Timothée Lesort
email: timothee.lesort@ensta-paristech.fr

Mathieu Seurin
email: mathieu.seurin@inria.fr

Xinrui Li
email: xinrui.li@ensta-paristech.fr

Natalia Díaz-Rodríguez
email: natalia.diaz@ensta-paristech.fr

David Filliat
email: david.filliat@ensta-paristech.fr

Deep unsupervised state representation learning with robotic priors: a robustness analysis

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Deep unsupervised state representation learning with robotic priors: a robustness analysis

Timothée Lesort 1 , Mathieu Seurin 1,2 , Xinrui Li, Natalia Díaz-Rodríguez and David Filliat Abstract-Our understanding of the world depends highly on our capacity to produce intuitive and simplified representations which can be easily used to solve problems. We reproduce this simplification process using a neural network to build a low dimensional state representation of the world from images acquired by a robot. As in [START_REF] Jonschkowski | Learning state representations with robotic priors[END_REF], we learn in an unsupervised way using prior knowledge about the world as loss functions called robotic priors and extend this approach to high dimension richer images to learn a 3D representation of the hand position of a robot from RGB images. We propose a quantitative evaluation metric of the learned representation that uses nearest neighbors in the state space and allows to assess its quality and show both the potential and limitations of robotic priors in realistic environments. We augment image size, add distractors and domain randomization, all crucial components to achieve transfer learning to real robots. Finally, we also contribute a new prior to improve the robustness of the representation. The applications of such low dimensional state representation range from easing reinforcement learning (RL) and knowledge transfer across tasks, to facilitating learning from raw data with more efficient and compact high level representations. The results show that the robotic prior approach is able to extract high level representation as the 3D position of an arm and organize it into a compact and coherent space of states in a challenging dataset.

I. INTRODUCTION

The environment we live in is a complex mixture of multiple physics laws and interactions, hard to fully describe and understand. However, humans are likely to interact with it without detailed knowledge of the whole environment and its underlying functioning. For this, the human brain constructs simple models of the world in order to come up with an easy, though approximate, understanding of it that is sufficient to perform tasks.

This paper aims at reproducing this behavior for robots. We want to build a simple representation of the world that retains enough information to make a machine able to use it to interact afterwards, i.e., to perform an assigned task. Finding such a minimal representation (e.g., the position of an object extracted from an image) is the standard way to implement behaviors in robots. However, this is most of the time done in a task specific and supervised way. In this paper, we want to learn such representation with no supervision, based on generic learning objectives. This representation is trained with a deep neural network using images and rewards gathered from robot actions in a given environment and has to estimate, for each image, a state which is the representation we want to learn. Instead of using a ground truth as in supervised training, we make use of an approach that ensures consistency between the states' representation and the rewards gathered by the robot during exploration in the task. For this purpose, the states are constrained by robotics priors [START_REF] Jonschkowski | Learning state representations with robotic priors[END_REF], which are an expression of the knowledge we have about physics. The rewards are used in a way such that the representations learned are not bound to learn a concretely specific task, but instead, are aimed at serving to learn a broad variety of tasks. It is, however, essential to include a task to learn the concept of causality.

The main contribution of this paper is the extension of the use of the robotic priors approach with a siamese network to train a deep convolutional neural network to learn 3D representations of a robot's hand position. The network is trained with images from the robot head's camera, information on the actions performed by the robot, and rewards. The neural network learns a state representation usable for the robot to perform a reaching task defined by the reward. Moreover, we propose a new quantitative evaluation of the learned representation using nearest neighbors in the learned state space and generate new settings simulation data with added difficulty such as static and mobile distractors, and perform domain randomization [START_REF] Sadeghi | CAD2RL: Real single-image flight without a single real image[END_REF], [START_REF] Tobin | Domain randomization for transferring deep neural networks from simulation to the real world[END_REF] to test the scalability of the robotic priors in more challenging domains. Furthermore, we identify cases with partial degradation in the state representation learned space and propose a new alignment reference-point prior to improve it.

II. RELATED WORK

Robotic Priors: The term of prior in Bayesian statistics refers to the prior probability distribution, but as in the articles [START_REF] Bengio | Representation learning: A review and new perspectives[END_REF], [START_REF] Jonschkowski | PVEs: Position-Velocity Encoders for Unsupervised Learning of Structured State Representations[END_REF], [START_REF] Jonschkowski | State representation learning in robotics: Using prior knowledge about physical interaction[END_REF] and [START_REF] Jonschkowski | Learning state representations with robotic priors[END_REF], we use this term as a reference to an a priori knowledge we have about the world and not to a probability distribution. This knowledge comes from various domains which define several kind of priors: Task-Specific, Generic, and Robotic Priors. These priors can be exploited to train neural networks in order to learn physically plausible representations. Furthermore, we believe, as in [START_REF] Bengio | Representation learning: A review and new perspectives[END_REF], that incorporating strong and diverse priors into learning will bring the learning process closer to intelligence. The priors we use (as in [START_REF] Jonschkowski | Learning state representations with robotic priors[END_REF]) are similar to those in [START_REF] Scholz | A physics-based model prior for object-oriented mdps[END_REF] because they are physically grounded and aim at building representations of the world that are consistent with physics. Our approach can also be compared with [START_REF] Pinto | The curious robot: Learning visual representations via physical interactions[END_REF], which uses several kinds of robot interactions to train a siamese neural network. The difference is that they retrieve the executed actions from images to learn the representation, while we use the executed actions to impose a constraint on the representation. The final network they train is able to produce different actions with a Baxter robot, such as pushing, grasping or pocking, but in an open loop fashion. On the contrary, our approach is able to extract information from each image so as to produce closed loop controllers.

State Representation Learning The goal of state representation learning [START_REF] Lesort | State representation learning for control: An overview[END_REF] is to find a mapping from a set of observations to a set of states that makes possible to describe an environment with enough information, for example, to fulfill a given objective. This state representation learning can be viewed as searching a small set of hidden parameters which explain the observation. In our approach we impose a dimension on the state, and use the priors to guide the neural network in learning task-specific state representations in this given dimension. This is an alternative approach to selecting a state representation from a set ( [START_REF] Seijen | Efficient abstraction selection in reinforcement learning[END_REF], [START_REF] Konidaris | Efficient skill learning using abstraction selection[END_REF]), or creating an autoencoder to compress information into a lower dimensional state ( [START_REF] Lange | Autonomous reinforcement learning on raw visual input data in a real world application[END_REF], [START_REF] Finn | Deep spatial autoencoders for visuomotor learning[END_REF]), [START_REF] Van Hoof | Stable reinforcement learning with autoencoders for tactile and visual data[END_REF].

An important aspect of our approach compared to other state representation works is the usage of representation constraints based on both physics and a given task, that is exploited to find relevant information, instead of trying to encode all available information. This characteristic bears some similarity with approaches such as Embed to Control [START_REF] Watter | Embed to control: A locally linear latent dynamics model for control from raw images[END_REF], which learns states that follow linear dynamics, or the approach of [START_REF] Van Hoof | Stable reinforcement learning with autoencoders for tactile and visual data[END_REF], [START_REF] Goroshin | Learning to linearize under uncertainty[END_REF], [START_REF] Boots | Closing the learningplanning loop with predictive state representations[END_REF] which learn states that make possible to reconstruct the next observation with models such as PSRs (predictive state representation) [START_REF] Singh | Predictive state representations: A new theory for modeling dynamical systems[END_REF]. However, optimizing reconstruction is often a weak criterion to learn state representations, as the learning process may focus on the reconstruction of the most visible features and ignore small but relevant parts of the observations. Another approach related to ours is Time-Contrastive Networks, where a constraint on time continuity coherence is used to learn states from a dual camera setting using different points of view [START_REF] Sermanet | Time-contrastive networks: Self-supervised learning from multi-view observation[END_REF]. Other works that learn representations for roboticsrelated tasks other than control (scene recognition, odometry and keypoint matching) that do not use reconstruction but rather ego-motion equivariance include [START_REF] Agrawal | Learning to see by moving[END_REF] and [START_REF] Jayaraman | Learning image representations equivariant to ego-motion[END_REF].

Model Architecture Several approaches rely on neural networks with an autoencoder or variational autoencoder architecture ( [START_REF] Seijen | Efficient abstraction selection in reinforcement learning[END_REF], [START_REF] Konidaris | Efficient skill learning using abstraction selection[END_REF], [START_REF] Lange | Autonomous reinforcement learning on raw visual input data in a real world application[END_REF], [START_REF] Finn | Deep spatial autoencoders for visuomotor learning[END_REF]). However, in our approach, the priors are used as loss functions that encode constraints between states, a configuration that we address using Siamese networks (e.g., [START_REF] Chopra | Learning a similarity metric discriminatively, with application to face verification[END_REF], [START_REF] Xing | Distance metric learning, with application to clustering with side-information[END_REF], [START_REF] Pinto | The curious robot: Learning visual representations via physical interactions[END_REF]), which use two (or more) copies of a network with tied weights to process two (or more) inputs whose relation has to be imposed. This strategy constructs a coherent space of representations where each state representation is learned depending on each other.

We follow the common approach of using pre-trained convolutional networks on large image datasets and fine-tune them on a robotic task. We use ResNet18 network [START_REF] He | Deep residual learning for image recognition[END_REF] with additional fully connected layers that constrain the output to be low dimensional.

III. METHODOLOGY A. Robotic Priors

Robotic priors are used to provide the model with basic knowledge about the environment dynamical features. They add constraints to make the learned representation altogether consistent with simple, physical and task specific rules. Each prior is formalized as a cost function implemented through a siamese network. By minimizing them, the model is trained according to the prior and can learn a task-specific representation. The four priors we used are the ones presented in [START_REF] Jonschkowski | Learning state representations with robotic priors[END_REF]. We will use the following notations:

• I(t) is the image perceived at time t • s(t) is the state at time t and ŝ(t) is its estimation.

• φ is a function where given an image I(t), it returns a state s(t). φ is its estimation

• r(t) is the reward at time t • a(t) is the action performed a time t • D is the input data (images, actions, rewards) • ∆s(t) = s(t + 1) -s(t)
The definitions of loss functions associated to the priors and its related assumption are as follows:

Temporal coherence Prior: Two states close to each other in time are also close to each other in the state representation space.

L T emp (D, φ) = E[ ∆ŝ t 2 ] , (1)
Proportionality Prior: Two identical actions should result in two proportional magnitude state variations.

L P rop (D, φ) = E[( ∆ŝ t2 -∆ŝ t1 ) 2 |a t1 = a t2 ] , (2)
Repeatability Prior: Two identical actions applied at similar states should provide similar state variations, not only in magnitude but also in direction.

L Rep (D, φ) = E[e -ŝt 2 -ŝt 1 2 ∆ŝ t2 -∆ŝ t1 2 | a t1 = a t2 ] , (3)
Causality Prior: If two states on which the same action is applied give two different rewards, they should not be close to each other in the state representation space.

L Caus (D, φ) = E[e -ŝt 2 -ŝt 1 2 | a t1 = a t2 , r t1+1 = r t2+1 ] ,
(4) This last prior is the only one giving information about the task and helps discovering the underlying states which lead to rewards.

B. New prior proposition

Thus far we described original priors in [START_REF] Jonschkowski | Learning state representations with robotic priors[END_REF]. However, our experimental section will show that these are often not robust enough to learn a coherent state space when (static and moving) distractors are present, or when domain randomization occurs. In particular, we observed that when multiple training episodes were used, each sequence was often represented in its "own" part of the representation space instead of creating a larger space including all sequences. This overfitting behavior is quite logical as none of the priors tends to bring the sequences closer to one another. To bring sequences together, we introduce a new reference prior:

Reference point Prior: Two states corresponding to the same reference point should be close to each other

L Ref (D, φ) = E[ ŝti -ŝtj 2 | s ti = s tj = s Ref ] (5)
where s Ref is the embedded state of a reference point. This prior aims at stabilizing the representation by adding extra knowledge on some states of the system, with the idea of giving the robot a signal when he reaches a certain configuration, that acts as a reference or calibration coordinate. In order to apply the 5 th prior in our experiments, we need a reference point that acts as an anchor for the representation, and choose its location either 1) randomly (where the problem of some sequences not containing this point may arise), or 2) ad-hoc, where a point contained in each sequence is chosen.

C. Network architecture: Siamese Networks

The architecture of our network relies on a pre-trained ResNet18 network [START_REF] He | Deep residual learning for image recognition[END_REF], appended with a 512 neurons fully connected layer and a final fully connected layer representing the low dimensional state space (3 neurons in our experiments).

Training using the priors needs the simultaneous estimation of several states to perform the optimization process. This is the main reason why our approach uses siamese networks (Fig. 1). These neural networks use two copies of the same network that share all their parameters. With this method the cost functions can be applied on two states computed at the same time on different images. The cost functions also require to choose the right set of images as input for the siamese networks. This sampling depends on the prior to be optimized, e.g., in order to use the temporal prior, a set of two consecutive images should be taken, while for the causality prior, we search for a set composed of two images where the same action was performed while giving different reward. Once the set of image pairs is sampled, we can compute the states by forward propagation on each siamese network. Then, given all outputs, we calculate the prior loss and compute the gradient with respect to the prior loss, and update the weights accordingly. The ResNet18 and fully connected layers weights are shared among both the siamese networks branches, while the first X layers of the ResNet18 are frozen during training (X = 0 or 3 depending on the experiment).

For training, we used a batch size of 10, a learning rate of 10 -4 with a decay of 3 × 10-6 using the ADAM optimizer for 15 epochs. During training, all priors show not to be minimized the same way, as we observe the L Caus reaching lower values than the rest. However, the final equilibrium is only possible with the influence of all priors.

D. Assessment metrics

The best evaluation of the quality of the learned state space would be the performance of a reinforcement learning algorithm applied on the target task. However, this approach is computationally very expensive and data-hungry, and we therefore propose several more direct ways to assess the learned state space.

1) K-Nearest Neighbors quality evaluation criterion: The assessment for ŝt should point out that there exists a bijection between it and s t . However, the transformation from s t to ŝt can be quite arbitrary and it is not easy to estimate if the transformation keeps all the required structure of the original state space. We therefore use an assessment of the representation's quality which is based on a Nearest-Neighbors approach as in [START_REF] Sermanet | Time-contrastive networks: Self-supervised learning from multi-view observation[END_REF] for example. Since the priors want to impose local coherence (especially the temporal prior), a good representation should have local coherence, and therefore, the associated ground truth states should be close. While the nearest neighbor coherence can be assessed visually, we derive a quantitative metric from this information. Using the ground truth value for every image, we compute the distance between the value of the original image and the value on the nearest neighbor images retrieved in the learned state space 1 .

For an image I, this criterion is computed as follows:

KNN-MSE(I) = 1 k I ∈KN N (I,k) ||φ(I) -φ(I )|| 2 (6)
where KNN(I, k) returns the k nearest neighbors of I in the learned state space and φ(I) gives the ground truth (s) associated to I.

2) NIEQA: NIEQA [START_REF] Zhang | A new embedding quality assessment method for manifold learning[END_REF] is a more complex evaluation that measures the local geometry quality and the global topology quality of a representation. NIEQA local part checks if the representation is locally equivalent to an Euclidean subspace that preserves the structure of local neighborhoods. NIEQA objectives are therefore aligned with our goal. If KNN-MSE is correlated with NIEQA, it means that KNN-MSE could also be a good measure to assess the quality of the representation, especially locally. The global NIEQA measure is also based on the idea of preserving original structure in the representation space, but instead of looking at the neighbors, it samples "representative" points in the whole state space. Then, it considers the preservation of the geodesic distance between those points in the state space. We refer the reader to [START_REF] Zhang | A new embedding quality assessment method for manifold learning[END_REF] for more detail on its implementation.

We also experimented with distortion [START_REF] Indyk | Algorithmic applications of low-distortion geometric embeddings[END_REF], but this measure was found to bring no more information and we therefore omit these results. The data acquisition environment is produced by a simulation of a Baxter robot being in front of a table (Fig. 2) with ROS Gazebo simulator. We generate image sequences taken with the robot's head camera. Images thus contain a front view of what the robot is able to see with its camera (i.e., a table with objects and the robot arms).

IV. EXPERIMENTS A. Task and Environment Description

We consider a "reaching" (pushing button) task with a static button on the table. We record (640x400 pixels) RGB images taken by the static head camera of the robot. Three rewards are recorded: 0 when the left gripper is not touching the button, 1 when touching it, and -1 when the robot gripper is out of the field of view of the frame. The goal of this task is to learn a representation consistent with the actual robot's left hand position. In this context, actions are defined by elementary movement of the hand in the operational space between timestamps t and t + 1.

The input images are resized to 224*224 pixels and normalized per channel as in [START_REF] He | Deep residual learning for image recognition[END_REF]. We record for each image, its timestamp, the associated reward and which action has been made between image at time t and image at time t+1. The actions are computed on the fly as position deltas in the cartesian space while the arm is moving. With these actions we can find pairs of images where the same action is performed, and therefore, compatible with proportionality and repeatability priors. Furthermore, with the reward information we can find which images generate a reward with which action. Those images are then gathered to constitute an image set compatible with the causality prior's cost function.

It should be emphasized that, in this work, the goal is not to solve a robotic task (i.e learning a policy that reaches a certain goal) but to learn a mapping from the raw input images to a compressed representation. This representation should not take into account noise in the input (for example, randomly moving objects, or noise in the pixels) and needs to be relevant to the task at hand (i.e could be used by a policy gradient method to solved the task, for example, but we leave this to future studies).

B. Datasets

We used several datasets (Fig. 3) to validate our approach. These are designed to show the robustness of the robotic priors by changing the level of noise (distracting objects, changing background) and demonstrating the generality of those priors (2 different tasks are considered):

• Dataset 1: 2D Navigation Mobile Robot: baseline reproducing [START_REF] Jonschkowski | Learning state representations with robotic priors[END_REF], top-down view of a robot moving in a colored empty squared room, 11 sequences, 99 frames long 2 . This simulation environment and data generator is open source and as well available as part of the S-RL Toolbox [START_REF] Raffin | S-RL Toolbox: Environments, Datasets and Evaluation Metrics for State Representation Learning[END_REF]. In order to evaluate the limits of the robotic priors, we generate different datasets on our reaching task:

C. Baseline models

In order to have a baseline on which to compare our models, we used a convolutional denoising autoencoder (DAE) and a supervised learning approach, where the later uses the same network as the priors-based model, but trained using the ground truth (GT) states of the arm, i.e., the hand's real position. We used a batch size of 10, a learning rate of 10 -4 with a decay of 3 × 10-6 using the ADAM optimizer.

For autoencoders [START_REF] Baldi | Autoencoders, unsupervised learning, and deep architectures[END_REF], we used the same network as the priors for the encoding part (i.e., a pretrained ResNet18 with the same inner dimension as the priors (3)). For the decoding part we used 5 deconvolutional layers (no ResNet features/residual connections). We used a batch size of 20, with a Gaussian noise on the input image, a learning rate of 10 -4 with a decay of 3 × 10-6 using the ADAM optimizer.

D. Results

We successfully replicated 2D state results in [START_REF] Jonschkowski | Learning state representations with robotic priors[END_REF] with sataset 1 (see Table I). Compared to Autoencoders, priors improve quantitative performance no matter the metric used, which seems coherent since we feed the model more information. No matter the choice of location of the reference point (including choosing random points and despite the point being not always present in all sequences), the 5 th prior slightly improves the results. In addition, fine tuning all the ResNet layers (0f experiment) slightly improves the results. Results in 2D extrapolated similarly to 3D (dataset 2, see Table II) as we obtain equally satisfying results on the button pushing task with moving distractors. Fig. 4 shows the corresponding learned state space; one can clearly see the button area represented by the cluster of red dots (positive reward) and in gray (negative reward) the border of the field. These quantitative results show the bad quality of the state space learned by the autoencoder. The original robotic priors give better results, but some of the rewarded positions are still badly represented (red points on the left of the blue cloud). Finally, the 5 priors succeed in representing the overall shape of the state space correctly. Fine tuning the whole ResNet gives contrasted results: a small improvement in KNN-MSE, but a slight degradation in NIEQA. To further test the robustness of the priors, we learn states on dataset 3, where a distractor (the right arm) is static, but in different position from sequence to sequence. From the quantitative point of view (see Table III), the main result worth noticing is the original priors [START_REF] Jonschkowski | Learning state representations with robotic priors[END_REF] failing (and even performing worse than autoencoders). As is illustrated in Fig. 6, it generates 26 clusters of data points. In fact, each sequence is clustered into its own small subspace. This behavior is due to the fact that the distractors are mostly static and are more difficult to filter out than the distractors of the previous dataset that were moving randomly and were therefore easier to identify as not related to the task. The 5 th prior (when using a reference point close to the button) succeeds in solving this problem, by forcing the model to bring closer state representations that correspond to the same reference point and reaching performances closer to the supervised learning ones. Finally, we tested the priors on the most complex dataaugmented Colorful75 dataset 4 (see Table IV). The problem faced by this benchmark is similar to the one faced by the Complex-3D dataset: sequences are not brought together but stay apart from each other (see 6. However, in this case, the reference prior was not able to solve the problem. While being better than autoencoders, their performance remained far from supervised learning. Qualitatively, even though the problem is less obvious because of the sample density, the issue is illustrated in the left plot of Fig. 6 where we use as reference point the position of the button. Instead of having a gray barrier around that corresponds to the limits of the playground for the robot, gray states are scattered everywhere. Using a fixed starting position of the arm as a reference point, the right plot of Fig. 6 shows even worse performance, meaning that the further from the reward position the reference point is chosen, the more disturbed the representation gets.

Qualitative results, however, show that the 5 priors approach achieves results that are richer and more task-representative than autoencoders, and closer to those achieved with super- , if all dimensions range between (0,1) or between (-1e5,1e5), the end goal is to have dimensions that are coherent with the task Fig. 5. Effect of static distractors in dataset 3 on the 4 priors approach learned state space. As we can see, for every type of distractor, there is a different cluster of points; it means that the original 4 priors are not able to bring together states that should be close in the representation space. vised learning (on the real hand position). Fig. 7) shows an example of the nearest neighbor images retrieved in the dataset for each learned state space. It can be seen that the autoencoder focuses on the color of the background and the right arm position to retrieve the closest state, while the 5 priors and the supervised learning effectively focus on the robot hand position, and discard these distractors. V. DISCUSSION Our results show that robotic priors are an effective way of learning state representations with fast convergence (less than 15 epochs in all tests). Generally, robotic priors outperform autoencoders, but they also have limits worth remarking, concerning their reproducibility. The first remark is the sensibility of priors to distractors. While the original priors gracefully ignore distractors in settings where they are moving within a data sequence (as in dataset 2 and in [START_REF] Jonschkowski | Learning state representations with robotic priors[END_REF]), this does not equally generalize to the case where distractors are static but their position changes from one recorded sequence to another (as the right arm in dataset 3). The original priors are not robust either to domain randomization, and fail to bring sequences together when the context changes too much from sequence to sequence (resulting in the per-sequence "clustered" results on Complex-3D and Colorful75 datasets -Figs. 6 and 6-). It is in such cases, where the proposed 5 th reference point prior shows its two main advantages over using only four. Using the fixed point prior, representations are not only better, but they help avoiding the "one cluster per data sequence" problem by coherently shaping the state space. However, any setting (4 or 5) of priors usage greatly helps at sculpting the geometry of the task, specially the positive reward space (see middle and right images red states in Fig. 4), with respect to the DAE's representation.

A downside to the priors approach is the need to select relevant image pairs with associated rewards in every batch for the priors to work, which adds extra computation and attention required. Nonetheless, the idea of having a kind of reference point, or something that tells the robot "this context is the same" can be very useful in representation learning, and in future work, is something worth exploring.

Our benchmarks used NIEQA and the proposed KNN-MSE metrics. KNN-MSE seems to agree on the same ranking as NIEQA (both local and global) and when they did not agree, the scores were still close to each other. However, NIEQA 3is computationally intensive as compared to KNN-MSE and is therefore of limited interest for future work.

We also show that, despite having learned representations of states that are consistent with the task via a qualitative evaluation in terms of the closest nearest neighbors and the geometry of the space represented, visualizing Nearest-Neighbors is not sufficient to assess the quality of the representation: despite the nearest neighbors looking very close to the original image in 7, the first plot in 6 shows that the representation is not clean nor representative for the task (rewards are mixed together, no global shape, etc.).

VI. CONCLUSION

In this paper we extend the approach from [START_REF] Jonschkowski | Learning state representations with robotic priors[END_REF] to prove its scalability to different vision based tasks, to static and dynamic distractors and to domain randomization. Furthermore, we propose a new assessment method called KNN-MSE. It shows coherent scores and leads to results very similar to the more computationally complex NIEQA approach.

However, we show that there is room for future exploration with robotic priors. To mitigate the vulnerabilities of the original priors, we proposed a new prior that enhances results on the Static-Button-Distractors dataset and helps fixing the clustered sequence problem, but found its limits facing strong domain randomization. The presented approach, nevertheless, provides evidence that a deep network trained on generic robotics priors can learn meaningful state representations without using labeled input images.

Future work should explore the coupling of the priors with other state learning paradigms, such as learning simple forward and reward models to learn a state space [START_REF] Munk | Learning state representation for deep actor-critic control[END_REF], perform a more controlled investigation on the effect of different distractor objects and tackle more complex tasks, with different environments and several moving goals [START_REF] Raffin | S-RL Toolbox: Environments, Datasets and Evaluation Metrics for State Representation Learning[END_REF]. It also remains to evaluate the transferability of the learning approach from learning in simulated environments to learning with real robots, including the application to solving the task with reinforcement learning.

Fig. 1 .

 1 Fig. 1. Example of neural net architecture with two Siamese networks and frozen feature extractors (ResNet).

Fig. 2 .

 2 Fig. 2. Left: Baxter's camera view for Static-Button-Distractors dataset 2. Right: Baxter's left hand ground truth position and its coded reward

• Dataset 2 :

 2 Static-Button-Distractors: Small moving distracting objects are present in the scene, but not relevant for the task: 2 colored cubes and 1 lever; no data augmentation occurs. The amplitude of the actions can either be 0.05, -0.05 or 0 for all 3 axes (26 different actions possible), and the dataset contains 53 sequences of 90 frames length.• Dataset 3: Complex-3D-Data: In this case, we make the second (right, non operative) arm visible as well (having different position in each recorded sequence) and acts as a static distractor. We added more actions: instead of using a fixed amplitude of 0.05, it now ranges between 0.068 and -0.068 for all 3 dimensions. This database is made of 26 sequences of 200 frames each. • Dataset 4: Colorful75: We added domain randomization[START_REF] Sadeghi | CAD2RL: Real single-image flight without a single real image[END_REF],[START_REF] Tobin | Domain randomization for transferring deep neural networks from simulation to the real world[END_REF], i.e., every object and the table changes color from sequence to sequence. We used the same action amplitude as in dataset 3. It contains 75 sequences of 250 frames length each. A sample of each dataset is shown in Fig.3.

Fig. 3 .

 3 Fig. 3. A sample of each dataset (1-4), created for our benchmark

Fig. 4 .

 4 Fig. 4. Learned state space on Static-Button-Distractors (dataset 2): Left: Denoising Autoencoder. Middle: 4 Priors. Right: 5 Priors. The scale of each dimension is not indicated on the plots because they are irrelevant (i.e., if all dimensions range between (0,1) or between (-1e5,1e5), the end goal is to have dimensions that are coherent with the task

Fig. 6 .

 6 Fig. 6. Results of applying the 5 priors on colorful75 (dataset 4). Left: 5 priors using button position as ref. point. Right: 5 priors using starting hand position as ref. point. The 5th prior tames the overfitting effect exhibited in 6.

Fig. 7 .

 7 Fig. 7. Nearest neighbors retrieved for each of the models on the Colorful75 Dataset 4. The neighbors should represent the same button-hand relative position.Performance is shown in a left-right decreasing performance for the supervised (hand position) learning, 5 robotic priors and the autoencoder (better seen in video material). We can see that Supervised learning and Robotic Priors are very close (in terms of hand position), whereas the autoencoder matches the color of the table but misses the hand position (its representation doesn't encode the relevant information)

TABLE I

 I Mobile Robot (DATASET 1) RESULTS. xF MEANS X RESNET FROZEN LAYERS, GT: GROUND TRUTH (ROBOT POSITION)

	Criterion	GT	Superv 4Priors	5Priors	AE	5Priors
				3f	3f		0f
	KNN-MSE	0.172 0.185	0.253	0.217	1.7	0.205
	NIEQA local	0	0.076	0.32	0.18	0.67	0.15
	NIEQA global	0	0.003	0.09	0.04	0.87	0.019

TABLE III Complex

 III 3D Data (DATASET 3) RESULTS. xF MEANS X RESNET FROZEN LAYERS, GT: (HAND POSITION) GROUND TRUTH

	Criterion	GT	Superv 4Priors 5Priors AE	5Priors
							0f
	KNN-MSE	0.035 0.071	0.28	0.078	0.148 0.082
	NIEQA local	0	0.07	0.75	0.39	0.55	0.45
	NIEQA global	0	0.003	0.99	0.05	0.58	0.10

A low distance means that a neighbor in the ground truth is still a neighbor in the learned representation, and thus, local coherence is conserved

In this case there are 16 actions; the robot gets -1 reward if it touches a wall, +10 when it is in the top left corner (close to the yellow and red wall) and otherwise, no reward

We used the implementation provided by the authors of[START_REF] Zhang | A new embedding quality assessment method for manifold learning[END_REF]

ACKNOWLEDGMENT

We thank Clement Masson and Alexandre Coninx, for generating the data and reproducing the dataset in [1], respectively, as well as for fruitful discussions. This work is supported by the DREAM project through the European Union Horizon 2020 research and innovation program under grant agreement No 640891.


Devauchelle-Pensec Valérie

Rhumatologie Dubrana Frédéric

Chirurgie Orthopédique

Chirurgie infantile HU Weiguo, Chirurgie plastique, reconstructrice Bertrand

Endocrinologie, diabète Véronique

Thérapeutique Karine

Meur Le

Néphrologie Yannick

Nen Le

Chirurgie Dominique

Orthopédique

Pneumologie Christophe

Cardiologie Jacques Mansourati

Marianowski Rémi

Oto-Rhino-Laryngologie Merviel

Philippe Gynécologie

Misery Laurent

Parasitologie Dermato-Vénérologie Nevez Gilles

Bactériologie-Virologie Christopher

Pierre-Yves Salaun

Biophysique Jacques

Pédiatrie Stindel

Éric Biostatistiques

Serge Timsit

Valeri Neurologie

Urologie Walter Antoine

Michel

Bernard-Marcorelles Pascale

Anatomie Sylvain

Médecine Physique

Pédopsychiatrie Cornec Guillaume

Rhumatologie Couturaud Divi

Pneumologie GENTRIC Jean-Christophe Francis

Hery-Arnaud Geneviève

Bactériologie-Virologie Huet Olivier

Anesthésiologie-Réanimation L'her Erwan

Réanimation Le Gac Gérald

Génétique Le Marechal

Cédric Génétique

L E Roux

Biophysique Éric

Hématologie Montier

Tristan Biologie

Nousbaum Jean-Baptiste

Gastroentérologie Pradier Olivier

Cancérologie Renaudineau

Seizeur Romuald

Chirurgie digestive TROADEC Anatomie Thereaux Jérémie

Marie -Bérengère

Pierre Chiron Benoît

Hillion Sophie

Immunologie Le Berre Rozenn

Maladies Infectieuses Le

Gal Solène

Ven Florent

Cardiologie

Histologie, embryologie Talagas Matthieu

Anatomie Arnaud

Bactériologie-Virologie Sophie

Brenaut Emilie

Dermato-Vénéréologie Cornec-Le Gall

Emilie Néphrologie

Guillou Morgane

Addictologie Magro

Elsa Neurochirurgie

Robin Philippe

Schick Ulrike

Cancérologie

Lucas Derriennic Jérémy

Marine Sevray
email: marine.sevray@hotmail.fr

Emilie Brenaut

Yann Grangier

Laurent Misery

Florence Poizeau

Frédéric Staroz

PARTIE II

Keywords: skin retraction, shrinkage, cutaneous specimens, skin carcinoma, melanoma, margins

Maîtres de Conférences des

ans. La majorité (78,8%) des lésions étaient malignes (51% de carcinomes basocellulaires, 11% de carcinomes épidermoïdes, 8% de mélanomes). La rétraction du lambeau (29%) était significativement plus importante que celle de la lésion (21%) (p<0,001). La plus petite marge se rétractait en moyenne de 10%. En analyse multivariée, la localisation et le temps de fixation étaient significativement liés à l'importance de la rétraction. La rétraction du lambeau était de 17% en longueur et de 15% en largeur. La rétraction de la marge était calculée à 19% en longueur et 12% en largeur. Le chirurgien localisait correctement la plus petite marge seulement dans 55% des cas.

Discussion

ABSTRACT Introduction:

In previous studies, skin retraction of dermato-pathological specimens after the surgical excision of tumours was calculated at 30% for the surface, with approximately 20% for the length and 15% for the width. The aim of this study was to analyze the retraction of the specimens, the lesions and the margins of cutaneous specimens.

Methods:

In this observational, prospective and monocentric study, patients who had an excision of a skin tumour between January 2013 and July 2014 were randomly included.

Before excision, the surgeon collected the following data: localization of the lesion, specimen length and width in millimetres, lesion length and width in millimetres and the smallest margin in millimetres designed on a schema. After formalin fixation, the pathologist collected the same information and the duration of formalin fixation. Then with a microscope, he measured the smallest histological margin and noted whether the localization of the smallest margin was the same as the smallest margin indicated by the surgeon. The percentage of retraction was calculated for the various measures.

Results: A total of 104 patients was included. There were 52% male with a mean age of 68.3 years. Seventy-eight percent of the lesions were malignant (51% were basal cell carcinoma, 11% squamous cell carcinoma and 8% melanoma). The retraction of the area of the specimen (29%) was significantly greater than the retraction of the tumour (21%) (p<0,001). The retraction of the smallest margin was 10%. On multivariate analysis, the localization and the duration of fixation were independent predictors of the specimen area retraction. The retraction of the specimen was 17% in length and 15% in width. The retraction of the margins was calculated at 19% in length and 12% in width. The surgeon correctly evaluated the localization of the smallest margin in 55% of cases.

Discussion: Our study provided additional data regarding the retraction of the tumours and margins. We demonstrated that the retraction of the specimen's area was greater than that of the lesion's area. The guidelines for surgical excision of skin cancers recommend a clinical margin before excision, but the evaluation of the sufficiency of the margins is based on histological measurement. Our data are useful for the understanding of the sufficiency of the margins.

PARTIE I : INTRODUCTION

L'exérèse chirurgicale est le traitement de choix de la majorité des tumeurs cutanées malignes, mais aussi pour les tumeurs bénignes lorsqu'elles deviennent gênantes pour le patient. Son but est d'assurer localement l'excision de toute la tumeur et de pouvoir bénéficier d'une analyse anatomo-pathologique.

L'examen anatomo-pathologique des lésions cutanées est nécessaire pour déterminer le type de lésion et le caractère complet de l'exérèse sur les coupes examinées en renseignant les marges.

La tumeur et ses marges, latéralement et en profondeur, sont excisées pour éviter tout risque de tumeur résiduelle. Il existe le plus souvent une invasion infraclinique que seul l'examen histologique peut mettre en évidence.

On peut distinguer 2 marges. La marge clinique choisie par le chirurgien après avoir réalisé un examen clinique minutieux de la tumeur et la marge histologique mesurée par l'anatomopathologiste entre la tumeur et la périphérie de la pièce opératoire qui a été fixée.

Cette dernière doit être interprétée en prenant en compte les phénomènes de rétraction cutanée, qui est la capacité de la peau de pouvoir se rétrécir grâce à ses propriétés élastiques et contractiles.

Les recommandations concernant la prise en charge chirurgicale des lésions tumorales sont établies pour chaque type de tumeur maligne. Les cancers cutanés les plus fréquemment rencontrés par les dermatologues sont les carcinomes cutanés (basocellulaires et épidermoïdes) avec une incidence en constante augmentation. 10 mm sur zone à risque (zones péri-orificielles, cuir chevelu, zones non insolées, radiodermite, inflammation, cicatrice de brûlure ou ulcère chronique), ou supérieur ou égal 20 mm en zone à moindre risque (autres localisations de l'extrémité céphalique, tronc et membres). Les critères histologiques de mauvais pronostic sont l'invasion périnerveuse, le degré de différenciation cellulaire moyen à non différencié, le type desmoplastique, mucoépidermoïde, acantholytique, le niveau de Clark IV et l'épaisseur de plus de 3 mm.

Pour les CE sans aucun critère de mauvais pronostic les marges chirurgicales à respecter sont de 4-6 mm. Pour les CE avec au moins un critère de mauvais pronostic clinique ou histologique, les marges chirurgicales à respecter sont supérieures ou égales à 6 mm.

Enfin pour les mélanomes, les recommandations datent de 2016 (3).

Les marges chirurgicales à respecter sont de 0,5 cm pour les mélanome in situ, de 1 cm pour les mélanomes de Breslow 0,1-1 mm et les mélanomes de Dubreuilh, de 1-2 cm pour les mélanomes de Breslow 1,1-2 mm et de 2cm pour le mélanome avec un Breslow supérieur à 2 mm.

Pour ces 2 dernières tumeurs cutanées, le compte rendu histologique doit préciser la taille des marges, latérales et profondes, mesurées à l'examen microscopique.

Pour les carcinomes de mauvais pronostic et les mélanomes, les dossiers des patients doivent être présentés en réunion de concertation pluridisciplinaire (RCP). Il est indispensable de prendre en compte le degré de rétraction cutanée du lambeau, de la lésion mais aussi des marges pour comprendre les différences entre les marges cliniques et histologiques.

Différents travaux ont déjà été menés sur la rétraction du lambeau cutané. La rétraction globale de la surface d'exérèse est de 31% entre le temps pré-opératoire et après excision (4) et d'environ 20% en longueur et 15% en largueur (5)(6)(7). La majorité de la rétraction cutanée s'effectue quelques minutes après excision, grâce aux propriétés contractiles intrinsèques de la peau (5-7).

Les facteurs influençant cette rétraction diffèrent selon les études. Les auteurs s'accordent pour dire que la localisation de la lésion a une influence sur la rétraction cutanée mais pour certains la rétraction est plus importante au niveau cervical, des membres et du visage (4,7), alors que pour d'autres c'est au niveau du tronc (5,6).

Pour ce qui est de l'âge, certains auteurs ont retrouvé une influence (5,(8)(9) et d'autres non (6)(7).

Il y a donc peu de données sur ce sujet et elles sont discordantes. C'est pourquoi nous avons mené cette étude observationnelle, prospective et monocentrique à partir de 104 exérèses cutanées.

L'objectif principal de l'étude était de mesurer la rétraction cutanée du lambeau, de la lésion et des marges.

Nous avons également recherché s'il y avait des différences de variation de rétraction en fonction non seulement de la localisation mais aussi de l'âge du patient, du sexe, du type de lésion, de la taille avant excision et du temps de fixation.

Enfin, nous avons voulu savoir si l'examen clinique permettait de déterminer de façon fiable dans quel secteur de l'exérèse se trouvait la plus petite marge.

INTRODUCTION

After surgical excision of skin tumours, the retraction of the specimen's area has been calculated at approximately 30% from the moment before excision to 5 minutes after excision [START_REF] Dumas | Study of skin retraction applied to the treatment of skin tumors. Mapping of the human body[END_REF]. Formalin fixation added only a small amount of retraction, and the majority of tissue shrinkage occurred immediately after excision [2,3]. The power of the retraction varied significantly according to the region of the body [START_REF] Dumas | Study of skin retraction applied to the treatment of skin tumors. Mapping of the human body[END_REF]. Retraction has been calculated at approximately 20% for the length and 15% for the width of the specimen [2][3][4]. No study evaluated the retraction of the lesion, the specimen and the margin separately for all skin tumours type. These data would be useful for interpreting the margins of the histopathological result. The guidelines for the surgical excision of skin cancer (skin carcinoma and melanoma) recommend a clinical margin before excision, but there are no recommendations for the histological margins. Nevertheless, the evaluation of the sufficiency of the margins is based on this histological measurement. There are discrepancies between surgical and histopathological measurement; therefore, dermatologists and surgeons often discuss whether another larger excision is necessary in multidisciplinary meetings. The aim of this study was to analyse the retraction of the lesions, the specimens and the margins of cutaneous specimens.

MATERIAL AND METHODS

In this observational, prospective and monocentric study, patients who had a skin excision by the surgeon in the study (YG) between January 2013 and July 2014 were randomly included.

Measurements were taken at three different times:

1) Before excision, the surgeon collected the following data: localization of the lesion, specimen length and width in millimetres, lesion length and width in millimetres and the smallest margin in millimetres designed on a schematic diagram, with the orientation of the specimen (Figure 1).

2) After formalin fixation, the pathologist collected the same information (length and width of the specimen and the lesion, smallest margin in millimetres) and the duration of formalin fixation.

3) After fixation, cutting and staining, the specimen slide was analysed with a microscope by one of the four pathologists who participated in the study. Information collected included the diagnosis of the tumour and the localization of the smallest histological margin with its measurement in millimetres. All measurements, except the microscopic, were performed with a standard millimeter ruler. As the surgeon did elliptical excision, we noted whether the localization of the smallest margin was the same as the smallest margin indicated by the surgeon. The percentage of retraction was calculated for the various measurements.

We calculated the areas of the specimen and lesion before excision (S1) and after formalin fixation (S2) with the formula of the area of an ellipse: S= length x width x π/4, and the percentage of the retraction before excision and after formalin fixation was calculated with the formula R = 1 -(S2/S1).

We calculated margin length and width with the formula: (diameter of specimen -diameter of lesion)/2 to obtain additional data regarding margins in addition to the smallest margin measured.

Our primary objective was to analyse the percentage of retraction of the lesion, specimen and margins of cutaneous specimens before excision and after formalin fixation. The other objectives were to analyse the percentage of retraction according to gender, age, localization, area before excision, duration of fixation and the type of lesion. We also analysed the percentage of concordance between the surgeon-estimated margin and the pathologist's confirmed smallest margins, and when the margins were concordant, we calculated the percentage of retraction of the smallest margin.

Statistical analysis

Our data were analysed with descriptive and analytic methods. The quantitative variables were described using means and standard deviations. The qualitative variables were described using frequencies and percentages. The retraction of the specimens and the lesions were compared with paired t-tests. Linear regression was performed to study the association between the retraction as the dependent variable and a set of characteristics as the explanatory variables (gender, age as a continuous variable, localization, specimen or lesion area before excision, duration of fixation as a continuous variable and type of lesion).

Univariate linear regressions and adjusted linear regressions were performed to eliminate potential confounders. For all statistical analyses, type 1 error was set at 5%. All data were analysed using RStudio Version 1.0.136 (RStudio, Inc, Boston, MA, USA).

RESULTS

One hundred and four patients were included. The population was composed of 52% of men, with a mean age of 68.3 ± 17.5 years (range 12-92). The characteristics of the lesions are described in Table 1.

Among the 11 squamous cell carcinoma (SCC), 9 (82%) were located in the head and neck, and 2 (18%) were located in the limbs. Basal cell carcinomas (BCC) (n = 53) were located in the head and neck in 37 cases (70%), in the trunk in 12 cases (23%) and in the limbs in 4 cases (7%). Melanoma were located in 3 cases (37.5%) in the head and neck, in 3 cases (37.5%) in the trunk and in 2 cases (25%) in the limbs. The length, width and area before excision and after fixation are presented in Table 2.

The percentage of retraction of the specimen and the lesion are presented in Figure 2.

The retraction of the area of the specimen (29%) was significantly greater than the retraction of the lesion (21%), p<0.001. Among the 82 malignant lesions, 8 (10%) had a positive margin or a margin smaller than 1 mm.

For the malignant lesions, we analysed the concordance of localization of the smallest margin estimated by the surgeon and confirmed by the pathologist on microscopy. In 45 cases (55%), it was concordant, in 23 cases (28%) it was discordant, and information was missing in 14 cases (17%). In the 45 concordant cases, the mean percentage of retraction of the smallest margin was 1%. Among these 45 concordant cases, the size of the smallest margin was the same for the surgeon and the pathologist in 12 cases (27%), greater according to the surgeon's measurement in 17 cases (38%) and greater according to the pathologist's measurement in 16 cases (36%). Because of milimeter measurements inaccuracy of the surgeon with a standard millimeter ruler compared the use of a microscope for the pathologist we obtained negative measurements. The sum of positive and negative measurements explained the low mean retraction of 1%.

In malignant lesions, the retraction was analysed according to the diagnosis of the 3 main categories of malignant lesions (Table 3). Bowen's disease, pre-epitheliomatous keratosis, trichoblastoma and composite tumour were not analysed because of their low frequency.

The percentages of retraction of the estimated margins calculated for BCC, SCC and melanoma were 17%, 15% and 31% for length, respectively, and 3%, 19% and 33% for width, respectively. The differences were not significant.

We analysed the retraction according to gender, age, localization, area before excision, duration of fixation and type of lesion with linear unadjusted and adjusted regression analyses (Table 4).

Only the localization of the lesion was associated with the specimen area retraction on unadjusted linear regression analysis. After adjustment for other patient and lesion characteristics, localization (p <0 .001) and duration of fixation (p=0.04) were independently associated with specimen area retraction. No factor was significantly associated with the percentage of retraction of the lesion, neither on univariate nor on multivariate regression analysis.

DISCUSSION

In this study, based on 104 cutaneous specimens, the mean retraction of the specimen's area was calculated at 29%. This outcome was consistent with a study by Dumas et al., in which the mean area retraction was evaluated at 31% five minutes after excision [START_REF] Dumas | Study of skin retraction applied to the treatment of skin tumors. Mapping of the human body[END_REF]. Previous studies highlighted that the majority of tissue shrinkage occurred immediately after excision and prior to fixation because of intrinsic contractile properties of the tissue itself [2][3][4]. Formalin fixation added only a small amount of retraction. Retraction in length and width was evaluated at respectively 17% and 15% for the specimen and 11% and 13% for the lesion. These results were consistent with the results of previous studies; retraction was calculated between 16% and 21% for length and between 18% and 10% for width [2][3][4]. Blasdale et al. conducted a study on BCC and reported a mean retraction of the whole specimen widest diameter of 14%, and a significant difference between the 19% shrinkage of normal skin compared with skin containing tumour tissue which shrank by only 11% [5]. Concerning factors influencing retraction, the localization was significantly associated with the percentage of retraction.

Retraction was greater in the upper extremities than that in the lower extremities, the trunk or the head and neck. In previous studies [START_REF] Dumas | Study of skin retraction applied to the treatment of skin tumors. Mapping of the human body[END_REF][2][3], retraction was also greater in the trunk and limbs than that in the head and neck. In our study, gender and age were not independent factors of retraction. In other studies, retraction was less with greater age [2,6,7]. Silverman et al. studied 407 malignant melanomas and proposed a formula to determine an in vivo diameter: in vivo diameter = (1.18 or 1.25 or 1.33) x in vitro diameter with 1.18 when age <50, 1.25 when age 50-59 and 1.33 when age ≥60 [7], however previous studies and ours demonstrated no effect of age on the retraction [3,5]. In our study, the longest formalin fixation was associated with a smallest retraction, by contrast with previous studies [2,3].

Our study provides additional data regarding the retraction of tumours and their margins for all skin tumours type. The retraction of the specimen's area was greater than that of the lesion's area. The retraction of the margins was calculated as 19% for length and 12% for width. The retraction of the smallest margin was 10%. Of this result we can estimate the smallest margin before excision with the formula: microscopic margin/0,9 (1-10%=0,9). The guidelines for the surgical excision of skin cancers (skin carcinoma and melanoma) recommend a clinical margin before excision [8,9]. The margins recommended by the guidelines vary by country, and there is actually no international consensus [8]. There is no recommendation regarding the histological margin, whereas the evaluation of correct margins is based on this histological measurement. There are discrepancies between surgical and histopathological measurements; therefore, dermatologists and surgeons often discuss in multidisciplinary meetings whether another larger excision is necessary. Sufficient removal is essential because incomplete removal is considered a poor prognostic indicator, as incomplete removal of lesions is a risk factor for local recurrence. For BCC, incomplete removal of the tumour ranges from 6% to 25%, depending on the improper intra-operative evaluation of the extent of the tumour [10]. A previous study showed that narrow margins (1-3 mm) were inadequate for the excision of small, well-demarcated, primary nodular BCCs of the face, with a high rate (20%) of incomplete excision [11]. When the excision is incomplete, another surgery is generally recommended. It is more complicated when the excision is complete but with a narrow margin. Only Mohs micrographic surgery can claim that excision is complete, owing to the analysis of all margins. In any case, it is essential to have a correct margin. To interpret the histological margin, it is useful to have data regarding retraction.

The surgeon correctly evaluated the localization of the smallest margin in only 55% of cases, demonstrating the difficulty for the clinician in evaluating the correct margin, because some tumours infiltrate lateral margins at a greater depth and some lesions are poorly limited. Some tools can help the surgeon or dermatologist to delimit margins of the tumour. In particular, the use of reflectance confocal microscopy was associated with a better rate of complete excision of melanoma and lentigo maligna compared with dermoscopically determined margins, as well as for basal cell carcinoma, although the data were more limited [START_REF] Edwards | Diagnostic accuracy of reflectance confocal microscopy using VivaScope for detecting and monitoring skin lesions: a systematic review[END_REF].

Dermoscopy and high-frequency ultrasound are also used to improve delimitation of margins [START_REF] Hayashi | Detection of the tumor margin of basal-cell carcinoma using dermoscopy and high-frequency ultrasound with narrow pieces of surgical tape as skin markers[END_REF].

The limitations of this study are the monocentric recruitment of patients and the heterogeneity of the diagnoses. Another limitation is the precision of the measurements in millimetres, for the margins in particular (especially for benign lesions for which margins are narrow). For the pathologist, a limitation is represented by the difficulty in macroscopically determining the limits of the tumour that can be modified by the disappearance of erythema after formalin fixation. Also, we could not study more accurately the difference in retraction according to the different areas of the face due to the insufficient number of cases. The study of the periorbital areas, which in practice seems to retract significantly after the excision, could be particularly interesting.

A complementary study could be useful with inking methods of the specimen margins and the lesion margins to determine more precisely these different measurements, and also to analyse retraction in more detail according to location, especially the face, which is a recurrent problem in current practice.

Only one surgeon performed the excision, so the surgical method was reproducible. The surgeon in our study performed elliptical excision, so there was a narrow and a large margin.

Elliptical excision is a standard method of skin tumour removal, but round excision with dogear repair can be considered as a good method, with better wound healing. Nevertheless, no study has compared these methods to compare the rate of incomplete removal [START_REF] Mj | Comparison of wound closure by means of dog ear repair and elliptical excision[END_REF][START_REF] Seo | Round excisions lead to shorter scars and better scar positioning than traditional elliptical excisions[END_REF].

Our study provides new data on the retraction of lesions and specimens, and especially of margins. These data are important to determine whether the excision of the lesion is complete, especially for BCC and SCC. Nevertheless, larger studies are needed to determine which differences could be tolerated before planning new interventions.

PARTIE III : CONCLUSION

Notre étude qui a inclus 104 patients a permis de mettre en évidence une rétraction du lambeau de 29% significativement plus importante que celle de la lésion qui était de 21%.

Pour la plus petite marge, avec des excisions elliptiques, la rétraction était en moyenne de 10% et estimée à 19% dans la longueur et 12% dans la largeur.

Pour ce qui est des facteurs ayant un impact sur l'importance de la rétraction, on retrouvait un résultat significatif seulement pour la localisation et le temps de fixation. Celle-ci était plus importante au niveau des membres supérieurs et quand le temps de fixation était court.

Alors que l'on pourrait s'attendre à une différence de rétraction entre les lésions bénignes et les lésions malignes du fait de l'infiltration des tissus par la tumeur, cette différence n'a pas été mise en évidence. Il en est de même pour l'âge et le sexe.

Quand on regarde la concordance de localisation de la plus petite marge entre celle évaluée par le chirurgien et celle mesurée en histologie on retrouve seulement 55% de concordance.

Cette discordance peut être expliquée par l'infiltration de la tumeur en profondeur et le fait que les tumeurs malignes sont souvent mal délimitées, avec des extensions infra-cliniques.

Lorsqu'elle était concordante entre le chirurgien et le pathologiste, la rétraction de la plus petite marge était en moyenne de 1% avec toutefois des écarts types importants (+/-44). Dans

  FIGURES …………………………………………………………………………………………………………………… 32

  : Notre étude apporte des nouvelles données notamment sur la rétraction de la tumeur et des marges. Elle démontre une rétraction plus importante du lambeau que de la lésion. Ces données sont importantes à connaître car les recommandations sur les marges chirurgicales sont basées sur la mesure clinique alors que le caractère suffisant de la marge est basé sur l'examen anatomo-pathologique. Pour interpréter la marge histologique et décider d'une éventuelle reprise chirurgicale, il est nécessaire d'intégrer la notion de rétraction à la réflexion et d'avoir des données sur la rétraction du lambeau mais aussi de la marge.

  La RCP est une réunion qui se déroule dans les services avec une activité d'oncologie, au cours de laquelle se discutent la situation d'un patient, les traitements possibles en fonction des dernières études scientifiques ainsi que l'analyse des bénéfices et les risques encourus. Elle rassemble au minimum trois spécialistes différents. Son objectif est de prendre une décision collégiale, basée sur les recommandations de bonnes pratiques, pour que la prise en charge de chaque patient soit optimale. La question du caractère suffisant ou non des marges après l'exérèse d'un cancer cutané est souvent soulevée, afin de statuer sur une simple surveillance ou la nécessité d'une reprise chirurgicale. Cette discussion est le plus souvent basée sur la mesure des marges histologiques présentes sur le compte rendu d'anatomo-pathologie alors que les recommandations indiquent des marges cliniques à respecter exprimées en millimètres. Il y a donc une discordance entre des recommandations exprimant des marges chirurgicales cliniques et des décisions prises sur des marges histologiques.

FIGURESFigure 1 :

 1 FIGURES

Figure 2 :

 2 Figure 2: Percentage of retraction of specimen and lesion.

  notre étude, la lésion se rétractant moins que le lambeau cutané nous attendions une rétraction de la marge plus importante. Ce résultat s'explique par la présence de données négatives lorsque le chirurgien trouvait une marge plus petite que le pathologiste, probablement du fait de la différence de précision de mesure entre le chirurgien qui utilisait un double décimètre standard alors que le pathologiste mesurait avec son microscope. Cette situation peut également illustrer la difficulté d'apprécier cliniquement la marge, avec l'existence de facteurs confondant comme l'inflammation réactionnelle au processus tumoral. Notre étude apporte des nouvelles données concernant la rétraction de la tumeur et des marges. Pour interpréter la marge histologique et décider d'une éventuelle reprise chirurgicale, il est nécessaire d'intégrer la notion de rétraction à la réflexion. Les limites de notre étude ne nous permettent pas de déterminer des critères objectifs pour aider les praticiens lors des RCP. Deux études récentes de 2019, apportent d'autres données sur la rétraction des marges cutanées en oncodermatologie. Moret et al. (10) ont étudié la rétraction des marges en comparant les mesures des marges préopératoires, postopératoires et histologiques de 79 tumeurs. Ils retrouvent une rétraction significative des marges de 0,4 à 0,6 mm entre les mesures préopératoires et postopératoires et de 0,4 à 0,5 mm entre les mesures préopératoires et histologiques. Cependant ils mettent en évidence une augmentation significative entre les mesures postopératoires et histologiques qu'ils expliquent par la présence d'une zone péri-lésionnelle inflammatoire que le chirurgien peut considérer comme étant tumorale alors que le pathologiste comme une zone saine. Ils n'ont pas retrouvé de facteur lié au patient influençant la rétraction. Friedman et al. (11) démontrent, après avoir étudié 252 cas d'exérèse de mélanome, que la rétraction moyenne de la largeur du lambeau entre le temps préopératoire et après fixation formolée est de 14% sans influence de l'âge, du sexe, de l'indice de masse corporelle ou de la localisation de la tumeur. Ils constatent aussi que les marges histologiques sont en moyenne 37% plus petites que les marges chirurgicales. Notre étude, ainsi que celles ayant porté sur le même sujet, montrent que les données sur la rétraction post opératoires devraient vraisemblablement être prises en compte pour déterminer la prise en charge du patient. Une étude avec un effectif de patients plus important, une méthode d'encrage spécifique et des mesures plus précises, serait utile pour compléter notre étude et pouvoir à terme intégrer la notion de rétraction cutanée aux recommandations.

Table 4 :

 4 Percentage of retraction according to gender, age, localization, area before excision, duration of fixation and type of lesion.

			Retraction		Retraction of		Retraction
			of area	p-	area	p-	of smallest
			specimen	values*	lesion	values*	Margin
			Mean (SD)		Mean (SD)		Mean (SD)
	Gender	Male (n=54) Female (n=50)	30 (15) 28 (12)	0.33	21 (22) 22 (22)	0.79	11 (25) 9 (28)
	Age*	≤ 70 years (n=49) > 70 years (n=55)	31 (15) 27 (12)	0.06	26 (23) 17 (21)	0.57	15 (22) 6 (29)
	Localization	Head/neck (n=59)	24 (12)		21 (22)		10 (23)
		Trunk (n=26) Superior limb (n=8)	35 (13) 43 (15)	<0.001	24 (23) 30 (16)	0.14	19 (28) -6 (44)
		Inferior limb (n=11)	31 (7)		8 (21)		2 (17)
	Area specimen	<400 mm² (n=62)	26 (13)
	before excision**	>400 mm² (n=42)	34 (13)	0.06	-	-	-
	Area lesion	<100 mm² (n=73)			28 (13)
	before excision**	>100 mm² (n=31)	-	-	32 (14)	0.75	-
	Duration of	24 hours (n=39)	31 (14)		22 (22)		12 (29)
	fixation**	48 hours (n=27)	28 (14)		18 (21)		18 (26)
		72 hours (n=17)	28 (11)	0.18	25 (28)	0.84	0 (12)
		96 and 120 hours	27 (13)		21 (19)		4 (28)
		(n=21)
	Type of lesion Benign (n=22) Malignant (n=82)	32 (13) 29 (14)	0.35	20 (24) 22 (22)	0.81	8 (18) 11 (28)

*Univariate linear regression analysis **Statistical tests used continuous variables

cm sur zone à risque intermédiaire de récidive ou de plus de

cm sur zone à bas risque de récidive, les marges chirurgicales à respecter sont supérieures ou égales 4 mm. Pour les CBC de mauvais pronostic, comprenant les formes histologiques agressives (sclérodermiforme, infiltrant et métaplasique), les formes récidivées et les CBC nodulaires localisés sur une zone à haut risque de récidive de taille supérieure à 1 cm, les marges chirurgicales à respecter sont de 5 à 10 mm. Pour ces derniers, la chirurgie micrographique de Mohs est recommandée car le taux de récidive est plus faible avec cette technique. Pour tous les CBC, le compte rendu histologique doit préciser si l'exérèse est complète, incomplète ou « au raz », latéralement et en profondeur, sans obligatoirement préciser la taille histologique de la plus petite marge. Concernant les carcinomes épidermoïdes (CE), les recommandations ont été établies par L'Institut National du Cancer et la Haute Autorité de Santé en 2009 (2). Ils sont classés en 2 groupes distincts, selon des critères cliniques et histologiques de mauvais pronostic. Les critères cliniques de mauvais pronostic sont la récidive locale, l'adhérence au plan profond, des signes neurologiques d'envahissement, l'immunodépression, le diamètre de plus de

Pour la prise en charge des carcinomes basocellulaires (CBC), les recommandations sont régies par l'Agence nationale d'accréditation et d'évaluation en santé (1). Les CBC sont classés en trois groupes : bon pronostic, pronostic intermédiaire et mauvais pronostic.

Pour les CBC de bon pronostic, comprenant les CBC superficiels et les CBC nodulaires primaires de moins de 1 cm sur une zone à risque intermédiaire de récidive (front, joue, menton, cuir chevelu et cou) ou de moins de 2 cm sur une zone à bas risque de récidive (tronc et membres), les marges chirurgicales à respecter sont de 3 à 4 mm. Pour les CBC de pronostic intermédiaire, comprenant les CBC superficiels récidivés et les CBC nodulaires de moins de 1 cm sur zone à haut risque de récidive (nez et zones péri orificielles de l'extrémité céphalique) ou de plus de

ACKNOWLEDGEMENTS

We acknowledge the contributions of Aurélie Adriansen, Jocelyne Perrot and Laurence Moreau, pathologists who contributed to analyse the specimens, as well as Patrice Plantin for his encouragement and Sébastian Costa for correcting the English language.

TAKE HOME MESSAGES

The retraction of the area of the specimen was significantly greater than the retraction of the lesion, which impacts the margins.

The localization and the duration of fixation were independent predictors of the specimen area retraction.

The surgeon correctly evaluated the localization of the smallest margin in just over half of the cases.

These data are useful for interpreting the sufficiency of margins on the histopathological report, especially for skin carcinomas.

SEVRAY (Marine