrained business processes, and (iii) evaluation of the technical do-ability of the developed approach for ensuring the correctness and optimization of time-aware cloud resource allocation to business processes.

Resilient composition of drone services for delivery

In recent years, drones and unmanned aerial vehicles, have proliferated rapidly around the globe in both military and civilian spheres. Drones are used in situations where manned flight is considered too risky, difficult or simply costly. They can be operated by either humans or programs. For instance, drones are increasingly used nowadays for package delivery.

SOC provides powerful mechanisms to abstract the functional and non-functional or QoS properties of a drone in the form of Drone-as-a-Service (DaaS). The functional property of a DaaS describes the delivery of a package from a given source to a destination following a skyway network. The non-functional properties of a DaaS are battery capacity, flight range, payload, and speed.

In paper [8], the authors propose a resilient drone service composition framework for delivery considering the recharging constraints and the dynamic conditions. An optimal set of candidate drone services is selected using the skyline approach at the source node in a skyway network. The authors introduced a formal model to represent constraint-aware drone services. They propose a deterministic look ahead algorithm to build an initial offline composition plan. The resilient service composition approach is heuristic-based. It incorporates the intrinsic and extrinsic factors affecting the drone services at runtime. The authors designed, implemented and evaluated through simulation a framework that enables the target compositions. The experimental results show that the proposed framework adapts to the runtime service failures and meets the users' expectations like minimum delivery time and cost. They also compared their obtained results versus Brute-Force and without look ahead approaches. The experiments show that the proposed approach guarantees the resilience of delivery services for the increasing number of failure rates.

Thread-level resource consumption control of tenant custom code in a shared JVM for multi-tenant SaaS

Software as-a-Service (SaaS) is a software distribution model in which a thirdparty provider hosts applications and makes them available to consumers in cloud setting. SaaS is one of three main categories of cloud computing, alongside Infrastructure as-a-Service and Platform as-a-Service. It is closely related to the application service provider. Prospective consumers can invoke and use SaaS according to the pay-as-you-go business model. SaaS providers commonly support customization of their services to allow them to attract larger tenant bases. The nature of these customizations in practice ranges from anticipated configuration options to sophisticated code extensions. From a SaaS provider viewpoint, the latter category is particularly challenging as it involves executing untrusted tenant custom code in the SaaS production environment. Proper isolation of custom code in turn requires the ability to control resource consumption of each tenant.

The authors of paper [9] present a practical solution for thread-level resource consumption control of tenant provided custom code. This solution provides control mechanism for four types of resources: CPU, memory, network, and storage. Usage data are gathered using the Java Resource Consumption Management (JSR-284) Application Programming Interface (API). In case of CPU and memory, where this API is not capable of imposing limits, both the Java runtime environment bytecode and tenant code are instrumented with usage control checkpoints which ensures that CPU and memory usage of tenants remain within their service-level agreements limits. The authors validate their finding through case studies and experiments. The results show that the proposed solution outperforms containers in terms of tenant accommodation capacity and performance overhead.

Research contributions

In response to the specified general needs, a set of high-quality papers from crosscommunity scientific papers have been submitted by experts from various disciplines, such as business-process management, distributed systems, computer networks, wireless and mobile computing, cloud computing, cyber-physical systems, networking, scientific workflows, services science, services computing, data science, management science, and software engineering. The main content and contributions of these papers are as follows. First, a set of topics and subtopics that require research leading toward Future Generation of SOC Systems was specified. Second, the special issue accepted papers present outstanding, original contributions, including theoretical and empirical evaluations, as well as practical and industrial experiences, with emphasis on advanced results that solve open research problems and have significant impact on the field of service-oriented computing.

1 .

 1 Service engineering and management, including: legacy systems migration and modernization service design, specification, discovery, customization, composition, and deployment service innovation, governance, and change and workload management theoretical foundations of service engineering service execution, monitoring and reconfiguration service engineering and management, services and data, services in the cloud and on the edge, services for the internet of things, services for software network functions and software defined networks, services in organizations, business, and society quality of service, security, privacy, and trust architectures for multi-host container deployments microservices deployment and management 2. Services and Data: services for big data and compute-intensive applications data mining and analytics AI services in data processing data-provisioning services services-related linked open data automated knowledge graph creation 3. Services in the cloud and on the edge: migration to virtual infrastructures service deployment and orchestration in the cloud cloud and edge services and workflow management cloud and edge brokers and coordination across multiple resource managers workload transformation edge AI and distributed intelligence services AI, machine learning, neural network, and data analytic techniques in edge processing analytics and knowledge generation services lightweight service deployment and management services and edge gateway architectures 4.Services for the Internet of Things (IoT) embedded and real-time services RFID, sensor data, and services related to IoT services for IoT platforms and applications AI services in IoT secure intelligent IoT-edge systems secure intelligent coordination and networking between edge and cloud service-oriented protocols for IoT applications REST APIs and services for IoT platforms and applications trust and privacy management in intelligent IoT-edge systems 5.Services for softwareized network functions and software defined networks service network function management and orchestration AI services in routing machine-learning algorithms for IoT applications services for novel and emerging networking protocols named data networking virtualized network and transport mechanisms virtualized network functions and services virtualized service function chaining 6.Services in organizations, business, and society: services science AI services in organizations, business, and society social networks and services cost and pricing of services service marketplaces and ecosystems service business models enterprise architecture and services quality of service and energy efficiency for intelligent application systems service chatbots

Acknowledgments

The Guest Editors wish to thank all authors for sharing the outcomes of their research, which make this special issue possible. The Editors are grateful to the reviewers for their thoughtful and constructive comments and suggestions. The Guest Editors wish to express their gratitude to Professor Erik Cambria, the Special Issue Editor. The Guest Editors are also grateful to the members of the Journal Editorial Office, in particular Jacqueline Zhu and Mohammed Samiullah who provided excellent support and services.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

[6] Forti S., Gaglianese M., Brogi A.

Lightweight self-organising distributed monitoring of fog infrastructures (2021) in press

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