Mathieu Gonzalez
email: mathieu.gonzalez@b-com.com

Amine Kacete
email: amine.kacete@b-com.com

Albert Murienne
email: albert.murienne@b-com.com

Eric Marchand
email: eric.marchand@irisa.fr

L6DNet: Light 6 DoF Network for Robust and Precise Object Pose Estimation with Small Datasets *

Keywords: Deep Learning for Visual Perception, RGB-D Perception, Visual Servoing

published or not. The documents may come

I. INTRODUCTION

T HE goal of object pose estimation is to predict the rotation and position of an object relative to a known coordinate frame (usually the camera coordinate frame). This computer vision problem has many applications such as augmented reality or robotics. In the former case, it allows a realistic insertion of virtual objects in an image as described in [START_REF] Marchand | Pose estimation for augmented reality: a hands-on survey[END_REF] and shown in Fig. 1. In the latter it can be used as an input for a robotic arm to grasp and manipulate the object such as in [START_REF] Wang | Densefusion: 6D object pose estimation by iterative dense fusion[END_REF]. Although heavily studied, this problem is still relevant as it is unresolved due to its complexity. Indeed some scenes can be highly challenging due to the presence of cluttering, occlusions, changes in illumination, viewpoint, and textureless objects. Nowadays color and depth (RGB-D) sensors are smaller and cheaper than ever, making them relevant for object pose estimation. Indeed, compared to Fig. 1: To estimate the pose of an object we propose to use a single RGB-D image (a) to predict the position of a set of sparse 3D keypoints (shown as spheres in b) in the camera coordinate system, which are then registered in 3D with corresponding points in the world coordinate system (shown as cubes in b) to retrieve the pose (c) that can be used to insert a virtual object (d) in the scene as an AR application color-only (RGB) sensors, the depth channel provides relevant information for estimating the pose of textureless objects in dimly lit environments.

Classical object pose estimation approaches are either based on local descriptors followed by 2D-3D correspondences [START_REF] Marchand | Pose estimation for augmented reality: a hands-on survey[END_REF], or on template matching [START_REF] Tejani | Latent-class Hough forests for 3D object detection and pose estimation[END_REF], [START_REF] Hinterstoisser | Model based training, detection and pose estimation of texture-less 3D objects in heavily cluttered scenes[END_REF], [START_REF] Kehl | Deep learning of local RGB-D patches for 3D object detection and 6D pose estimation[END_REF]. However the challenging cases listed above limit their performance. To address these limitations most recent methods solve the problem of object pose estimation with a data driven strategy using for example Convolutional Neural Networks (CNNs) [START_REF] Wang | Densefusion: 6D object pose estimation by iterative dense fusion[END_REF], [START_REF] Rad | BB8: A scalable, accurate, robust to partial occlusion method for predicting the 3D poses of challenging objects without using depth[END_REF], [START_REF] Peng | PVNet: Pixel-wise Voting Network for 6DoF pose estimation[END_REF], [START_REF] Tekin | Real-time seamless single shot 6D object pose prediction[END_REF], [START_REF] Li | CDPN: Coordinates-Based Disentangled Pose Network for real-time RGB-Based 6-DoF object pose estimation[END_REF], [START_REF] Park | Pix2Pose: Pixel-wise coordinate regression of objects for 6D pose estimation[END_REF], [START_REF] Li | DeepIM: Deep Iterative Matching for 6D pose estimation[END_REF], [START_REF] Xiang | PoseCNN: A convolutional neural network for 6D object pose estimation in cluttered scenes[END_REF], [START_REF] Tekin | H+O: Unified egocentric recognition of 3D hand-object poses and interactions[END_REF], [START_REF] He | Pvn3d: A deep pointwise 3d keypoints voting network for 6dof pose estimation[END_REF]. These approaches work in a holistic way, considering a whole RGB or RGB-D image as an input and making a single estimation of the pose. While some methods are hybrid, using a learning-based approach followed by a geometrical solver [START_REF] Rad | BB8: A scalable, accurate, robust to partial occlusion method for predicting the 3D poses of challenging objects without using depth[END_REF], [START_REF] Peng | PVNet: Pixel-wise Voting Network for 6DoF pose estimation[END_REF], [START_REF] Tekin | Real-time seamless single shot 6D object pose prediction[END_REF], [START_REF] Li | CDPN: Coordinates-Based Disentangled Pose Network for real-time RGB-Based 6-DoF object pose estimation[END_REF], [START_REF] Park | Pix2Pose: Pixel-wise coordinate regression of objects for 6D pose estimation[END_REF], [START_REF] He | Pvn3d: A deep pointwise 3d keypoints voting network for 6dof pose estimation[END_REF], others use an end-to-end CNN to predict the pose [START_REF] Wang | Densefusion: 6D object pose estimation by iterative dense fusion[END_REF], [START_REF] Li | DeepIM: Deep Iterative Matching for 6D pose estimation[END_REF], [START_REF] Xiang | PoseCNN: A convolutional neural network for 6D object pose estimation in cluttered scenes[END_REF].

Some older methods however have proven to be reliable using patch voting approaches coupled to a learning algorithm [START_REF] Tejani | Latent-class Hough forests for 3D object detection and pose estimation[END_REF], [START_REF] Kehl | Deep learning of local RGB-D patches for 3D object detection and 6D pose estimation[END_REF], [START_REF] Riegler | Hough networks for head pose estimation and facial feature localization[END_REF], [START_REF] Fanelli | Real time head pose estimation with random regression forests[END_REF], [START_REF] Kacete | Real-time eye pupil localization using Hough regression forest[END_REF]. Those strategies predict a set of pose hypothesis from local patches using data driven functions and, from this set of hypothesis, retrieve a pose.

We argue that we can leverage the robustness brought by local approaches with a two stages strategy, predicting the pose in an intermediate Euclidean 3D space and retrieving it with a geometrical solver. The intermediate representation makes it natural to apply a voting strategy to the set of pose hypothesis. Our hybrid strategy allows us to correctly supervise our CNN training, not being dependent on the choice of pose representation, not requiring a custom loss function to compute the pose error and not having to predict rotation and translation separately. Moreover, like [START_REF] Tekin | H+O: Unified egocentric recognition of 3D hand-object poses and interactions[END_REF] we argue that predicting keypoints in 3D and solving a 3D-3D correspondence problem yields to more accurate results rather than predicting in 2D and solving a 2D-3D correspondence problem.

In this paper we tackle the problem of pose estimation considering a single RGB-D image as input. We design a robust and accurate algorithm to predict the pose of a generic rigid object in a scene. Our contributions are :

• We propose an hybrid pipeline in two parts: a data driven block that predicts a set of 3D points in the camera coordinate system and a geometrical block. The latter retrieves the pose given the estimated points and a priori chosen keypoints in the world coordinate system, minimizing a registration error. • We propose to use two CNNs in cascade in the former part. First we predict the 2D location of the object in the image, classifying local patches extracted from the image with a CNN. Then we use a regression CNN to predict a set of possible 3D positions of points in the camera coordinate system. The position hypothesis are then robustly aggregated to obtain a single estimation of the 3D location of the points. • We demonstrate performance improvements in terms of accuracy over state-of-the-art methods of RGB-D pose estimation on the standard LineMod [START_REF] Hinterstoisser | Model based training, detection and pose estimation of texture-less 3D objects in heavily cluttered scenes[END_REF] dataset and study the impact of some parameters of our method. We also validate our approach within a visual servoing experiment.

II. CLOSE WORK

We will limit ourselves to learning based methods as the literature on object pose estimation is vast. We can separate those methods into two main categories: patch-based methods and holistic methods. The latter can be as well separated into two categories: direct and indirect strategies.

Patch-Based Methods. Patch-based methods output multiple pose hypothesis for a single image [START_REF] Tejani | Latent-class Hough forests for 3D object detection and pose estimation[END_REF], [START_REF] Kehl | Deep learning of local RGB-D patches for 3D object detection and 6D pose estimation[END_REF], [START_REF] Riegler | Hough networks for head pose estimation and facial feature localization[END_REF], [START_REF] Fanelli | Real time head pose estimation with random regression forests[END_REF], [START_REF] Gall | Hough forests for object detection, tracking, and action recognition[END_REF]. The predictions, called votes, which are obtained from local patches in the image are then aggregated to get a single estimation, which is more robust than each vote taken independently. Hough based methods is such a type of voting scheme. Hough Random Forests (HRFs) have been introduced by [START_REF] Gall | Hough forests for object detection, tracking, and action recognition[END_REF] to estimate the Hough transform with a learning based approach for object detection, tracking in 2D and actions recognition. The concept of HRFs has also been applied to object pose estimation by [START_REF] Fanelli | Real time head pose estimation with random regression forests[END_REF] to predict the translation and rotation of human heads. In that case, both the nose 3D position and Euler angles are regressed. Those methods rely on binary tests to describe the split hypothesis used in random forests. [START_REF] Tejani | Latent-class Hough forests for 3D object detection and pose estimation[END_REF] proposes to use a split function based on a template patch descriptor. It also proposes to train a random forest using only object patches. As HRFs are based on handcrafted split functions, their performance is limited by image variations. To overcome this, Hough Convolutional Neural Networks (HCNNs) have been introduced by [START_REF] Riegler | Hough networks for head pose estimation and facial feature localization[END_REF] as an alternative to HRFs. A CNN was designed by [START_REF] Riegler | Hough networks for head pose estimation and facial feature localization[END_REF] to regress at once the probability of a patch belonging to the foreground as well as the object pose. In all cases a non parametric clustering algorithm is then used on object patches to robustly retrieve the pose. Direct Holistic Methods. Recently, most studies [START_REF] Wang | Densefusion: 6D object pose estimation by iterative dense fusion[END_REF], [START_REF] Li | DeepIM: Deep Iterative Matching for 6D pose estimation[END_REF], [START_REF] Xiang | PoseCNN: A convolutional neural network for 6D object pose estimation in cluttered scenes[END_REF], [START_REF] Do | Deep-6DPose: Recovering 6D object pose from a single RGB image[END_REF], [START_REF] Kehl | SSD-6D: Making RGB-based 3D detection and 6D pose estimation great again[END_REF] take a whole image as an input and try to leverage the capabilities of CNNs by directly estimating the pose. PoseCNN [START_REF] Xiang | PoseCNN: A convolutional neural network for 6D object pose estimation in cluttered scenes[END_REF] proposes an end-to-end CNN to perform 3 related tasks: semantic labeling, translation prediction from the object estimated 2D center and depth and rotation inference. To correctly supervise the network training, [START_REF] Xiang | PoseCNN: A convolutional neural network for 6D object pose estimation in cluttered scenes[END_REF] uses a specific loss called PoseLoss, defining the error as an average euclidean distance between rotated point clouds. SSD6D, [START_REF] Kehl | SSD-6D: Making RGB-based 3D detection and 6D pose estimation great again[END_REF], uses a CNN to predict the object class with its bounding box, as well as to classify discretized viewpoints and in-plane rotations to create a set of pose hypothesis. Thus, the network loss is a parametric combination of multiple losses. DenseFusion, [START_REF] Wang | Densefusion: 6D object pose estimation by iterative dense fusion[END_REF], combines color and depth channels in a deep network to fuse them, creating a set of features which are then used by a CNN to predict the pose. It can be further rapidly refined by a network in an iterative manner. In some recent works [START_REF] Do | Deep-6DPose: Recovering 6D object pose from a single RGB image[END_REF], [START_REF] Sundermeyer | Implicit 3D orientation learning for 6D object detection from RGB images[END_REF], [START_REF] Mahendran | 3D pose regression using convolutional neural networks[END_REF] the choice of representation for rotations has been studied as it shows to have an impact on the accuracy of the pose estimation [START_REF] Mahendran | 3D pose regression using convolutional neural networks[END_REF]. Indirect Holistic Methods. On the other side some methods [START_REF] Rad | BB8: A scalable, accurate, robust to partial occlusion method for predicting the 3D poses of challenging objects without using depth[END_REF], [START_REF] Peng | PVNet: Pixel-wise Voting Network for 6DoF pose estimation[END_REF], [START_REF] Tekin | Real-time seamless single shot 6D object pose prediction[END_REF], [START_REF] Li | CDPN: Coordinates-Based Disentangled Pose Network for real-time RGB-Based 6-DoF object pose estimation[END_REF], [START_REF] Pavlakos | 6-DoF object pose from semantic keypoints[END_REF], [START_REF] He | Pvn3d: A deep pointwise 3d keypoints voting network for 6dof pose estimation[END_REF], [START_REF] Wu | Single image 3d interpreter network[END_REF], [START_REF] Grabner | 3d pose estimation and 3d model retrieval for objects in the wild[END_REF] are inspired by classical pose estimation from 2D-3D correspondence. However CNNs are used to address the limits imposed by handcrafted features. To do so the 2D location of the projection of prior chosen 3D keypoints is predicted in the image. The pose is then retrieved using a 2D-3D geometrical solver e.g. a Perspective-n-Points (PnP) algorithm. For example BB8, [START_REF] Rad | BB8: A scalable, accurate, robust to partial occlusion method for predicting the 3D poses of challenging objects without using depth[END_REF] coarsely segments the object and apply a deep convolutional network to the local window around the object to predict the 2D location of the projection of the 8 corners of the object bounding box. This estimation is followed by a PnP that recovers the pose. [START_REF] Tekin | Real-time seamless single shot 6D object pose prediction[END_REF] proposes a single-shot CNN that classifies the object, predicts a confidence term as well as the 2D location of the projection of 9 keypoints in the bounding box. PVNet [START_REF] Peng | PVNet: Pixel-wise Voting Network for 6DoF pose estimation[END_REF] proposes to apply an offset based approach to predict the 2D location of a set of keypoints on the object surface. To do so, they segment the object in the image and predict a vector field on the segmented object, the spatial probability distribution of each keypoint is then retrieved and used in an uncertainty driven PnP to estimate the pose. H+O [START_REF] Tekin | H+O: Unified egocentric recognition of 3D hand-object poses and interactions[END_REF] estimates at once hand-object poses as well as objects and actions classes from RGB images. A CNN predicts the 3D position of 21 points of the object bounding box and the object pose can be retrieved from 3D-3D correspondences. PVN3D [START_REF] He | Pvn3d: A deep pointwise 3d keypoints voting network for 6dof pose estimation[END_REF] uses 6 different networks to estimate the pose: 3 (including [START_REF] Wang | Densefusion: 6D object pose estimation by iterative dense fusion[END_REF]) are used to extract and fuse features from a single RGB-D image and 3 are used to predict a set of 3D keypoints and the objects segmentation.

III. PROPOSED APPROACH: OUR HYBRID, PATCH-BASED STRATEGY

Our goal is to achieve a robust and accurate 6-DoF pose estimation of a 3D object, i.e. to estimate the transformation T ∈ SE(3) of an object of interest, provided with a coordinate system called world coordinate system F w , in the camera coordinate system F c . We represent the transformation T between F c and F w as where R ∈ SO( 3) is a 3D rotation matrix and t ∈ R 3 is a 3D translation vector.

T = R t 0 1 (1)
The pipeline of the proposed strategy can be seen Fig. 2: we adopt a patch voting based approach inspired from [START_REF] Riegler | Hough networks for head pose estimation and facial feature localization[END_REF], [START_REF] Gall | Hough forests for object detection, tracking, and action recognition[END_REF], using multiple local information to predict a sparsified version of the object geometry in F c . First, we design and train a classification CNN to predict the class of patches extracted from the input image either as object or background. This allows us to roughly localize the object in 2D. Then, we design and train a regression network to predict for each extracted object patch the 3D position in F c of a set of prior chosen keypoints, selected in F w . Finally, by minimizing the 3D-3D registration error between corresponding estimated keypoints in F c and reference keypoints in F w we retrieve the 6D pose. Hence our method belongs to both the indirect and patch-based set of methods, contrary to most recent methods [START_REF] Peng | PVNet: Pixel-wise Voting Network for 6DoF pose estimation[END_REF], [START_REF] He | Pvn3d: A deep pointwise 3d keypoints voting network for 6dof pose estimation[END_REF] that are indirect and holistic.

A. 2D Localization

In this section we show how we take in account the visibility of the object in each patch. Indeed not all patches contain relevant information about the object pose. Unlike in [START_REF] Riegler | Hough networks for head pose estimation and facial feature localization[END_REF] who uses a single network for both classification and pose estimation, we first use a classification network to decide whether or not a patch contains a representation of the object. We argue that classifying the patches, keeping only relevant ones before transmitting them to the regression network allows the CNN to fit using only relevant information about the object pose. Moreover we do not need a sophisticated parametric loss function whose parameters have to be optimized to supervise the training.

Model. Our model is inspired by a light VGG-like architecture and can be seen in the first block of Fig. 2. It is composed of a set of convolutional layers to extract features from the images and max-pooling layers to introduce scale invariance followed by 2 dense layers to classify the extracted features. For the last layer, we use a sigmoid activation function, for each other layer we use the classical ReLu activation function. To help reduce overfitting dropout is also used on the first fully connected layer as it contains the most weights. Data. To train our classification network in a supervised manner, we need labeled data. We capture a set of images representing the object of interest from multiple points of view. The classification neural network is trained using a set of patches {P i = (I i , b i )} where I i is the RGB image of the patch of size [h × w], i.e. I i ∈ R [h×w]×3 and b i ∈ [0, 1] represents whether or not the object is visible in the image I i . We obtain it by producing a binary mask of the object created by a 2D projection of the object 3D model using its ground truth pose. To increase the robustness of our algorithm across changes in illumination we proceed to do data augmentation by randomly modifying patches brightness.

Training. We denote the classification function f θc optimized over θ c which represents our CNN weights. The classification parameters are optimized by minimizing over the training data set:

θ * c = arg min θc L c (b, b). (2)
where b = f θc (I) and L c is the classical weighted binary cross entropy.

Inference. Given an unseen image, we extract K patches from the image in a sliding window fashion, with K depending on the window stride d (in our experiment K can vary from to a few hundreds to a few thousands with d going from 4 to 48 pixels) and get a set of patches

P = {P i , i ∈ [1, K]}. Each patch is then fed to the classification network f θ * c whose output is bi = p(b i |I i ) = f θ * c (I i ), i ∈ [1, K]
where p denotes the probability. We show in Fig. 3 some heat maps obtained using the probability estimated for each patch. We can see that the patches extracted from the object have a high probability of being classified as object while the patches extracted from the background have a low probability. As we can see the probability maps are very similar to 2D segmentation. However our method gives coarser results and needs less data than classical segmentation methods. Moreover our strategy is flexible as we can tune the patch extraction stride to balance inference time and segmentation precision.

B. 3D Points Prediction

We now show how we predict the position of a set of 3D keypoints in F c , using the object patches classified in the previous step. We use a regression network to predict the 3D location of a set of M points in F c . First, using a point selection algorithm like the farthest point sampling algorithm we create a set of M 3D keypoints, denoted S = X j ∈ R 3 , j ∈ [1, M ] , chosen in the object model in F w . For a given pose T of the object in F c we express the points in S in F c , and denote the set S T := {Y j := TX j , j ∈ [1, M ]}. Our goal is to estimate the location of the points in S T i.e. to estimate the location of the keypoints of S in F c . We argue that it is easier for the neural network to predict points in a euclidean space than to predict a pose over SE [START_REF] Tejani | Latent-class Hough forests for 3D object detection and pose estimation[END_REF]. Indeed even if a geodesic distance exists over SE(3) using the twist parametrization, optimization over this distance is complex [START_REF] Hou | Computing cnn loss and gradients for pose estimation with riemannian geometry[END_REF]. Like [START_REF] Li | CDPN: Coordinates-Based Disentangled Pose Network for real-time RGB-Based 6-DoF object pose estimation[END_REF] we argue that rotations and translations should be treated differently or at least that adaptation is required to learn to regress coherently in SE(3). In a way with our change of variables we suppress the direct impact of the peculiarities of rotation space as every variable stays in R 3 . Furthermore we argue that establishing 2D-3D correspondences is more ambiguous than 3D-3D correspondences for object pose estimation. Indeed the PnP algorithm aims at minimizing the 2D projection errors of keypoints. However, there may be small reprojection errors between keypoints that are large in 3D. Comparisons between 2D-3D and 3D-3D correspondences can be found in [START_REF] He | Pvn3d: A deep pointwise 3d keypoints voting network for 6dof pose estimation[END_REF].

Model. The architecture of the regression network can be seen in the second block of Fig. 2. We use an architecture that is very close to the classification network because we showed that we could reliably extract information from the patches with it. However we change the fully connected part, adding one layer and using more weights for each layer to give the regression CNN more flexibility. Data. We extract only object patches P i from the image. A regression neural network is trained using a set of patches P = {P i = (I i , δ i )} where I i is the RGB-D image of the patch, i.e., I i ∈ R [h×w]×4 and δ i ∈ R 3×M is a set of M 3D vectors, called offsets and defined in Equation 3:

δ i = {δ 1,i , δ 2,i , ..., δ M,i } = {Y 1 -C i , Y 2 -C i , ..., Y M -C i } (3)
with Y j ∈ S Ti ∀j ∈ [1, M ], T i is the pose of the object visible in the i th patch and C i ∈ R 3 is defined by :

C i =    ui-cx fx Z i vi-cy fy Z i Z i    (4)
with f x , f y , c x , c y the camera intrinsics, (u i , v i ) the 2D position of the center of the i th patch and Z i the value of the patch depth at location (u i , v i ). Equation 4 corresponds to the 3D backprojection of the 2D center of the i th patch, using a pinhole model. Thus, δ i is a set of M vectors, each one going from the 3D center of the patch and one of the M points in S Ti . An example of offsets is visible in Fig. 4: for 3 patches extracted in the image, we show M = 9 offsets. The use of offsets is very interesting for object pose estimation for two reasons. First, offsets bring invariance translation that is necessary due to the fact that we consider local patches. Indeed, 2 patches extracted from 2 different images with different poses may be very resembling. If displacement vectors are not used, the difference in terms of pose can thus only be seen as noise by the network. On the contrary, if offsets are employed the variable to regress is more correlated to patches aspect. Second, let's consider the space of all possibles object translation denoted Ω t , if we do not use offsets then this space is at most R 3 . However when considering displacement vectors, the set of all possible offsets has an upper bound of D where D is the largest diameter of the object, thus Ω t ⊆ Ω δ = B(0, D) where B(0, D) is the ball of center 0 and radius D and necessarily we have

Ω δ ⊂ R 3 .
The manifold in which predictions exist is reduced when using offsets, making the learning procedure easier for a data driven algorithm.

where δ = g θr (I) and L r is the mean absolute error:

L r (δ, δ) = 1 3M ||δ -δ|| 1 (6)
where ||.|| 1 is the usual L 1 norm, thus L r represents the averaged L 1 distance between the estimated and ground truth points. The L 1 norm is preferred to the L 2 norm because it is less sensitive to outliers, that are robustly handled by the Gaussian kernel of the mean-shift algorithm (see below) during the voting step.

Inference and Voting. Given the patches extracted in Sec. III-A and their associated estimated probability, we discard the patches which probability is lower than a threshold τ .

Thus we get a set:

P τ = I i | bi > τ, i ∈ [1, K] that can be written: P τ = {I i , i ∈ [1, N ]}
where N is the number of object patches that can go from a few tens to a few hundreds. For the i th patch I i fed to the regression network we get M predicted 3D offsets g θ * r (I i ) denoted δi = δj,i , j ∈ [1, M ] . We can then get an estimation of the 3D location of the transformed points by adding the position C i of the 3D center of the patch obtained from 4. This way we get a set of M estimated points positions Ŷj,i , j ∈ [1, M ] in F c . When we take in account all the N patches we get N × M points:

V := Ŷj,i , i ∈ [1, N ], j ∈ [1, M ]
that can be viewed as M clusters of N points or votes in the F c . We denote the j th cluster of points Vj := Ŷj,i , i ∈ [1, N ] . The votes must then be aggregated to get a robust estimate of the 3D position of each point in the F c . We denote the aggregation function h : R 3×N -→ R 3 . It is necessary to aggregate the N 3D votes in a robust manner to limit the impact of possible outliers, hence h is chosen to be a non-parametric estimator of the maxima of density. In our case we use a mean-shift estimator [START_REF] Comaniciu | Mean shift: A robust approach toward feature space analysis[END_REF], [START_REF] Cheng | Mean shift, mode seeking, and clustering[END_REF] which iteratively estimates the local weighted mean in 7:

m(X) = i k(X i -X)X i i k(X i -X) (7)
where k is a kernel function such as a Gaussian kernel:

k σ (X- Y) = exp(-||X-Y|| 2 2σ 2
) which gives less weight to outliers. The parameter σ was not optimized here but it can simply be chosen to optimize a pose error metric on a validation set. Thus we can define the set ŜT := Ỹj := h( Vj ), ∀j ∈ [1, M ] which corresponds to the aggregated centroid of each cluster in F c . We show Fig. 5 such examples of votes.

C. 3D-3D Correspondence Alignment

In this section we show how to retrieve the pose using the estimated 3D keypoints in F c that we obtained in the previous step and their corresponding reference keypoints in F w . Once the centroids have been voted we align the estimated points and their corresponding reference to get a pose estimation from the estimated location of the points. To do so we seek to find the transformation T * ∈ SE(3) that minimizes:

T * = arg min T M j=1 ||TX j -Ỹj || 2 2 (8)
where T can also be represented with a minimal representation q ∈ se(3) where se(3) is the Lie algebra associated to SE(3), X j ∈ S, Ỹj ∈ ŜT and ||.|| 2 is the euclidean norm of R 3 . That is finding the pose that best fits the points estimated by the aggregation of votes in F c . This problem is called the Orthogonal Procrustes Problem and can be solved using SVD decomposition as shown in [START_REF] Arun | Least-squares fitting of two 3-D point sets[END_REF] or an Iteratively Reweighted Least Square algorithm [START_REF] Fitzgibbon | Robust registration of 2D and 3D point sets[END_REF], [START_REF] Malis | Experiments with robust estimation techniques in real-time robot vision[END_REF] to discard outliers and obtain a robust estimation. To further refine the pose we can apply an Iterative Closest Point (ICP) algorithm [START_REF] Besl | Method for registration of 3-D shapes[END_REF]. This consists in solving 8, using the 3D model points and the points measured by the RGB-D camera projected in 3D using 4.

IV. EXPERIMENTS

We now present the results we obtained on the LineMod [START_REF] Hinterstoisser | Model based training, detection and pose estimation of texture-less 3D objects in heavily cluttered scenes[END_REF] dataset. This section is divided in four parts: first we present the technical details of our implementation, then we evaluate our method in terms of classification accuracy, 3D points regression accuracy and we measure the object pose accuracy using a standard metric and compare it to state-of-the-art results. Finally we compute the average inference time for a given object and study the impact of some hyper-parameters such as the level of patch density on both pose accuracy and inference time. Last but not least, a visual servoing task based on the proposed method is also considered.

A. Implementation Details

Training. To build our training data we extract patches in a sliding window fashion. We train the classification network for 100 epochs and the regression network for 500 epochs. We use a learning rate of 10 -4 with the Adam optimizer. A dropout of 50% is used for the classification CNN and and dropout of 20% and 10% is used on the two first fully connected layers of the regression CNN. We implement the neural networks using the tensorflow [START_REF] Abadi | TensorFlow: Large-scale machine learning on heterogeneous systems[END_REF] framework. Keypoints Selection. Inspired by [START_REF] Peng | PVNet: Pixel-wise Voting Network for 6DoF pose estimation[END_REF], we select the keypoints using the farthest point sampling algorithm which allows us to get a good coverage of the object. In our experiments we chose to use M = 9 points. Inference. Our algorithm is implemented in Python. During the inference we extract patches with a stride d of 4 pixels. We chose to set the threshold τ at 0.98.The votes are aggregated using the mean-shift algorithm and a gaussian kernel with variance σ 2 = 40 2 mm. We use open3d ICP, on the sub map defined by the estimated bounding box. For testing we use a Nvidia RTX2070 and an Intel Xeon @3.7 GHz. The patch size is chosen to be h × w = 64 × 64 unless precised otherwise.

B. Datasets

The LineMod dataset consists of about 15 000 RGBD images of 13 objects with multiple recorded poses in a variable and cluttered environment. It is widely used by the pose estimation community. We use the same method as [START_REF] Wang | Densefusion: 6D object pose estimation by iterative dense fusion[END_REF], [START_REF] Rad | BB8: A scalable, accurate, robust to partial occlusion method for predicting the 3D poses of challenging objects without using depth[END_REF], [START_REF] Peng | PVNet: Pixel-wise Voting Network for 6DoF pose estimation[END_REF] to select training and testing images. The dataset being small (about 100 images for training, yielding tens of thousands of patches), it is very challenging for CNN based approaches as highlighted in [START_REF] Xiang | PoseCNN: A convolutional neural network for 6D object pose estimation in cluttered scenes[END_REF]. This makes some methods like [START_REF] Peng | PVNet: Pixel-wise Voting Network for 6DoF pose estimation[END_REF], [START_REF] Xiang | PoseCNN: A convolutional neural network for 6D object pose estimation in cluttered scenes[END_REF] need synthetic data. Very large datasets such as the YCB-Video dataset [START_REF] Xiang | PoseCNN: A convolutional neural network for 6D object pose estimation in cluttered scenes[END_REF] may not be available for some objects as their creation is expensive in time as well as complex. Using data augmentation on the brightness we manage to get state of the art results without needing additional synthetic data, contrary to [START_REF] He | Pvn3d: A deep pointwise 3d keypoints voting network for 6dof pose estimation[END_REF], [START_REF] Peng | PVNet: Pixel-wise Voting Network for 6DoF pose estimation[END_REF] that need, in their present state, to use 20 000 new synthetic images per object.

C. Classification Accuracy

In this subsection, we measure the performance of the classification network. Having a bad classification accuracy could lead to multiple patches being misclassified. A high false positive rate would create noise in the Hough space and complexify the task of finding the maximum density. On the contrary, a high false negative rate would reduce the number of patches used for regression and thus the number of votes, leading to a less robust estimation. We can see in table I that for every object we get a high true negative rate above 99.5 % meaning we do not pollute the vote space. The true positive rate is more variable but stays above about 90%, so not too many patches are discarded.

D. 3D Points Regression Accuracy

In this subsection, we study the accuracy of the regression network. For each object we measure the average euclidean distance between the estimated position of each keypoint after it has been aggregated and its ground truth position

We can see in table II that the euclidean distance between predicted and ground truth points is on average of 11.8 mm

E. Object Pose Accuracy

Metric. We use the standard 6 DoF metric developed in [START_REF] Hinterstoisser | Model based training, detection and pose estimation of texture-less 3D objects in heavily cluttered scenes[END_REF], the average distance of model points (ADD-S). A pose is considered correct if the value of the ADD-S is less than 10% of the object diameter D. We report the results in table III. As we can see we obtain on average very close results to [START_REF] He | Pvn3d: A deep pointwise 3d keypoints voting network for 6dof pose estimation[END_REF] while using about 200 times less data which shows the superiority of our method in the small data regime. For some objects we even obtain better results than [START_REF] He | Pvn3d: A deep pointwise 3d keypoints voting network for 6dof pose estimation[END_REF].

F. Inference Time

Inference time is greatly dependent on the choice of the density with which patches are extracted. The lower the stride is, the more patches have to be extracted and fed to the networks and the longer the inference will be. However we expect the accuracy to be growing with the number of patches extracted. This balance allows our method to be suitable to a wide range of methods. The flexibility it brings lets the user tune the extraction stride to better meet the application needs. To decrease inference time we retrained a light 2D detection algorithm (namely tiny YOLOv3 [START_REF] Redmon | Yolov3: An incremental improvement[END_REF] with a darknet backbone) on the driller. As the training set is very small the estimated bounding box is coarse but sufficiently precise to reduce inference time which is reported in table IV. As we can see, using a stride of 12 to 16 we can reach real time inference while losing little accuracy. To speed up the voting step we chose to use only 3 clusters that are selected to minimize their respective variance. We also report inference times and accuracy for different strides in Fig. 7.

G. Ablation studies.

Influence of patch size. In this section we study the influence of different patch sizes for 4 LineMod objects on the pose estimation accuracy. Patch size is an important parameter and depends on the object size and texture. For example textureless Fig. 7: Inference time (in ms) and accuracy for the driller for varying strides (in pixels) Fig. 8: ADD-S (%) for different patch size (in pixels) and objects. objects may be better represented using larger patches that can capture some of the object shape. The influence on inference time can be seen for the driller in table V, as expected inference time grows with patch size as more convolutions are needed. The pose estimation accuracy can be seen in figure 8 and shows that pose accuracy grows with patch size, up to 64 × 64 and then goes down for most objects.

Importance of depth for the regression network. In this section we study the influence of depth for the offset prediction. A regression CNN is trained using only the RGB channels as input. We compute the object pose accuracy using the ADD-S metric on 6 different objects and report the results in table VI. As we can see we obtain slightly better results with this method for some objects. This shows that locally an RGB patch can be more discriminant than a depth patch, this can be explained by the fact that depth patches show little details and variation compared to color. However this depends on the object. For example many patches extracted on the object can or lamp just have a slightly curved depth. The depth patches extracted from the driller show very little details compared to the RGB, contrary to the cam that shows little texture on the RGB while being textured for the depth.

Importance of voting. In this section we validate the voting approach. For two small objects we use only one 80 × 80 patch to regress 3D points that are directly used to estimate the 3D transform. Doing so we obtain an ADD-S of 44.2% for the ape and 51.7% for the duck, compared to 78.2% and 85.2% which clearly shows the benefits of using multiple patches.

H. Visual Servoing Experiment

To illustrate that ou approach is well suited for robotics application, We also propose to validate our approach within a visual servoing experiment [START_REF] Chaumette | Visual servo control, Part I: Basic approaches[END_REF]. Such experiment required that the pose estimation algorithm is not only precise but fast and stable over time. We consider a positioning task with respect to an object. The aim of a positioning task is to reach a desired pose of the camera r * , starting from an arbitrary initial pose. We proposed to consider a position-based VS (PBVS) scheme [START_REF] Chaumette | Visual servo control, Part I: Basic approaches[END_REF] for which the relative pose (position and orientation) between the current and desired camera position has to be estimated. This relative pose will be estimated using the approach presented in this paper.

The PBVS task is achieved by iteratively applying a velocity to the camera in order to minimize ∆T which is defined such that ∆T = T * T -1 (where both T * and T are computed using L6DNet at the desired and current position). The control law is then given by (see [START_REF] Chaumette | Visual servo control, Part I: Basic approaches[END_REF] for details): v = -λL + ∆r (9) where λ a positive scalar and L + is the pseudo inverse of the interaction matrix L that links the variation of the pose to the camera velocity v. The error is defined by ∆r = (t, θu), where t describes the translation part of the homogeneous matrix ∆T related to the transformation from the current F c to the desired frame F c * , while its rotation part R is expressed under the form θu, where u represents the unit rotation-axis vector and θ the rotation angle around this axis.

Once the displacement ∆r to be achieved is computed using our approach, it is immediate to compute the camera velocity using a classical PBVS control law [START_REF] Wilson | Relative end-effector control using cartesian position-based visual servoing[END_REF], [START_REF] Chaumette | Visual servo control, Part I: Basic approaches[END_REF]:

v = -λ R t θu (10)
In such approaches, the quality of the positioning task and camera trajectory is then dependent on the quality of the estimation of the relative pose.

Experiments have been carried out on a 6 DoF gantry robot, with an Intel D435 mounted on the end-effector. Fig. 9 illustrates the behavior of the considered VS control law. The displacement to be achieved is ∆r = (-400mm, -140mm, -240mm, 6.22 o , 36.80 o , 38.36 o ). The transformation between the initial and desired poses (and particularly the rotation around the y and z axes and translation along the x and z axis) is very large and makes this experiment very challenging. The final error is ∆r = (1.2mm, -1.6mm, -0.4mm, -0.09 o , -0.18 o , 0.07 o ). Note that the evolution of the errors and of the velocities are very smooth and that the camera trajectory is close to the expected straight line (despite a coarse eye-to-hand calibration) which demonstrated both the accuracy and efficiency of the proposed approach on long image sequences. V. CONCLUSIONS

In this paper, we introduced a novel approach to estimate 6-DoF object pose in a RGB-D image. Our method leverages the strengths of patch voting based strategies and hybrid learninggeometrical methods, using patches extracted from the image to predict a set of sparse 3D keypoints representing the object geometry in F c . Those points are then put in correspondence and aligned with reference keypoints to retrieve the pose. We showed that our strategy is more robust and accurate than state-of-the-art and efficient to control a camera mounted on a robot end-effector in real-time.

Fig. 2 :

 2 Fig. 2: Overview of our pipeline solution: first (a), patches are extracted from an RGB-D image and classified as object or background. Next (b), for each object patch, a regression CNN predicts a set of vectors estimating the position of specific 3D keypoints in Fc. Those votes are then aggregated in a non parametric way to obtain a robust estimation of the points in Fc. (c) by minimizing the registration error between corresponding estimated keypoints in Fc and reference keypoints in Fw we retrieve the 6D pose. The pipeline is illustrated here with patches of size 48 × 48.

Fig. 3 :

 3 Fig. 3: Examples of probability maps for the cat, driller and can from the LineMod dataset

1 2 3 Fig. 4 :

 134 Fig. 4: Example of 3 patches extracted from an RGB-D image with the estimated offsets for each patch in red and the corresponding points represented by colored spheres, the center of each patch is shown by a black sphere Training. We denote the regression function g θr where θ r is the vector of weights of the network. The regression parameters are optimized by minimizing over the training data set: θ * r = arg min θr L r (δ, δ)(5)

Fig. 5 :

 5 Fig. 5: Example of predicted 3D points. From left to right: the cropped input image, the cluster of 3D votes Vjwhere each color corresponds to votes for a single point, the aggregated points Ỹj obtained by mean-shift (best seen in color). The aggregated point of cluster Ṽ3 is hidden behind the driller point cloud.

Fig. 6 :

 6 Fig. 6: Some qualitative examples of pose estimation results on LineMod. The pose estimation is represented as the blue bounding box and the ground truth pose as the green bounding box

Fig. 9 :

 9 Fig. 9: Visual servoing experiment: (a) initial view (the 3D model of the target is superimposed in the image according to the estimated pose) (b) final image (c) error ∆r in (meter and radian) (d) camera velocities (in meter/s and radian/s) (e) camera position over time.

TABLE I :

 I True positive rate (TPR) and true negative rate (TNR) (in %) for each object using our classification network

		ape	ben.	cam	can	cat	drill.	duck
	TPR	98.2	89.8	92.8	91.0	97.5	95.1	91.3
	TNR	99.9	99.5	99.6	99.7	99.7	99.7	99.9
		hole. iron	lamp eggbox	glue	phone MEAN
	TPR	97.1	94.9	88.4	94.2	90.7	89.6	93.1
	TNR	99.7	99.5	99.5	99.8	99.8	99.5	99.7

TABLE II :

 II Average euclidean distance and standard deviation (in mm) between ground truth and predicted 3D points for each object

		ape	ben.	cam	can	cat	drill.	duck
	Avg.	7.2	12	16.9	11.7	9.4	12.8	10.1
	Std.	4.5	7	65.6	6.7	5.5	8.3	6.3
		hole.	iron	lamp	egg.	glue	phone MEAN
	Avg.(mm)	10.2	10.6	12.4	14	14.6	11.1	11.8
	Std. (mm)	19.6	36.9	42.6	8.8	14.4	22.9	19.2

TABLE III :

 III Percentage of correctly predicted poses using the ADD-S metric on the LineMod dataset compared to state-of-the-art methods. Eggbox and glue are considered as symmetric objects.

	Input	RGB		RGB-D
	Method	[7]	[2] w. ref. [14]	Ours	Ours + ICP
	ape	43.6	92.0	97.3	91.2	97.3
	ben.	99.9	93.0	99.7	100.0	100.0
	cam	86.9	94.0	99.6	95.2	98.4
	can	95.5	86.0	99.5	98.1	99.5
	cat	79.3	93.0	99.8	98.4	99.7
	drill.	96.4	97.0	99.3	98.8	99.8
	duck	52.6	87.0	98.2	82.2	98.0
	hole.	81.9	92.0	99.8	93.7	98.8
	iron	98.9	97.0	100.0	99.1	99.9
	lamp	99.3	95.0	99.9	98.6	99.1
	egg. (sym.)	99.2	99.8	99.7	99.3	99.3
	glue (sym.)	95.7	100.0	99.8	99.2	99.0
	phone	92.4	93.0	99.5	98.3	99.6
	MEAN	86.3	94.3	99.4	96.3	99.1
	Input image (cropped)	Ground truth and estimation	Ground truth and refined estimation
		Estimated pose		Ground truth

TABLE IV :

 IV Inference times (in ms) and pose accuracy (ADD-S %) for the driller, using tiny YOLOv3 and different strides (pixels).

	Stride Bbox estimation Patch extract. Classification Regression. Voting	3D-3D solving	Total	ADD-S
	4	8.8	83.4	187.1	69.1	176.5	0.3	525.2	98.7
	8	9	20.8	51.2	23	46.4	0.2	150.6	98
	12	8.7	3	11	9	11.1	0.3	43.1	96.3
	16	8.9	1,9	8,6	7.6	7.7	0.3	35	95.3
	20	8.6	1.2	7.6	6.4	5.4	0,3	29.5	94.3
	24	9	1	7.4	5.5	4.6	0.3	27.8	90.4

TABLE V :

 V Total inference time (in ms) for each patch size (in pixels) using tiny YOLOv3 and a stride of 4 pixels

	Patch size (pixels)	32	48	64	80
	Total inference time (ms) 391.6 413 525.2 634.9

TABLE VI :

 VI Comparison of ADD-S using RGB only and RGB-D.

	Objects RGB ADD-S (%)	RGB-D ADD-S (%)
	ape	91.9	91.2
	cam	94.4	95.2
	can	99.1	98.1
	drill	99.8	98.8
	lamp	98.5	98.6
	phone	97.6	98.3
	MEAN	96.9	96.7

This paper was recommended for publication by Editor Cesar Cadena upon evaluation of the Associate Editor and Reviewers comments. * This work was supported by State aid managed by the National Research Agency under the future investment program bearing the reference ANR-17-RHUS-0005 (FollowKnee project).


G Clave

Prof. Dr L Garoux

] C Boulanger

Dr P Hesemann

Prof. Dr C Grison

Dr G Clavø

C Boulanger

Ecological Recycling of a Bio-Based Catalyst for Cu Click Reaction: a New Strategy for a Greener Sustainable Catalysis

Keywords: Ecological recycling, rhizofiltration, ecocatalysis, bio-based catalytic chemistry, click reaction

We report the elaboration of novel bio-sourced ecocatalysts for the Cu catalyzed azide-alkyne cycloaddition reaction (CuAAC). Ecocatalysis is based on the recycling of metals issued from rhizofiltration of metal rich effluents, and an innovative chemical valorization of the subsequent biomass in the field of catalysis. Taking advantage of the remarkable ability of Eichhornia crassipes to accumulate Cu(II) into its roots, these can be directly used for the preparation of copper containing ecocatalysts, called EcoCu, which appear as highly active catalysts in the CuAAC reaction. Furthermore, the recycling of Cu from the reaction mixture via E. crassipes is carried out ecologically. The resulting EcoCu 2 material displays reusability for the CuAAC reaction under identical experimental conditions without a loss of its catalytic activity.

Introduction

Some intensive mining activities, quarrying and industrial metallurgic activities are responsible for the pollution of soils and aquatic systems in the form of metal trace elements (TEs). [1] This is incredibly worrying, since the soil plays an essential role largely determining food production and water quality. Moreover, TEs are some of the most harmful compounds. They are not biodegradable and persist in contaminated organisms and ecosystems. Today, preserving the quality of soils and water has become a priority. There is a real need to develop innovative and efficient technologies to restore polluted sites and ecosys-tems. Phytoremediation is used to solve environmental problems caused by TEs. The most heavily researched phyotechnologies are phytoextraction and rhizofiltration. In the case of phytoextraction, TEs are extracted by plants and stored in their leaves. [1a, 2] With the rhizofiltration, the process occurs in an aquatic medium and TEs are bioconcentrated into roots. [1b] However, their development is still restricted by the fact that contaminated biomass is not recovered; the aerial parts of metal hyperaccumulating plants or the roots of aquatic plants are considered as contaminated wastes. Our group has recently proposed the new concept of ecocatalysis as a unique use of phytoextraction. [3] Taking advantage of the remarkable adaptive capacity of some plants to hyperaccumulate TEs, [4] ecocatalysis is based on the novel use of metal species of plants origin as reactants and catalysts of fine organic chemical reactions. Showing for the first time that the above-ground parts of land plants that hyperaccumulate Zn, Ni and Mn could be transformed into ecocatalysts. The first results showed that these ecocatalysts could be used as new generation Lewis acid catalysts [1a, 5] . Multicomponent reactions, Diels-Alder [6] and domino reactions [7] are particularly efficient. Soft oxidation reactions like epoxidation [8] or the chaining in situ of the oxidation/epoxide opening/oxidative cleavage sequence [9] could be compared favourably with the current industrial processes to access platform molecules. The polymetal systems obtained from the biomass produced by phytoextraction are original (unusual oxidation levels, new associated chemical species, effects of synergy). They can be used as heterogeneous catalysts in synthetic transformations giving access to molecules with high added value for fine and industrial chemicals (perfumes and cosmetics, [5b] medicines and oligomers of biological interest, [10] highly functionalised aromatic heterocyclic compounds, [11] key intermediaries of varied industrial chemical processes and biopesticides). [12] We have recently reported bio-based and bio-sourced EcoPd catalysts, which enable innovative recovery of metal charged biomass from plants used in rhizofiltration to extract palladium from synthetic solutions. [1b] We have shown that the obtained EcoPd catalysts exhibited high catalytic activity in Heck and Suzuki cross-coupling reactions and required considerably lower EcoPd quantity compared to conventional palladium catalysts. The developed synthetic protocols based on the use of bio-based catalysts present several advantages: low catalyst loading, high catalytic activity and selectivity, short re-action times, eco-friendly reaction conditions, and the possibility of catalyst recovery and reuse.

Here, we report greener bio-based alternatives for catalysis taking into account new environmentally safe and sustainable catalytic processes. Our approach is based on three principles: i) a focus on homogeneous catalysis involving a non-endangered metal, through the example of the Cu(I)-catalyzed Azide-Alkyne Cycloaddition (CuAAC) [13] ii) the preparation of a biobased catalyst obtained by rhizofiltration of contaminated aqueous media iii) an ecological catalyst recycling via a second rhizofiltration procedure of the primary reaction mixture (Scheme 1).

The main objective of this work is to demonstrate for the first time that homogeneous catalysts involving low cost metals can be easily recycled through an eco-friendly and efficient technology based on rhizofiltration. In other terms, we wish to show that ecological recycling can be considered as a "resource" of metal catalysts.

Results and Discussion

Rhizofiltration of Cu(II) rich effluents

EcoCu 1 was obtained via rhizofiltration of Cu(II)-containing aqueous media. Previously, Bacopa monnieri, Lolium multiflorum and Eichhornia crassipes have been studied to test their ability to accumulate copper into their roots. It was found that Bacopa monnieri accumulates efficiently copper into its roots, [14] whereas Lolium multiflorum accumulates both copper and palladium. [15] Its main asset relies on its well-developed root biomass. Finally, Eichhornia crassipes was also known to accumulate copper, to multiply easily and to form an amazing quantity of root biomass. For these reasons, E. crassipes has all the assets to be used as bioaccumulator for Cu(II) and for the synthesis of Cu-based ecocatalysts [16] .

Thus, the Cu-based ecocatalysts were synthesized via rhizofiltration using E. Crassipes, using an acidic aqueous copper(II) nitrate solution(c Cu(NO3)2) = 11.5 mg/L). After 6 days of rhizofiltration, the copper concentration in roots and leaves of E. crassipes was determined by ICP-MS analysis after drying. The results are shown in Table 1. We observed that the concentration of copper in the root biomass of E. crassipes and the bioconcentration factors (BCF: Cu concentration in roots divided by Cu concentration in water) are very high. Moreover, the translocation factors (TF: Cu concentration in shoot divided by Cu concentration in root) in the petiole and leaves of E. crassipes remain low, indicating that Cu principally remained on the roots.

Transformation of biomass into EcoCu 1 . EcoCu 1 derived from Eichhornia crassipes was prepared from harvested plants' roots following the described procedure (see experimental part, section 3.1.). The roots were calcined at 550 8C for 6 h in order to remove organic matter. The resulting ashes were treated with concentrated hydrochloric acid, transforming the metal oxides to the corresponding chlorides. After filtration, evaporation of the acid yielded the EcoCu 1 catalyst.

ICP-MS characterization of the EcoCu 1

Table 2 shows mineral composition of the EcoCu 1 catalyst. The analysis showed that Cu was the major transition metal in the ecocatalyst (4.3 wt%). Small amounts of Fe were also observed, together with Mg, Ca, Na and K. These elements are present as they are essential for plant growth. Because of the natural origin of the EcoCu 1 catalyst, some questions may arise regarding the reproducibility of the composition of the ecocatalyst. For this reason, the preparation of EcoCu 1 catalyst was replicated 10 times. Table 2 described the average of the obtained data.

Acidity characterization of the EcoCu 1 catalyst

In the CuAAC reaction, the electron density of the metal is essential to promote the stepwise cycloaddition process. There- fore, we studied the Lewis and Brønsted acid properties of the EcoCu 1 catalyst. We compared this ecocatalyst with commercial copper(II) chlorides, i. e. anhydrous CuCl 2 and CuCl 2 .2H 2 O. Lewis acidity is usually defined by its strength and its hardness according to the HSAB principle, described by Pearson [17] . A conventional method was used: the pyridine adsorption/desorption on the catalysts, monitored via infrared spectroscopy. This method enables a comparison of the Lewis acid strength and Brønsted acidity between different catalysts by monitoring pyridine infrared absorption bands between 1400 and 1660 cm À1 . Infrared spectra of pyridine adsorbed on EcoCu 1 , on commercial anhydrous CuCl 2 , and on CuCl 2 .2H 2 O were recorded at 150 8C in order to distinguish physisorbed pyridine from pyridine coordinately bonded to Lewis acid sites. The absorption bands around 1450 cm À1 observed on the spectra are characteristic of strongly bonded pyridine to Lewis acid sites (Figure 1). Because the frequencies of these absorption bands were similar in the three catalysts, we can conclude that the strength of the Lewis acidity is not significantly different between Eco-Cu 1 , anhydrous CuCl 2 and CuCl 2 .2H 2 O. Besides, the absorption band, characteristic of the pyridinium ion, was observed at 1530 cm À1 with EcoCu 1 . The presence of pyridinium cations in the material treated at 150 8C indicates that EcoCu 1 displays no-ticeable Brønsted acidity contrary to both commercial copper(II) chlorides.

XRD of the EcoCu 1 catalyst

XRD analyses were performed in order to determine the crystalline structure of the complexes in the EcoCu 1 catalyst (Figure 2). One polymetallic compound was detected: K 6 Fe 2 O 5 . This compound is an efficient catalyst for the industrial ethylbenzene dehydrogenation to styrene process [18] . Manganese was present in the manganosite form MnO, in the presence of sodium chloride and calcium sulfate hydrate. Copper was not present in a crystalline form.

Surface properties of the EcoCu 1 catalyst

Finally, the surface properties of the EcoCu 1 catalyst were determined via nitrogen sorption. We observed that the material displays rather low porosity with a specific surface area S BET of 12.0 m 2 /g and a mesopore volume V meso of 0.07 cm 3 /g. The nitrogen uptake appears in particular at high P/P 0 values indicating broad pore size distribution and an average pore size larger than 10 nm, which is due in particular to intergranular porosity.

Eco-CuAAC Click Reaction

The copper(I) catalyzed 1,3-dipolar cycloaddition of azides with alkynes is an ideal model reaction for different reasons. This first example of "click-chemistry" [19] is based on "fusion" mechanisms between two molecules with perfect atom-economy. Moreover, the modern copper-catalysed reaction illustrates the interest of using non-endangered metal, Cu, to promote the selective formation of substituted 1,2,3-triazoles. Finally, the CuAAC has been widely used in synthesis [13a] , medicinal chemistry [20] , molecular biology [20b, 21] , and materials science [22] due to the chemical ligation properties. [13a, 23] Numerous applications are continually reviewed and enriched by new results in many areas. For example, the reaction is very important for the labelling of bio-macromolecules [24] or functional tools to understand complex biological systems [25] to elaborate valuable tools for biochemists. These results illustrate the interest to synthesize triazoles using aqueous systems. In the context of Green Chemistry, the development of ligand-free catalysts is an additional challenge. It is a double advantage in terms of cost (the high cost of the ligands limit the industrial interest of the process) and of purification (the delicate step of separation between ligand and product is avoided).

Here, we investigated the capacity of EcoCu 1 to promote the CuAAC transformation in a model reaction between benzyl azide and propargyl alcohol (Table 3).

Thermal treatment of plants' roots used to produce EcoCu 1 determines the oxidation state of copper present in EcoCu 1 : under air flow, Cu(II) species are exclusively formed. It is generally accepted that Cu(II) salts are not efficient catalysts in the CuAAC reaction. Sodium ascorbate, a natural and aqueous soluble reducing agent, is the reagent of choice to generate an active Cu(I) catalyst in situ. [13b] The treatment of yellow EcoCu 1 (II) by sodium ascorbate yielded the gray-green EcoCu 1 (I) in five minutes at room temperature. We further used a tertiary amine (triethylamine, TEA) as ligand and/or base. The expected role of this compound is the stabilisation of the Cu(I) species [26] and the neutralization of BrØnsted acidity in EcoCu 1 (see IR studies above), which can be a disadvantage in the catalytic cycle due to the formation of a copper(I) acetylide intermediate.

We observed that EcoCu 1 is an highly active catalyst for 1,3dipolar cycloaddition reaction in various media (Table 3). Nearly total conversions were found for reactions carried out in water, ethanol, isopropanol, methyltetrahydrofuran and dimethylformamide. The polymetallic composition of EcoCu 1 did not seem to affect the interactions between the copper site and the substrate. The catalyst displays high selectivity; no formation of side products was observed, and the only formed product was the 1,4-subsituted triazole 3 a. In particular, no oxi-dative Glaser coupling was detected under aerobic conditions. This result illustrates the high regioselectivity of the EcoCu 1 catalyst in the CuAAC click reaction, in line with results obtained with the utilization of classical copper catalysts. A large difference was observed when TEA was replaced by K 2 CO 3 under air. Under these conditions, the coupling reaction of alkyne and the formation of hexa-2,4-diyne-1,6-diol was the main reaction we observed.

These results were interesting; the most efficient conditions described in the literature employed CuSO 4 in aqueous conditions or CuI, CuBr, Cu(OAc) 2 or Cu in organic solvents. The efficiency of CuCl ou CuCl 2 /NaAsc was rarely described [22b] . In order to unambiguously prove the catalytic activity of EcoCu 1 (I) derived from the system NaAsc -EcoCu 1 (II), the reaction was performed without adding NaAsc to the reaction mixture. Under these conditions, we observed no significant product formation.

In order to optimize the reaction conditions with water, we closely studied different other parameters of the reaction such as the presence of TEA, the quantity of sodium ascorbate, the quantity of added EcoCu 1 and the influence of the reaction time (Table 4). It is interesting to note that EcoCu 1 is active at room temperature. In an initial trial, we observed that the reaction went to completion after 4 h (entry 3). 5 mol% represented the ideal amount of Cu in EcoCu. An excess of sodium ascorbate was required and at least 5 eq. were necessary (entries 5-8). Surprisingly, TEA interfered negatively with the reaction. We observed higher catalytic activity in the absence of the amine (entry 5). The optimized reaction conditions are as follows: treatment of EcoCu 1 by sodium ascorbate and the addition of azide 2 a and alkyne 1 a in water led to the expected triazole 3 a quantitatively after only 1 h at room temperature.

In order to confirm the synthetic potential of EcoCu 1 in the CuAAC, we studied the general application of the reaction with various azides and alkynes. As shown in Table 5, the reaction proceeded with aliphatic, aromatic and functional substrates H 2 O 0

a Reaction conditions: 1 mmol 1a, 1 mmol 2a, 5 mmol NaAsc, 20 mmol TEA, 5 mol% Cu, 258C, 16h.

b Conversions reported were determined by GC-MS after calibration with hexadecane as internal standard c Blind experiment in which the ecocatalyst has been obtained by the same experimental methodology employed for EcoCu (calcination + acidic treatment) but with a plant that has not been in contact with the a CuNO 3 solution Table 4. Influence of TEA and NaAsc on the EcoCuACC Click reaction Entry TEA (eq.) NaAsc (eq.)

Mol% Cu time Yield a,b [%]
1 a 20 5 eq. 5 16 h > 99 2 a 20 5 eq. 1 5 days 58 3 a 20 5 eq. 5 4 h > 99 4 20 5 eq. 5 1 h 50 5 0 5 eq. 5 1 h > 99 6 0 2 eq. 5 1 h 44 7 0 1.5 eq. 5 1 h 7 8 0 1 eq. 5 1 h 0 a Reaction conditions: 1 mmol 1a, 1 mmol 2a, H 2 0, 258C.

b Yields reported were determined by GC-MS after calibration with hexadecane as internal standard such as propargyl ester, alkenyl, amino and alcohol moieties.

No rate difference was observed between primary and secondary azides. The activity of EcoCu 1 catalyst was comparable to the homogeneous Cu catalysts [27] and recent Cu(I) Schiff base network polymer heterogeneous catalysts described by Taskin et al. [28] Another interesting issue is the simplicity of the treatment. No chromatographic purification or other purification step was required. A simple addition of Me-THF or EtOAc allowed the isolation of the reaction products with a high degree of purity.

2.3. Ecological recycling and use of recycled EcoCu 2

CuAAC and rhizofiltration of reaction mixture

The concept of ecological recycling involves the reuse of metal containing waste via rhizofiltration. For this purpose, we studied a second rhizofiltration of the Cu containing reaction mixture of a CuAAC reaction with E. crassipes.

We studied the reaction between benzyl azide and phenylacetylene on a 371 mg scale under standard reaction conditions (2 eq. NaAsc, 25 8C, 1 h, H 2 O). The reaction product 3d was extracted with Me-THF. The metal content of the aqueous and organic layers were then analyzed by ICP MS. (Table 6).

The ICP-MS analysis indicates that 95 % of the copper remained in the aqueous layer. The result was similar with other elements. Surprisingly, significant amounts of sodium and calcium were present in the Me-THF phase. The presence of these cations could be explained by the contamination of glassware.

The straightforward rhizofiltration of the aqueous layer via E. crassipes led to the ecological recycling of Cu. The experimental conditions were similar above-mentioned (see chapter 2.1.1.). The roots of E. crassipes were directly transformed into the regenerated ecocatalyst labelled EcoCu 2 .

Characterization of EcoCu 2

ICP-MS analyses of recycled EcoCu 2 were performed after dilution of the mineralized solid in an aqueous solution of 1 % nitric acid (Table 7). Yield [Ref] 1 3b > 99 (92) > 99 [29] 2 3c > 99 -3 3d > 99 (78) > 99 [29] 4 3e 98 98 [28] 5 3f > 99 61 [28] 6 3 g > 99 85 [28] 7 3 h > 99 93 [28] 8 3i > 99 79 [28] 9 3j > 99 > 99 [30] 10 3k > 99 a Reaction conditions: 2 eq. NaAsc, 258C, 1h, H 2 0.

b Yields determined by GC-MS after calibration with an internal standard. Values between parentheses are isolated yields. The analysis showed that Cu was still the major transition metal in the EcoCu 2 . The ecocatalyst derived from ecological recycling was less concentrated in Cu (2.29 wt%) than EcoCu 1 derived from the first rhizofiltration (4.30 wt%), because the bioconcentration of E. crassipes was not quantitative in the adopted conditions. However, the copper level is still sufficient for ecocatalysis. A small amount of Fe was observed in both ecocatalysts EcoCu 1 and EcoCu 2 . Iron was the second most abundant transition metal in the ecocatalysts, with contents of 0.50 wt% in EcoCu1 and 1.35 wt% in EcoCu 2 . The quantities of Mg, Ca, Na and K were similar between the two materials.

XRD analysis of EcoCu 2 (Figure 3) has been performed in order to compare the structure of the EcoCu 1 and EcoCu 2 catalysts.

XRD analysis of the EcoCu 2 material showed that iron was present in the bernalite form. Thus, contrary to EcoCu 1 , iron was in the Fe(III) state. It is known that the of this mineral appears to be a challenge, because the synthesis of bernalite by crystallization from Fe(OH) 3 is difficult. Manganosite form MnO was not present, but graphite-3R was found. This could be the result of the incomplete combustion of lignine during the thermal treatment. Similar to EcoCu 1 , copper was present only in amorphous form.

Use of recycled EcoCu 1 into EcoCu 2

In order to prove the catalytic activity of EcoCu after ecological recycling, the CuAAC reaction between benzylazide and phe-nylacetylene has been performed with EcoCu 2 . Under the conditions of the model test reaction (2 eq. NaAsc, 25 8C, 1 h, H 2 0, 5 mol% Cu), 3d was quantitatively obtained. EcoCu 2 contained about 2 times less copper than EcoCu 1 , but its reactivity was maintained. This result demonstrates that the other metal species have no negative effect on the rate of the reaction. Also, this interesting result constitutes a proof of concept for ecological recycling in homogeneous catalysis.

Conclusions

We have shown for the first time that EcoCu catalysts enable the innovative recovery of metal charged biomass from plants used in rhizofiltration to decontaminate effluents rich in copper.

EcoCu produced from E. crassipes roots is a highly efficient homogeneous catalyst for the CuAAC reaction. The process is very simple, carried out in aqueous media, and does not require the presence of an amine. The products obtained with EcoCu catalysts do not require further purification.

Another special and innovative advantage is that EcoCu can be reused through ecological recycling of the reaction mixture via a second rhizofiltration cycle. The recycled EcoCu displays similar catalytic activity. This easy recovery of EcoCu is another valuable asset in terms of Green Chemistry.

2. 1 .

 1 EcoCu 1 Catalyst preparation and characterization 2.1.1. Preparation of the EcoCu 1

Scheme 1 .

 1 Scheme 1. Process of ecological recycling of EcoCu illustrated by the CuAAC click reaction.

Figure 2 .

 2 Figure 2. X-ray diffractogram of EcoCu 1 .

Table 1 .

 1 Copper concentration in roots and leaves of E. crassipes (wt% AE standard deviation), and BCF and TF calculation

	[Cu] in effluent (mg/L)	Roots	BCF	Leaves	BCF	TF
		(wt% AE SD)	(in roots)	(wt% AE SD)	(in leaves)
	11.5	0.27 AE 0.0013	234	0.0028 AE 0.015	2.4 (petiole)	0.010 (petiole)
				(petiole)

Table 2 .

 2 Mineral composition of EcoCu 1 catalyst derived from Eichhornia crassipes (wt% AE standard deviation) established by ICP-MS.Figure 1. IR spectra of pyridine adsorbed on EcoCu1, on commercial anhydrous CuCl 2 and CuCl 2 .2H 2 O.

	Na	Mg	Al	K	Ca	Fe	Zn	Cu
	2.4	1.3	0.5	2.3	7.7	0.5	0.00	4.3
	AE 0.021	AE 0.014	AE 0.025	AE 0.019	AE 0.017	AE 0.013	AE 0.016	AE 0.026

Table 3 .

 3 CuAAC Click reaction of benzylazide with propragyl alcohol in different solvent with EcoCu catalyst

	Entry	Solvent	Conversion (%) a,b
	1 a	H 2 O	> 99
	2 a	EtOH	> 99
	3 a	iPrOH	> 99
	4	MeTHF	> 99
	5	DMF	> 99
	6 c

Table 5 .

 5 CuAAC Click reaction of different azides and alcohols by the EcoCu methodology

	Entry	Azide	Alkyne	Product	Yield (%) a,b
		1	2	3	(this work)

Table 6 .

 6 ICP

	Aqueous layer
	Na	Mg	Al	K	Ca	Fe	Zn	Cu
	128.9	22.5	8.01	47.2	59.8	17.6	2.55	78.7
	AE 0.020	AE 0.030	AE 0.028	AE 0.017	AE 0.060	AE 0.022	AE 0.023	AE 0.018
	Organic layer
	Na	Mg	Al	K	Ca	Fe	Zn	Cu
	48.6	1.33	0.20	1.77	45.3	0.45	0.72	4.57
	AE 0.008	AE 0.002	AE 0.054	AE 0.032	AE 0.017	AE 0.015	AE 0.010	AE 0.013

MS analysis of aqueous and organic layers after the reaction performed with EcoCu 1 . (mg/L AE standard deviation).

Table 7 .

 7 ICP MS analysis of EcoCu 2 .Figure 3. X-ray diffractogram of EcoCu 2 .

	Na	Mg	Al	K	Ca	Fe	Zn	Cu
	0.97	1.20	1.05	1.10	3.55	1.35	0.02	2.29
	AE 0.018	AE 0.030	AE 0.034	AE 0.	AE 0.036	AE 0.041	AE 0.033	AE 0.037

Acknowledgements

This work was supported by the Centre National de la Recherche Scientifique (CNRS).