Tamara Dupuy

Clément Beitone

Jocelyne Troccaz

Sandrine Voros

2D/3D Deep Registration for Real-Time Prostate Biopsy Navigation

Keywords: Image Registration, Convolutional Neural Network, Image-guided Intervention, Prostate biopsy

The accuracy of biopsy sampling and the related tumor localization are major issues for prostate cancer diagnosis and therapy. However, the ability to navigate accurately to biopsy targets faces several difficulties coming from both transrectal ultrasound (TRUS) image guidance properties and prostate motion or deformation. To reduce inaccuracy and exam duration, the main objective of this study is to develop a real-time navigation assistance. The aim is to provide the current probe position and orientation with respect to the deformable organ and the next biopsy targets. We propose a deep learning real-time 2D/3D registration method based on Convolutional Neural Networks (CNN) to localize the current 2D US image relative to the available 3D TRUS reference volume. We experiment several scenarii combining different input data including: pair of successive 2D US images, the optical flow between them and current probe tracking information. The main novelty of our study is to consider prior navigation trajectory information by introducing previous registration result. This model is evaluated on clinical data through simulated biopsy trajectories. The results highlight significant improvement by exploiting trajectory information especially through prior registration results and probe tracking parameters. With such trajectory information, we achieve an average registration error of 2.21 mm ± 2.89. The network demonstrates efficient generalization capabilities on new patients and new trajectories, which is promising for successful continuous tracking during biopsy procedure.

INTRODUCTION 1.1 Clinical context and motivations

The accurate localization of targets and navigation towards them is critical to many clinical tasks especially for image-guided interventions on soft-tissue. 2D images are often used for intra-operative guidance and most often provide real-time information about the organs and the intervention, at the expense of a limited view of the 3D scene. On the other hand, preoperative 3D acquisitions usually include additional and better information for both visualization and navigation purposes. Therefore, the robust and real-time fusion of preoperative 3D image with intra-operative 2D image flow has a great potential for guidance, as it can cope with real-time anatomy deformation and provide a reliable estimate of the position of interventional targets.

A typical case is prostate biopsy, where navigation to biopsy targets faces several difficulties coming from both the transrectal ultrasound (TRUS) modality properties and prostate characteristics. Indeed, the real-time organ visualization is made difficult due to US modality which presents variable image quality (low signal to noise ratio, artefacts, speckle), poor sensitivity to cancerous tissue and limited 2D anatomical context. Moreover, the clinician's mental 3D representation is even more challenging due to the spherical, symmetrical and deformable characteristics of the prostate. The impossibility to figure out the effect of ultrasound probe motion on the prostate and related targets may make samples localization very uncertain. These difficulties may result in longer and uncomfortable examination procedure for the patient, but may also produce biased diagnosis and inappropriate therapeutic decision (about 30% of false negative and risk of overtreatment [START_REF] Gillies | Real-time registration of 3D to 2D ultrasound images for image-guided prostate biopsy[END_REF][START_REF] Karnik | Assessment of image registration accuracy in three-dimensional transrectal ultrasound guided prostate biopsy: Image registration accuracy in 3D TRUS-guided prostate biopsy[END_REF] ). Finally, wrong sample localization may also result in inaccurate treatment when using focal therapy application.

In this context where prostate cancer diagnosis and therapy are at stakes, providing real-time assistance during prostate biopsy interventions has led to several developments over the past two decades [START_REF] Cornud | TRUS-MRI image registration: A paradigm shift in the diagnosis of significant prostate cancer[END_REF][START_REF] Brown | Recent advances in image-guided targeted prostate biopsy[END_REF] .

First approaches focused on improving biopsy localization by using 3D/3D registration to include preoperative information. These approaches used either optimization-based 5 or deep-learning based methods [START_REF] Zeng | Label-driven magnetic resonance imaging (MRI)-transrectal ultrasound (TRUS) registration using weakly supervised learning for MRI-guided prostate radiotherapy[END_REF][START_REF] Zeng | Weakly non-rigid MR-TRUS prostate registration using fully convolutional and recurrent neural networks[END_REF][START_REF] Zhu | Feasibility of Image Registration for Ultrasound-Guided Prostate Radiotherapy Based on Similarity Measurement by a Convolutional Neural Network[END_REF][START_REF] Hu | LABEL-DRIVEN WEAKLY-SUPERVISED LEARNING FOR MUL-TIMODAL DEFORMABLE IMAGE REGISTRATION[END_REF][START_REF] Guo | Deep adaptive registration of multi-modal prostate images[END_REF] . They register preoperative 3D MR reference image to 3D TRUS image, acquired at the start of the procedure. However, these approaches do not take into account intra-operative anatomical deformations and result in limited accuracy. Moreover, the initial 3D TRUS image is most often reconstructed from probe sweeping (2D slices and their position information), which results in a biased 3D volume (tissue deformation due to probe sweep). To include updated anatomical deformations, other studies [START_REF] Baumann | Prostate biopsy tracking with deformation estimation[END_REF] propose to register the initial 3D TRUS image to 3D TRUS images acquired all along the procedure. However, they are computationally intensive and need long 3D acquisition time. Moreover, they are used only at static positions, just before getting each biopsy sample. Finally, even if this first kind of approaches enables a better localization of biopsy sampling, the clinicians must still rely only on limited 2D US flow and personal experience to navigate efficiently between two biopsy sites.

This has motivated another kind of approaches 1, 5, 12-15 focused on providing real-time navigation assistance to the clinicians. They aim at computing the current position of the probe relatively to the next biopsy target. This dynamic assistance is based on real-time 2D/3D registration which links the 2D live image to the initial 3D TRUS image. Optimization-based methods have still limited results in terms of accuracy [START_REF] Beitone | Towards real-time free-hand biopsy navigation[END_REF] , computational efficiency [START_REF] Xu | Real-time MRI-TRUS fusion for guidance of targeted prostate biopsies[END_REF][START_REF] Selmi | Hybrid 2D-3D ultrasound registration for navigated prostate biopsy[END_REF][START_REF] De Silva | 2D-3D rigid registration to compensate for prostate motion during 3D TRUS-guided biopsy: 2D-3D rigid registration to compensate for prostate motion[END_REF] , or clinical evaluation (limited data set or phantom) [START_REF] Gillies | Real-time registration of 3D to 2D ultrasound images for image-guided prostate biopsy[END_REF][START_REF] Tessier | Ring navigation: An ultrasoundguided technique using real-time motion compensation for prostate biopsies[END_REF] . More recently, deep learning-based strategies provided a new opportunity to develop robust real-time guidance. Related work is described in more details in the next section.

Finally, registration results must satisfy clinical requirements both in terms of accuracy and computational efficiency. Regarding accuracy, a consensus value of 0.5 cc exists concerning the smallest significant treatable tumour [START_REF] Gillies | Real-time registration of 3D to 2D ultrasound images for image-guided prostate biopsy[END_REF][START_REF] Karnik | Assessment of image registration accuracy in three-dimensional transrectal ultrasound guided prostate biopsy: Image registration accuracy in 3D TRUS-guided prostate biopsy[END_REF] and corresponds approximately to a sphere having a radius of 5 mm. Therefore, 5mm will be used as an acceptance range to evaluate the registration quality. Moreover, for real-time navigation assistance, the computational requirement is related to the TRUS guidance frequency (about 10-20 Hz). A computation time below 50 ms would provide real-time guidance.

2D/3D deep registration for real-time navigation assistance

This section extends to any 2D/3D real-time deep registration study considering, either slices location inside a volume, or volume reconstruction from slices. Most of the literature [START_REF] Hou | Predicting Slice-to-Volume Transformation in Presence of Arbitrary Subject Motion[END_REF][START_REF] Yu | Slice Localization for Three-Dimensional Breast Ultrasound Volume Using Deep Learning[END_REF][START_REF] Salehi | Real-Time Deep Pose Estimation With Geodesic Loss for Image-to-Template Rigid Registration[END_REF][START_REF] Almogadwy | A Deep Learning Approach for Slice to Volume Biomedical Image Integration[END_REF][START_REF] Li | Standard Plane Detection in 3D Fetal Ultrasound Using an Iterative Transformation Network[END_REF][START_REF] Chen | Real-time and multimodal brain slice-to-volume registration using CNN[END_REF][START_REF] Singh | Deep Predictive Motion Tracking in Magnetic Resonance Imaging: Application to Fetal Imaging[END_REF][START_REF] Miao | A CNN Regression Approach for Real-Time 2D/3D Registration[END_REF][START_REF] Miao | Real-time 2D/3D registration via CNN regression[END_REF] is focused on a supervised regression task, for end-to-end prediction of rigid transformation parameters only (rotations and translations) and most often uses convolutional neural networks (CNN) architectures. A majority of the methods predict slices localization with respect to a fixed reference volume by only inputting the moving slices. Few studies combined both 2D and 3D inputs in the same model [START_REF] Bhardwaj | Rigid and deformable corrections in real-time using deep learning for prostate fusion biopsy[END_REF][START_REF] Wei | TOWARDS FULLY AUTOMATIC 2D US TO 3D CT/MR REGISTRATION: A NOVEL SEGMENTATION-BASED STRATEGY[END_REF] . Even if most of these studies aim to solve 2D/3D registration, comparing them remains difficult, as data involved may be very different in terms of modality (mostly MRI, vs. US), source (clinical or phantom), motion generation (recorded or artificially simulated), datasets, and preprocessing (centered, initialized, segmented, etc.). Evaluation is also a crucial criterion for result interpretation. It depends also on the metrics used (mean squared error, target registration error, etc.), and transformation representation (quaternion, Euler angle, rotation matrix, fiducials, etc.).

We find several main structures among all these studies: (i) some use a hierarchical structure [START_REF] Zeng | Label-driven magnetic resonance imaging (MRI)-transrectal ultrasound (TRUS) registration using weakly supervised learning for MRI-guided prostate radiotherapy[END_REF][START_REF] Zeng | Weakly non-rigid MR-TRUS prostate registration using fully convolutional and recurrent neural networks[END_REF][START_REF] Miao | A CNN Regression Approach for Real-Time 2D/3D Registration[END_REF][START_REF] Miao | Real-time 2D/3D registration via CNN regression[END_REF][START_REF] Bhardwaj | Rigid and deformable corrections in real-time using deep learning for prostate fusion biopsy[END_REF][START_REF] Wei | TOWARDS FULLY AUTOMATIC 2D US TO 3D CT/MR REGISTRATION: A NOVEL SEGMENTATION-BASED STRATEGY[END_REF][START_REF] Hu | Weakly-supervised convolutional neural networks for multimodal image registration[END_REF] . It allows a coarse-to-fine registration by using results from a previous step to initialize the next one. First steps rely on networks performing either segmentation tasks [START_REF] Zeng | Label-driven magnetic resonance imaging (MRI)-transrectal ultrasound (TRUS) registration using weakly supervised learning for MRI-guided prostate radiotherapy[END_REF][START_REF] Zeng | Weakly non-rigid MR-TRUS prostate registration using fully convolutional and recurrent neural networks[END_REF][START_REF] Miao | A CNN Regression Approach for Real-Time 2D/3D Registration[END_REF][START_REF] Miao | Real-time 2D/3D registration via CNN regression[END_REF][START_REF] Bhardwaj | Rigid and deformable corrections in real-time using deep learning for prostate fusion biopsy[END_REF] , classification tasks [START_REF] Wei | TOWARDS FULLY AUTOMATIC 2D US TO 3D CT/MR REGISTRATION: A NOVEL SEGMENTATION-BASED STRATEGY[END_REF] , or registration initializations [START_REF] Zeng | Label-driven magnetic resonance imaging (MRI)-transrectal ultrasound (TRUS) registration using weakly supervised learning for MRI-guided prostate radiotherapy[END_REF][START_REF] Zeng | Weakly non-rigid MR-TRUS prostate registration using fully convolutional and recurrent neural networks[END_REF][START_REF] Miao | A CNN Regression Approach for Real-Time 2D/3D Registration[END_REF][START_REF] Miao | Real-time 2D/3D registration via CNN regression[END_REF] . (ii) Others decompose the registration problem into sub problems with a more local focus [START_REF] Zhu | Feasibility of Image Registration for Ultrasound-Guided Prostate Radiotherapy Based on Similarity Measurement by a Convolutional Neural Network[END_REF][START_REF] Miao | A CNN Regression Approach for Real-Time 2D/3D Registration[END_REF][START_REF] Miao | Real-time 2D/3D registration via CNN regression[END_REF] . It allows reducing the complexity of a problem and computation time, but also avoiding convergence towards local minima. Results of each sub problem are then averaged through either the calculation of the loss function [START_REF] Zhu | Feasibility of Image Registration for Ultrasound-Guided Prostate Radiotherapy Based on Similarity Measurement by a Convolutional Neural Network[END_REF] , or combined through concatenation on fully connected layer [START_REF] Miao | A CNN Regression Approach for Real-Time 2D/3D Registration[END_REF][START_REF] Miao | Real-time 2D/3D registration via CNN regression[END_REF] . (iii) Some others convert the registration problem into a classification problem. Classification can be difficult to exploit as most of registration problem parameters are related to continuous and complex representations. Classification can solve partly [START_REF] Wei | TOWARDS FULLY AUTOMATIC 2D US TO 3D CT/MR REGISTRATION: A NOVEL SEGMENTATION-BASED STRATEGY[END_REF] or totally 21 the registration problem. (iv) Finally, a few studies focus on dynamical structures by using recurrent network. LSTM have shown their values to model a complex temporal process and can be used to register a complete sequence of slices [START_REF] Singh | Deep Predictive Motion Tracking in Magnetic Resonance Imaging: Application to Fetal Imaging[END_REF] .

A promising work [START_REF] Prevost | 3D freehand ultrasound without external tracking using deep learning[END_REF] , we want to describe in more details, proposes a CNN for 3D US volume reconstruction from 2D US images, by estimating relative transform parameters between successive US frames. The network main input is the pair of successive images. Additional inputs include the optical flow between the two images, and current probe tracking information. The authors showed that incorporating such additional information to the pair of images significantly helped the network to be more accurate and robust, much more than changes in its architecture. But even with extremely simple probe movements, results reveal a drift along the reconstruction due to error accumulation when performing successive registrations. Even if this work presents different objectives compared to 2D/3D registration, it illustrates a promising method to correlate 2D information to global 3D localization using relative and successive information.

Objectives and contribution

To allow navigation assistance during biopsy procedures, the main objective of this study is to develop and evaluate a deep learning real-time 2D/3D registration method to localize the "live" 2D US prostate image relative to the available 3D reference volume (e.g. preoperative US). Similarly to most of the studies found in literature, we focused on supervised CNN to predict rigid transformation parameters. The proposed method is mainly inspired from Prevost [START_REF] Prevost | 3D freehand ultrasound without external tracking using deep learning[END_REF] for their network architecture as well as their additional inputs strategies. The main novelty of the presented study is to consider prior navigation trajectory information. By introducing the registration result information of the previous 2D US image, we intend to help the network to better estimate the current slice localization. This information is added as additional input to the network and not as a conventional initialization step. The benefit of such information is evaluated through this study.

METHOD

Being given a series of 2D US images (I 1 , I 2 , ..., I t ) acquired during a prostate biopsy exam, the aim is to register at each time t the current image I t to the 3D US reference volume. The resulting 2D/3D rigid transform is denoted as T t . Due to data construction (see Part 3.1), only the 3 rotational parameters (θx, θy, θz) are considered to describe the orientation of the slice with respect to the volume. They are represented using the Euler angle encoding.

Similarly to Prevost [START_REF] Prevost | 3D freehand ultrasound without external tracking using deep learning[END_REF] , we include the following inputs : (i) Pair of images: the current slice I t to localize and the previous one I t-1 . The pair is fed into the network as a 2-channel image (cropped to 150x250 pixels), so that the spatial information between them is coupled from the very first layer through the network's convolutions. This input is common in all the scenarii. (ii) Optical flow (optional input): this 2D vector field represents the relative in-plane motion between the two images. The two components of this vector field are concatenated to the pair of images to form a 4-channel image input that preserves the spatial correspondence. As in Prevost [START_REF] Prevost | 3D freehand ultrasound without external tracking using deep learning[END_REF] , the optical flow is based on Farnebäck algorithm 29 . (iii) Probe tracking information (optional input): the probe sensor information corresponding to the relative displacement between two successive images. We consider for relative displacement, again, only the rotation parameters that we concatenate to the 512-vector layer of the network. We simulated those relative displacements using two successive global ones (T -1 t * T t-1 ), to which we add a maximum random noise of 1°corresponding to the average inertial sensor noise [START_REF] Kok | Using Inertial Sensors for Position and Orientation Estimation[END_REF] .

We experiment 4 different scenarii by combining the proposed inputs: Scenario 1: only the pair of images, Scenario 2: pair of images + optical flow, Scenario 3: pair of images + probe tracking, Scenario 4: pair of images + optical flow + probe tracking.

Finally, to evaluate the contribution of prior trajectory information, another input (T prior ) is added to each of these scenarii. This prior information corresponds to the previous registration result T t-1 . This rotation parameter label vector is added on the same 512-vector layer of the network.

Network architecture and training

The CNN architecture is presented in Figure 1. It is composed of 12 convolutional layers, all followed by a rectified linear unit (ReLU) and max pooling layers. Then, the network consists in 6 fully connected layers, with a decreasing number of neurons to finally connect with the final layer, the 3 parameters vector corresponding to the rotation part of the rigid transform we wish to estimate.

Training is performed in a supervised way by adjusting the network's parameters to minimize the mean squared error between the network predictions and the labels (ground truth rotation parameters of T t ). Among several optimization techniques, we achieved good performance with the Nadam optimizer. The weights of the network were all initialized with a Gaussian distribution (mean=0, std=0.01). We used large batch size (500) to achieve better generalization among our data to reach the global minima. The initial learning rate is 1e-4 and the training is performed over 50 epochs, for which we obtain robust and rapid convergence. All these training parameters were mainly inspired from literature 28 and improved experimentally. Our model is trained on a Titan RTX GPU using TensorFlow via Keras.

EXPERIMENTS AND RESULTS

Data generation

Capturing a series of 2D US images along real clinical procedures with their relative localization to the reference volume requires probe tracking. To avoid the complexity of such acquisition in clinical routine, linked to the regulatory challenges of integrating system calibration bricks in the operating room, we used a previously developed biopsy simulator (Biopsym) [START_REF] Selmi | A virtual reality simulator combining a learning environment and clinical case database for image-guided prostate biopsy[END_REF][START_REF] Fiard | Simulation-based training for prostate biopsies: Towards the validation of the Biopsym simulator[END_REF] illustrated in Figure 2. This simulator is composed of a US probe mock-up attached to a haptic device (Phantom Omni, Sensable Devices Inc.) which records the position and orientation of the probe at 100 Hz. It gathers anonymized clinical data collected from real biopsy series, for which it provides for each patient: the 3D reference volume (e.g. preoperative US) and the associated prostate mesh. When a user moves the probe mock-up, the simulator generates a succession of 2D US images, resliced from the reference volume, and collects them as 2D image flow. Thus, each ground-truth slice localization with respect to the reference volume (T t ) is known from the haptic device tracking. Each series of 2D US images is thus associated to a real biopsy trajectory. The process is summarized in Figure 2.

Datasets

We asked a urologist to perform randomized biopsies (12 systematic biopsies spread homogeneously in different regions of the prostate) on the simulator. We recorded 7 trajectories that we applied to a large database composed of 70 US reference volumes from 70 different patients. These volumes were acquired during routine biopsy series with two different commercial US-based guidance systems (Urostation ® and Trinity ® from Koelis SAS), by clinicians from the Grenoble University Hospital. We took care to keep unknown trajectories and unknown patients for the testing set. To simulate a realistic acquisition frequency with significant motions between two slices, the time step between two successive images was set to 150 ms (6.6 Hz). Table 1 summarizes data split and characteristics. Where y is the rotation around the probe axis; (x,y) is the US probe plane and z the out-of-plane axis

Evaluation

Evaluating model predictions and their precision require to quantitatively compare predictions to labels (ground truth rotation parameters of T t ). To accurately represent the registration quality, it is particularly useful to measure its impact on the organ of interest in which targets are located. Target Registration Error (TRE) is the most frequently used metrics in image registration, because of its simplicity, fast computation, and ability to compare to most of the other studies in literature. This error is computed as defined in Equation (1). It is usually based on point pairs, most often fiducial landmarks manually defined by experts to establish the correspondence between two images. In the presented study, as a prostate surface mesh is associated to each 3D volume of the database, we used prostate mesh points (far more numerous than internal fiducials) to compute a robust TRE.

According to the data generation (see Part 3.1), the simulator's reoriented volumes and their meshes are saved during each slice generation. Being given prostate mesh points (p 2D i ) of such reoriented volumes, we compute the TRE between these resulting points after network's predicted registration Tt (p 2D i ) and the corresponding initial mesh points of the reference volume (p 3D i ) ( see Figure 3 ).

T RE(mm) = n i=1 p 3D i -Tt (p 2D i ) 2 n (1)
Since the TRE is a root mean square error, it gives an estimate of the standard deviation of the normal distribution of biopsy targets. To respect the confidence interval of 5 mm radius (clinical requirements cf 1.1), the TRE must be smaller than half of this value.

Results and discussion

Table 2 shows mesh-based TRE values before and after registration regarding the 4 scenarii in the presence of prior or not. The method with prior information outperforms the others, both in terms of accuracy and reliability. Scenario 3, which adds relative probe tracking information, achieves a mean TRE of 2.21 mm ± 2.89. These results meet clinical requirements (cf 1.1): with a response time of 28 ± 4 ms (below 50 ms) averaged on all test samples, and a TRE below 2.5 mm. They are even more promising considering that the TRE value before any registration corresponds to large initial displacements (∼ 30 mm), for which a classical registration method would fail. Furthermore, testing data includes only unknown trajectories on unknown 3D US patient volumes, which also demonstrates efficient generalization capabilities of the network. Figure 4-A illustrates the ground truth and predicted angles evolution over a trajectory, according to the 4 scenarii in the presence of prior, while Figure 4-B displays the associated TRE evolution over the same trajectory. It shows a good trajectory reconstruction without any drift Finally, our results highlight the usefulness of exploiting trajectory information especially through prior registration results and probe tracking parameters. In terms of computing time, the proposed method is able to perform 2D/3D registrations in real-time and can be successfully used for continuous tracking during a biopsy exam.

CONCLUSION

We developed a CNN to estimate the rotation parameters of a 2D/3D US registration transform in real-time. By adding trajectory information based on previous registration and probe tracking, we observe significant improvement of the registration quality. The network demonstrates efficient generalization capabilities on new patients and new trajectories. These results are comparable to related studies and achieve clinical requirements in terms of accuracy and computation time. They are even more promising considering that (i) input images are not preprocessed (only cropped) compared to other studies, (ii) US images present lower image quality than MRI images more often treated in the literature, (iii) complex and large displacements are tested as they are simulated in a realistic way from real biopsy procedure. However, we constructed the database in an artificial and simplified way because of some simulator limitations, which did not take into account the complexity of real cases. For now, motions do not include translation and 2D images do not include possible deformation of the organ. Moreover, 2D images do not present realistic US noise patterns as they are all extracted from the same reference volume. Further improvements will include the generation of new databases from data collected during real clinical biopsy procedure in response to these issues.

Moreover, this method is limited to static analysis, with only one previous step consideration. Since the navigation assistance is a global temporal process and we have just demonstrated the benefit of prior trajectory consideration, the next step will be to investigate the potential benefit of recurrent network to retain the global navigation trajectory. With the hypothesis of stereotyped trajectories between each biopsy procedure, such dynamical analysis could be even more promising.

Figure 1 .

 1 Figure 1. Method. A) Problem statement. The objective is to estimate the rigid transform parameters between a 2D US image and the reference volume in an end-to-end fashion, being given additional information such as previous registration prior, relative probe motion, and optical flow. B) Network Architecture

1 . 2 . 3 . 4 .Figure 2 .

 12342 Figure 2. Data generation process. A) Biopsym Simulator. B) Generation of the 2D US image flow from a clinical reference volume, associated with a realistic biopsy trajectory.

Figure 3 .

 3 Figure 3. TRE-based evaluation using meshes: Reference mesh and reoriented mesh associated with the current US slice.

Figure 4 .

 4 Figure 4. Temporal analysis over a complete trajectory, with time step between successive slices of 150 ms. A) Angle evolution: Ground truth (black curve) and predicted angles evolution w.r.t the 4 scenarios in the presence of prior. B) TRE evolution

Table 1 .

 1 Datasets

		Training	Testing	Trajectory characteristics
	Biopsym trajectory	5 trajectories x 67 patients = 30 300 samples for training 13 000 samples for validation	2 trajectories x 3 patients = 680 samples

(x,y,z) value : ± [ 30°, 180°, 20°]

Table 2 .

 2 Summary of the results obtained: Comparison with or without prior information, and comparison across the different scenarii. Scenario 1: pair of images only; scenario 2: pair of images + optical flow; scenario 3: pair of images + probe tracking information; scenario 4: pair of images with optical flow and probe tracking information

	(mm)	TRE before	TRE after Scenario 1	TRE after Scenario 2	TRE after Scenario 3	TRE after Scenario 4
	Without T prior 30.41 (±19.05)	8.36 (±4.67)	10.88 (±6.54)	9.02 (±5.50)	10.37 (±5.62)
	With T prior	idem	4.36 (±5.16)	4.03 (±5.4)	2.21 (±2.89)	2.60 (±3.22)

ACKNOWLEDGMENTS

Sincere thanks to clinicians from the Urology department of the Grenoble University Hospital, for their collaboration in data acquisition. This work was partly supported by the French Agence Nationale de la Recherche, "Investissement d'Avenir" program (grants MIAI@Grenoble Alpes under reference ANR-19-P3IA-0003 and CAMI Labex under reference ANR-11-LABX-0004)


Lison Martinet
email: lison.martinet@iphc.cnrs.fr

Cedric Sueur
email: cedric.sueur@iphc.cnrs.fr

Satoshi Hirata
email: hirata.satoshi.8z@kyoto-u.ac.jp

Jérôme Hosselet
email: jerome.hosselet@iphc.cnrs.fr

Tetsuro Matsuzawa
email: matsuzawa.tetsuro.8w@kyoto-u.jp

Marie Pelé
email: marie.pele@univ-catholille.fr

Cédric Sueur

Hubert Curien

Cédric Sueur

New indices to characterize drawing behavior in humans (Homo sapiens) and chimpanzees (Pan troglodytes)

Keywords: drawing, representativeness, efficiency, chimpanzee (Pan troglodytes), human (Homo sapiens), children

établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

"My drawing was not a picture of a hat.

It was a picture of a boa constrictor digesting an elephant." Antoine de Saint-Exupéry, The Little Prince Evidence in prehistoric caves and in museums underlines that drawing is one of the most characteristic behaviors of the human species, yet its definition remains vague. Indeed, drawing behavior is considered by some authors as the simple will to mark, to produce visible traces but it can also be etymologically understood as something more complex such as a design, or a goal to reach [START_REF] Martinet | Sortir du cadre : désanthropiser le concept de dessin en questionnant les primates non humains[END_REF]. This study considers drawing behavior in its simplest form, i.e. an active creation of visible marks that may or may not be figurative [START_REF] Macdonald | Alpha: the figure in the cage[END_REF]. Children start drawing what we call scribbles around their first year of age [START_REF] Golomb | The Child's Creation of a Pictorial World[END_REF]. At the age of 3-4 years, children begin to produce figurative drawings, i.e. they can be recognized by external observers [START_REF] Golomb | The Child's Creation of a Pictorial World[END_REF]. This progress is partly linked to the improvement of motor coordination, completed by the progressive integration of a visual vocabulary of patterns and graphic syntax aided by the child's cultural and living environment and of course by the maturation of their cognitive skills [START_REF] Cohn | Explaining "I can't draw": parallels between the structure and development of language and drawing[END_REF][START_REF] Saito | The origin of representational drawing: a comparison of human children and chimpanzees[END_REF]. During early childhood, crucial neurological transformations occur in cerebral tissues such as important increases in grey matter volumes until 4 years [START_REF] Coulbeau | Development of children's mental representations: effects of age, sex, and school experience[END_REF]. This organic substratum allows children for example to acquire the understanding of self and others, to regulate their emotions, but also to communicate and to enter a world filled with symbols [START_REF] Brownell | Socioemotional Development in the Toddler Years: Transitions and Transformations[END_REF]. Progressively the systems involved in the drawing behavior develop capacities such as visual perception, graphic production including action programming and planning, and visual imagery. In drawing, symbolism (i.e. the use of symbols such as marks or particular shapes) helps the subject to represent their thoughts by giving them symbolic meaning beyond their literal ones. Then DeLoache and collaborators [START_REF] Deloache | The three 'R's of pictoral competence[END_REF] stated "the realization of figurative drawing goes hand in hand with the appropriation of symbols". This early developmental stage of drawing is composed by traces and lines which have a universal nature, belonging to a culturally inherited symbolic system [START_REF] Golomb | Child Art in Context: A Cultural and Comparative Perspective[END_REF].

One of the first steps of children's early symbolic drawing development is tadpole figures [START_REF] Deloache | Becoming symbol-minded[END_REF]. Consisting of two lines (legs) attached to a round form (head), the tadpole figure arises around 3 years of age [START_REF] Cox | Children's Drawings of the Human Figure[END_REF] and is observed in Western as well in non-Western countries [START_REF] Gernhardt | Cultural perspectives on children's tadpole drawings: at the interface between representation and production[END_REF]13]. Thus, in the same way that children reorganize their spoken language to communicate efficiently, the appearance of these first recognizable drawings also allows them to be better understood by others [START_REF] Longobardi | Reconsidering the scribbling stage of drawing: a new perspective on toddlers' representational processes[END_REF]. An adult can easily understand what a 4-year-old child wanted to represent when they drew, because the outlined objects are recognizable. But what happens if this is not the case? Does this mean that drawings of very young children do not represent anything in particular?

For decades, researchers have suggested that the early phase of drawing -called scribbling -simply reflects a simple motor activity that is visually unplanned and only determined by the motor system of the arm, the wrist and the hand [START_REF] Piaget | La Psychologie de l'Enfant[END_REF]. This would mean that very young children do not take pleasure in their finished drawings, but only in the act itself.

Other studies acknowledge that the development of drawing follows a linear trajectory towards realism and that a child's spontaneous fortuitous realism eventually evolves into representative drawings [START_REF] Luquet | Le Dessin Enfantin[END_REF]. However, more recent studies tend to show evidence of pre-representative activities during scribbling [START_REF] Levin | Emergence of representation in drawing: the relation between kinematics and referential aspects[END_REF][START_REF] Longobardi | Reconsidering the scribbling stage of drawing: a new perspective on toddlers' representational processes[END_REF].

Drawing is part of the larger activity of creating meaning in young children. Children have multiple ways of making sense through the modes, means and materials they use to do so.

In their drawings, children encode a lot of information making them a way of constructing and depicting their thoughts in action [START_REF] Matthews | The Art of Childhood and Adolescence: The Construction of Meaning[END_REF][START_REF] Kress | Before Writing: Re-thinking the Paths to Literacy[END_REF]. A 2-or 3-year-old child is not capable of attributing meanings to the entirety of their drawing, which is often unstructured and complex. However, the child can attribute meaning to some parts of their drawing, and especially broken lines, which more easily describe the contours of an object than curved ones [START_REF] Levin | Emergence of representation in drawing: the relation between kinematics and referential aspects[END_REF]. Although caution should be used here because children can change their answers when asked several times about the meaning of their drawings, these kinematic aspects could be considered as precursors of a graphical representation (i.e., the act of producing in visible form a figure or an idea we have in mind). According to Willats [START_REF] Willats | Making Sense of Children's Drawings[END_REF], the developmental stages of drawing reflect attempts to represent the child's ever-increasing levels of perceptual understanding of the world in which they live. In this case, lines drawn in early childhood describe entire objects and are not simply random productions. These suggestions could be of use to answer the continuing debate over the representativeness of drawings by young scribblers. Although the loops, lines and stipples of a scribble usually have no sense for an adult, can we presume that it has no meaning for the young child? Like the young Saint-Exupéry, who complained that adults did not understand his drawing of an elephant eaten by a snake and that "they always need to have things explained", Longobardi [START_REF] Longobardi | Reconsidering the scribbling stage of drawing: a new perspective on toddlers' representational processes[END_REF] argues that the inability to detect representativeness in children's scribbles may be explained by the limitation of adults' interpretations rather than the absence of this intentionality. In this case, the representativeness of a drawing, namely its concrete and figurative character, would result from the perspectives of two individuals: the entity who produces it (here, a child) and an outside observer who evaluates it (here, an adult). These individuals could be considered to represent two elements: internal representativeness (for the individual who draws) and external representativeness (for the observer). All the aforementioned elements underline the necessity for further studies on drawing behavior to better understand the development of drawing abilities and more specifically the emergence of representativeness in human beings.

An additional factor to consider when seeking to understand the development of drawing behavior in humans may be its evolutionary emergence. Is drawing a typically human behavior or does it originate from ancestor species? This question can be answered by studying the evolution of drawing behavior in species that are genetically close to humans, such as great apes. So far, no spontaneous drawing behavior has been reported in great apes in the wild. Even known as the most meticulous tool makers and users [START_REF] Mcgrew | Chimpanzee Material Culture: Implications for Human Evolution[END_REF], no chimpanzee was ever observed using sticks to trace on the floor. Moreover, such marking behavior would be difficult to differentiate from other actions such as digging or exploring surfaces. Nevertheless, it is more and more common for captive individuals to use pencils and brushes on paper sheets or even draw on tactile tablets [START_REF] Martinet | Drawing in non-human primates: what we know and what remains to be investigated[END_REF]. Indeed, as Call [START_REF] Call | On space geckos and urban apes[END_REF] stated "testing non-human animals outside their 'natural' box is needed to fully probe their capabilities and limitations, something that is particularly desirable if our ultimate goal is to reconstruct the evolution of cognition" and in our case, the evolution of drawing. Drawing by chimpanzees has been considered in humanape comparative developmental studies [START_REF] Kellogg | The Ape and the Child: A Study of Environmental Influence Upon Early Behaviour[END_REF], and also in art and aesthetics research [START_REF] Morris | The Biology of Art: A Study of the Picture-making Behavior of the Great Apes and its Relationship to Human Art[END_REF]. In the first experimental study on drawing in chimpanzees, Schiller [START_REF] Schiller | Figural preferences in the drawings of a chimpanzee[END_REF] presented geometric figures to a female chimpanzee named Alpha who changed her scribbling patterns according to the stimuli provided. A number of studies have shown that chimpanzees maintain their graphic activity without any reinforcement, indicating a likely interest in drawing [START_REF] Morris | The Biology of Art: A Study of the Picture-making Behavior of the Great Apes and its Relationship to Human Art[END_REF][START_REF] Schiller | Figural preferences in the drawings of a chimpanzee[END_REF][START_REF] Hanazuka | The effects of the environment on the drawings of an extraordinary productive Orangutan (Pongo pygmaeus) artist[END_REF]. Beyond the sensation linked to locomotor movement, visual feedback seems to play a reinforcement role: drawing behavior decreases when the line drawn by the subject on the tactile screen disappears [START_REF] Tanaka | Finger drawing by infant chimpanzees (Pan troglodytes)[END_REF]. Although there are many studies on mark-making in chimpanzees, none reported drawings that were recognizable by observers (external representativeness), and researchers generally compared the productions to the scribbles of young human children. However, some results such as the trend to change scribbling patterns in presence of stimuli or patterns [START_REF] Saito | The origin of representational drawing: a comparison of human children and chimpanzees[END_REF][START_REF] Schiller | Figural preferences in the drawings of a chimpanzee[END_REF] or, according to Zeller [START_REF] Zeller | What's a picture ? A comparison of drawings by apes and children[END_REF], the manifestation of a choice for some features such as the colors used or patterns drawn leads to conclude that ape drawings "are definitely not random scribbles".

The most common way to establish whether a drawing is representative or not is to ask the individual who produced it about its meaning, which is often done with children. A signlanguage trained female chimpanzee named Moja was asked this question, and she answered "bird" [START_REF] Gardner | Comparative psychology and language acquisition[END_REF]. Of course, her answer is not reliable evidence of her internal representativeness of a bird; it is possible that she answered randomly, or was influenced or misinterpreted by the experimenters. Thus, despite numerous studies on this topic, it is still impossible to exclude the presence of goal-oriented behavior in drawing by very young children and chimpanzees. The use of a symbol requires understanding it, its abstract relation to what it stands for and being able to mentally represent it [START_REF] Deloache | The three 'R's of pictoral competence[END_REF]. In humans, the basic understanding of the analogical spaceobject-symbol relation emerges around 3 years of age [START_REF] Deloache | Rapid change in the symbolic functioning of very young children[END_REF]. At this age, a child can understand for example that the illustration of a cat asleep on a couch represents the cat currently sleeping on the living room couch. Besides, pretend play, a symbolic play where children express their imagination by using actions or objects to represent other objects or actions begins in toddlers of around 1-2 years old [START_REF] Matsuzawa | Pretense in chimpanzees[END_REF][START_REF] Fein | Pretend play in childhood: an integrative review[END_REF]. This capacity of pretense, which is evidence of representational abilities, has also been shown in chimpanzees even if it is less developed [START_REF] Matsuzawa | Pretense in chimpanzees[END_REF].

Other abilities, as the fact that they can track invisible displacement [START_REF] Collier-Baker | Do chimpanzees (Pan troglodytes) understand single invisible displacement?[END_REF] and use a scale model as a source of information for the location of a hidden item [START_REF] Kuhlmeier | Chimpanzees (Pan troglodytes) recognize spatial and object correspondences between a scale model and its referent[END_REF] prove that they are capable of mental representation. Then, although their mark-making is not, a priori, driven by a desire to represent an object, the absence of figurative drawings does not necessarily indicate an absence of symbolism for the chimpanzee or the young child [START_REF] Savage-Rumbaugh | Symbolic communication between two chimpanzees (Pan troglodytes)[END_REF][START_REF] Deloache | Symbolic functioning in very young children: understanding of pictures and models[END_REF]. Especially as in our sapiens ancestors, "the elaboration of nonfigurative patterns certainly participated in the development of a symbolic thought on which later prospered the invention of the figure and of a true iconographic language" [START_REF] Bon | Dis, dessine-moi un mammouth[END_REF].

Different methods have been used to investigate drawings of young children. The most well-known of these is the comparison of broken lines and curved lines to evaluate the kinematic aspects of the outlines that have been drawn [START_REF] Levin | Emergence of representation in drawing: the relation between kinematics and referential aspects[END_REF]. Although relevant, this method remains subjective as researchers directly question children about what their drawings represent. It cannot therefore be used with very young children (toddlers) or with great apes, as neither group are able to express themselves about their drawings. It is therefore necessary to find a new method of analysis for the objective study of drawing behavior in children and chimpanzees.

To achieve this goal, we asked children aged 3 to 10 years and adults with different levels of drawing skills (naive versus expert) to draw on tactile devices. Each participant was given two drawing tasks, namely to draw freely (free drawing condition) and to draw themselves (self-portrait condition) to assess a possible difference in results between a nonspecific and a specific task. Five female chimpanzees were also asked to draw freely on a touchscreen tablet. We then developed an innovative and objective index based on the lines drawn by both humans and chimpanzees. This was achieved through the use of spatial analysis. Also called the random walk analysis [START_REF] Bartumeus | Animal search strategies: a quantitative random-walk analysis[END_REF], this approach is commonly used in ecology to study the movements of animals. We considered the outline of the drawing as an animal's path (meaning a set of trajectories of different lengths [START_REF] Byrne | How did they get here from there? Detecting changes of direction in terrestrial ranging[END_REF]), and characterized the efficiency of the drawing, defined here as the correct reading of the drawing with a minimum of details. In other words, the external representativeness of the observer matches the internal representativeness of the individual who drew. The random walk analysis determines whether the distribution of drawing lines follows a power law or an exponential law. If the distribution follows an exponential law, we expect the drawing to be random, meaning that the individual who is drawing has no intention to represent anything. Contrarily, a power distribution should reflect a non-random and oriented behavior, as found for the daily paths of animals in their natural environments (i.e. goal-oriented and efficient movements, 41). On one hand, we could expect drawing to be random in chimpanzees (i.e. no internal representativeness) since no chimpanzee has ever produced a representative drawing -with a human eye-despite a demonstrated interest in the activity in several studies [START_REF] Morris | The Biology of Art: A Study of the Picture-making Behavior of the Great Apes and its Relationship to Human Art[END_REF][START_REF] Schiller | Figural preferences in the drawings of a chimpanzee[END_REF][START_REF] Hanazuka | The effects of the environment on the drawings of an extraordinary productive Orangutan (Pongo pygmaeus) artist[END_REF]. On the other hand, as chimpanzees are able to change their scribbling outlines and to manifest a preference for colors used or patterns drawn, their drawings might be not so random. Considering humans, we definitely expected a non-random and goal-oriented behavior in children and adults, with an index that increased with age.

Finally, we complemented this innovative spatial index for drawing by investigating the use of colors by individuals and the duration of drawing, since these indices are commonly used in drawing studies. We expected a less developed use of colors in chimpanzees and progressively a more important one with age in humans. Considering the duration of drawing in humans, we predicted a longer one with age in parallel with the improvement of motor and psychic abilities and the growing interest with age for this activity. To study and apprehend the variability of these drawing indices, the variables group (age), gender, test condition, gendercondition interaction and/or the group-condition interaction were used. The gender effect has already been proved to influence drawing in different ways [START_REF] Kirkorian | Drawing across media: a cross-sectional experiment on preschoolers' drawings produced usin traditional versus electronic mediums[END_REF][START_REF] Turgeon | Sex differences in children's free drawings and their relationship to 2D:4D ratio[END_REF][START_REF] Wright | Monochrome males and colorful females: do gender and age influence the color and content of drawings?[END_REF]. We tested the gendercondition interaction since we thought that, especially for children, the drawing's variables could be different according condition between girls and boys. Concerning the group-condition interaction, we first expected that the instruction might intimidate some children, especially the youngest, and potentially restrict their creative process. Then experts might react differently from naive adults by being more comfortable and inspired, especially for free drawing, resulting in a potentially longer drawing time and greater use of color.

Results

The spatial index µMLE

Chimpanzees showed a lower index µMLE than human participants (GLM Gaussian, p < .0001, t > 4.10, Fig. 1, Supplementary Table S1A). The index for 3-year-old children was lower than those recorded for 5-(p < .001, t = 3.43, Fig. 1, Supplementary Table S1B), 7-(p < .0001, t = 4.33), 9-(p < .001, t = 3.37) and 10-year-old children (p = .002, t = 3.05), but was similar to those of 4-and 8-year-old children and naive or expert adults. Five-year-old children had a higher spatial index µMLE than the naive (p = .032, t = 3.24) and the expert (p = .0016, t = 4.03) adults. Seven-year-old children showed an index higher than naive (p = .001, t = 4.14) and expert (p < .001, t = 4.93) adults. Similarly, 9-year-old children presented a higher spatial index than naive adults (p = .039, t = 3.19) and expert adults (p = .0023, t = 3.98). Ten-year-old children also had a higher index than expert (p = .008, t = 3.66) adults, and possibly also naive (p = .097) adults. No difference was found between the two adult groups, and no significant effects of the conditions and sex factors were observed.

Drawing duration

After model selection, we retained the most explicative model containing the groups and conditions factors. In both test conditions, 3-year-old children spent less time drawing (mean = 110±97 seconds) than all other participants (272±192 seconds) (GLM Gamma, p < .001, t > 3.32, Fig. 2, Supplementary Table S2). Furthermore, all human participants spent more time drawing in the free condition compared to the self-portrait condition (p < .0001, t = 4.52).

Fig 2. Boxplots of drawing duration (in seconds) for each group and for each condition.

Boxplots depict the median (bold bar), 25-75% quartiles (box), mean (cross) and outliers (points).

The use of colors a. Number of colors used

The results of the model (Supplementary Table S3A) indicate that chimpanzees used fewer colors than humans (across all groups; GLM Poisson, p ≤ .001, t > 3.29, Fig. 3A). After model selection, the factors conditions and sex were retained to explain the number of colors used in humans. The number of colors used is higher under the free condition than under the self-portrait condition (p < .0001, t = 5.06, Fig. 3A, Supplementary Table S3B). Furthermore, there is a gender-related difference in the use of color. Women and girls used significantly more colors than men and boys (p < .001, t = 2.97).

b. Number of color changes

Chimpanzees did not change the colors they used as much as the human participants did (GLM Negative binomial, p < .008, t > 3.34, Fig. 3B, Supplementary Table S4A). In humans, the number of color changes was higher in the free condition compared to the self-portrait condition (GLM Negative binomial, p < .0001, t = 4.45, Fig. 3B, Supplementary Table S4B).

Furthermore, men and boys changed the colors they used significantly less often than women and girls in all groups (p = .002, t = -3.11).

The meaning of drawings in children

When asked what their drawing represented in the self-portrait condition, 3-, 4-and 5-yearold children were much more likely to answer "me" when questioned directly after drawing than when they were asked the same question three days later (GLM Binomial, p < .0001, z = 5.16, Fig. 4, Supplementary Table S5). However, these three age groups showed some differences in their response consistency. Four-and five-year-old children were more likely to confirm that the drawing was self-representation immediately after drawing and few days later than the youngest children (p < .0001, z > 7.02, Fig. 4, Supplementary Table S5).

The comparison of the answers given by children several days after drawing in the two conditions (free and self-portrait) showed that 4-and 5-year-olds had a better memory of what they had intended to represent a few days after drawing than the youngest children (p ≤ .021, z > 2.30, Fig. 4, Supplementary Table S6). Three days after the drawing activity, the 3-year-old children seemed to find it easier to remember what they had drawn in the free drawing condition (52.9%) than to remember what they had intended to draw or indeed the initial instruction to draw themselves in the self-portrait condition (17.6%) (Fig. 4).

Discussion

This comparative and explorative study allowed us to define new and objective indices characterizing drawing in human and non-human primates. We used common measures in drawing studies (duration and colors) combined with an innovative spatial index that is commonly used in animal trajectories studies [START_REF] Edwards | Revisiting Lévy flight search patterns of wandering albatrosses, bumblebees and deer[END_REF]. This is the first study to use this mathematical index to understand drawings. This spatial index µ MLE is clearly lower for chimpanzees compared to human participants. This suggests the presence of a behavior that is less goal-oriented than that observed in humans, but which is still not random: even chimpanzees displayed a power-like distribution showing that their movements are constrained by cognitive or locomotor aspects that limit the randomness we could expect. However, these results conduct us not to conclude to the absence of internal representativeness in chimpanzees. This lack of efficiency is not surprising given their behavior when facing the touchscreen: most of them showed less interest than humans did, as proved by the fact that they were stimulated by the experimenters and their more limited use of colors. This is a surprising contrast to Zeller's study [START_REF] Zeller | What's a picture ? A comparison of drawings by apes and children[END_REF] which shows that chimpanzees and humans make similar use of colors in their pictures. This difference could be due to the use of the touchscreen, which does not require individuals to use materials such as pencils or paint. Only one chimpanzee, Hatsuka, appeared to be more attentive during test sessions, looking at her fingers and at the outlines produced on the screen. This variability among chimpanzees has already been described, with younger chimpanzees showing more interest [START_REF] Tanaka | Finger drawing by infant chimpanzees (Pan troglodytes)[END_REF]. However, Hatsuka's drawings were not characterized by a higher spatial index than those of other females. This inter-individual difference can be interpreted as a difference of interest in the tool used (i.e. motivation) but did not reveal different line features (i.e. goaldirectedness). All chimpanzees produced more or less the same type of very angular and locomotive features with no precise forms. However, these features are not random and it is difficult to conclude to the absence of internal representation in chimpanzees [START_REF] Martinet | Drawing in non-human primates: what we know and what remains to be investigated[END_REF]. This question, which has great fundamental implications, remains to be clarified through further experiments.

Among humans, results found were different from those expected. The spatial index µ MLE increased among the two youngest age groups in children and stabilized between the ages of 5 and 10. The spatial index µ MLE then decreased among adults to reach a similar level to that of 3-and 4-year-old children. The increase of this index in young children can be easily explained by the progressive development of more controlled and goal-oriented lines which often underlie the production of a figurative drawing. Goal-directedness and internal representation might be present in some children (at least in the four-year-olds, where external representation is also present). Three-year-old children would be more motivated by motor pleasure alone [START_REF] Baldy | Fais-moi un Beau Dessin: Regarder le Dessin de l'Enfant, Comprendre son Evolution[END_REF], explaining why their spatial index µ MLE is the lowest observed in children.

The marks produced on the tablet provided a visual satisfaction which encouraged the child to keep drawing on the blank parts of the screen. However, the index µMLE of 3-year-old children was higher than that observed for chimpanzees, allowing us to develop a hypothesis. First, there was a wide range of variability at this age because it is a period of learning how to draw, in which children begin to internalize some graphic elements (vertical lines, horizontal lines, crosses, dots) that they may or may not be able to reproduce efficiently in their drawings. Many of the children appeared to be in the first representation phase, called action representation, during which the child produces sounds that mimic the movement of the object they want to represent [START_REF] Levin | Emergence of representation in drawing: the relation between kinematics and referential aspects[END_REF][START_REF] Yamagata | Emergence of representational activity during the early drawing stage: Process analysis[END_REF], while others began to draw their first recognizable figures. Also, the better fine motor skills of children compared to chimpanzees can be argued. Indeed, even if 3-yearold children did not intend to represent something, the shapes and outlines that they produced (curved or directed to fill the entire available space) did not look like those realized by chimpanzees (which were less smooth). It demonstrates better mobility and control of the hand, the wrist and fingers [START_REF] Young | Evolution of the human hand : the role of throwing and clubbing[END_REF] on the part of children, which could naturally lead to greater efficiency (e.g. more variation in the length of the lines drawn). The spatial index µMLE increased in children up to the age of five, when children are in the intellectual realism phase [START_REF] Luquet | Le Dessin Enfantin[END_REF] and try to draw their idea as accurately as possible. This is made possible by the enhancement of their locomotor capacities. The child draws all the parts of the object they seek to depict in an efficient way, e.g. without abstraction or unnecessary details. Here, the primary goal is to be understood (external representativeness), with no aesthetic goal. This makes their drawings more efficient. Among adults, the spatial index µMLE decreased. Even if their drawings are very understandable, they appear to be more complex due to the compiling of numerous details, perspectives or shadows affecting the distribution of line lengths and consequently reducing their efficiency. Contrary to young children, adults may attempt to reach an ideal in their representations linked to social norms that young children have not yet acquired [START_REF] Itskowitz | The impact of age and artistic inclination on the use of articulation and line quality in similarity and preference judgments[END_REF]. The results concerning adults allow a better understanding and definition of our spatial index µMLE.

The presence of goal-oriented behavior during drawing is undeniable in adults, almost all of whom produced figurative drawings. They all have an internal representation of their drawings.

However, unlike 3-year-old children, the absence of external representation in adult drawings is due to an intention to draw in an abstract way (often observed in the expert group) rather than the absence of internal representativeness. Our spatial index therefore depicts the efficiency of a drawing layout, whether or not it is figurative. It should be noted that the spatial index µMLE is not affected by the gender of the individual or the condition in which a participant carried out their drawing. Adding an instruction (free or self-portrait condition) to guide the person drawing did not make the drawing layout more efficient.

Even if it does not affect our spatial index, condition has an effect on other measures such as the duration of drawing. Among humans, all groups spent more time drawing under the free condition than under the self-portrait condition. When free to draw, the participant was willingly using their imagination, and spending more time on their drawing. However, we noted a shorter drawing time for the youngest children, whatever the condition. Three-year-old children appeared to become quickly bored; their use of the tablet was different to that of their older counterparts, who clearly used it as a drawing support. The role of the tablet as medium and the use of fingers as tools could influence several components of the drawing including its efficiency [START_REF] Kirkorian | Drawing across media: a cross-sectional experiment on preschoolers' drawings produced usin traditional versus electronic mediums[END_REF]. Finger drawing seems to require less motor control than tools drawing, making it easier for the youngest children to produce more codable, efficient drawings, at least when they copy simple shapes [START_REF] Kirkorian | Drawing across media: a cross-sectional experiment on preschoolers' drawings produced usin traditional versus electronic mediums[END_REF]. However, finger drawing may be more difficult for older children and adults, who are more accustomed to draw with brushes or pencils resulting in less qualitative drawings. Holding and moving a tool does not require the same control (distal joints and flexion/extension of the fingers) than drawing with fingers which involves movements of the elbow and the shoulder [START_REF] Picard | iPads at school? A quantitative comparison of elementary schoolchildren's pen-on-paper versus finger-on-screen drawing skills[END_REF]. It could be more difficult for older children and adults to shift from distal to proximal control of their movements [START_REF] Picard | iPads at school? A quantitative comparison of elementary schoolchildren's pen-on-paper versus finger-on-screen drawing skills[END_REF] which could then impact their drawings' efficiency.

While drawing is generally accepted as the expression of a mental representation, the use of colors is commonly linked to personal aesthetics and is more difficult to evaluate objectively [START_REF] Baldy | Fais-moi un Beau Dessin: Regarder le Dessin de l'Enfant, Comprendre son Evolution[END_REF]. Although colors alone cannot characterize a drawing, they could help to understand the approach taken by the individual who is drawing. Children and adults used more colors and changed them more often under the free condition than in the self-portrait condition.

The less limited nature of free productions increased the use of colors, while the instruction "Draw yourself" seemed to constrain color use and led individuals to use fewer elements when composing the drawing. Besides, the use of colors is consistent with the duration of drawing which is higher under the free condition. A gender difference was found for both the number of colors used and the number of colors changes. Women and girls changed the colors they used more frequently and used significantly more colors than men and boys. This gender effect on the number of colors used has already been found in humans, with girls showing a more diverse use of color than boys [START_REF] Wright | Monochrome males and colorful females: do gender and age influence the color and content of drawings?[END_REF][START_REF] Milne | Color in children's drawings: the influence of age and gender[END_REF]. Gender differences in the use of colors in general have also been shown in studies of drawing by non-human primates [START_REF] Zeller | What's a picture ? A comparison of drawings by apes and children[END_REF]. Turgeon [START_REF] Turgeon | Sex differences in children's free drawings and their relationship to 2D:4D ratio[END_REF] showed a gender difference in color use solely in older children (7-9 years old), whereas we found a difference even in younger children, a finding that is consistent with previous studies [START_REF] Wright | Monochrome males and colorful females: do gender and age influence the color and content of drawings?[END_REF].

Turgeon [START_REF] Turgeon | Sex differences in children's free drawings and their relationship to 2D:4D ratio[END_REF] noted that the number of colors used can be directly linked to the subject of the drawing, with some requiring more colors than others (e.g. a flower versus a car). In our case, the gender effect appears in both the constrained (self-portrait) and the free conditions. This gender difference in the use of colors has already been studied, notably from a biological perspective by studying the level of prenatal androgen exposure, even if minimal support was found to assess its role [START_REF] Turgeon | Sex differences in children's free drawings and their relationship to 2D:4D ratio[END_REF]. The importance of social influence is very often highlighted in descriptions of a 'sex role socialization' process [START_REF] Wright | Monochrome males and colorful females: do gender and age influence the color and content of drawings?[END_REF]. Our study shows that this gender difference persists beyond childhood into adulthood.

To complement the analyses of our different indices, we asked the youngest children (between 3 and 5 years of age) about the meaning of their drawings (i.e., internal representativeness) in free and self-portrait conditions. We asked the children not only at the end of the drawing session but also few days later. Remembering and implementing instructions require the storage and the manipulation of information. For the younger ones for who this exercise could be difficult, we did not hesitate to recall the drawing instruction "do you remember, I ask you to draw yourself". We naturally repeated it to children who looked at the experimenter, asked her to repeat or told her they did not know what to draw. We did not, or very rarely, have to repeat for the oldest children. The fact that we have to recall the instruction could also be a sign of a lack of concentration on the part of the child. For the self-portrait condition, approximately 80% of the 4-and 5-year-old children answered "me" immediately after having drawn, identifying themselves in their drawing. This contrasts with the 3-year-old children, who answered "me" significantly less frequently than the older children. Some answered "nothing" or "I do not know" which may confirm, as our indices do, the absence of an internal representation process for most children of this age. At this age, children are able to form a mental image of themselves [START_REF] Piaget | La Psychologie de l'Enfant[END_REF], so a misunderstanding of the instruction is not a plausible explanation for our results. On this basis, several hypotheses can be considered. It is possible that three-year-old children perhaps did not apply our instruction due to a lack of motivation. Also, some of them could have struggled with keeping the instruction in mind during the drawing session. Another hypothesis is that they were simply not capable of carrying out the task since they had not yet integrated the graphical elements necessary for the production of a tadpole man due to developing motor and/or cognitive abilities. We can also consider that despite the habituation phase, some of them were too shy to answer when we asked them. Many 3-year-old children told the experimenter that they "did not know how to do it". This answer can be understood in two ways which are most probably linked: (1) under-developed locomotor control or (2) a partial or incomplete internalization of the graphic elements necessary to draw the figure of a man (round, vertical and horizontal lines). A final hypothesis is that 3-year-old children realized that their drawing did not look like them and therefore could not answer "me" when they saw it finished. Among the few 3-year-olds who managed to draw something figurative (i.e., external representativeness), several responded "a man", showing that they did not recognize themselves, which is characteristic of the early period of figurative drawing [START_REF] Cox | Young children's human figure drawing: cross-sectional and longitudinal studies[END_REF].

It should be noted that the condition in which the drawing was made (free and self-portrait) did not affect the child's memory of its initial meaning. Like for the self-portrait condition, 3-yearold children did not remember the meaning they had given to their free drawings as well as the oldest children did. In addition to our indices, these results tend to show that the internal representativeness may not well be elaborated in the 3-year-old children, affecting their outlines' efficiency and therefore the external representativeness of their drawings.

Our study uses an innovative index in this domain and reveals differences between chimpanzees and human beings in their capacities to draw, and further differences between humans at different ages. It is important to note that humans learn to draw -a main activity in nursery school -whilst chimpanzees do not. This can explain some of the differences observed between human and non-human primates. From an early age, a human child raised in an industrial country lives in a graphic environment (books, television, and advertising) that might contribute to the emergence of their figurative conception of drawing [START_REF] Baldy | Fais-moi un Beau Dessin: Regarder le Dessin de l'Enfant, Comprendre son Evolution[END_REF]. Following this idea, it could be interesting in the future to conduct cross-cultural studies with children living in a less graphic environment. However, one difficulty here would be testing children with technology they are not used to. Chimpanzees can be taught to draw [START_REF] Iversen | Visually guided drawing in the chimpanzee (Pan troglodytes)[END_REF][START_REF] Iversen | Model-guided line drawing in the chimpanzee (Pan troglodytes)[END_REF][START_REF] Iversen | Establishing line tracing on a touch monitor as a basic drawing skill in chimpanzees (Pan troglodytes)[END_REF] and adults of this species show better control of their movements than younger ones [START_REF] Saito | The origin of representational drawing: a comparison of human children and chimpanzees[END_REF]. Then, like in humans, the fine motor skills of chimpanzees improve with age and training, suggesting that the lack of external representativeness in this species is not explained solely by a lack of adequate motor skills. The meticulous examination of productions made by trained chimpanzees over several years could then be an important next step for future studies. Our spatial index µMLE already reveals the high reliability of efficiency for the lines traced on screens by individuals. The results presented here are preliminary but already show the relevance of pursuing research on new graphical representation clues. New indices should now be developed to understand the degree of representativeness in drawings by primates, and possibly in other animal taxa.

Methods

Ethics

Drawings by human participants were confidentially collected. Study protocol followed the ethical guidelines of our research institutions and ethical approval was obtained from the Strasbourg University Research Ethics Committee (Unistra/CER/2019-11). Informed consent was obtained from all adult participants and from a parent or legal guardian for children.

Informed consent for publication of identifying images in an online open-access publication has been obtained too.

All chimpanzees were tested in a dedicated testing room and their participation in this study was voluntary [START_REF] Matsuzawa | Cognitive Development in Chimpanzees[END_REF]. Regular feeding, daily enrichment and ad libitum access to water, leaves, and grasses of live plants were provided [START_REF] Matsuzawa | WISH cages: constructing multiple habitats for captive chimpanzees[END_REF]. Animal husbandry and research methods complied with international standards (Weatherall report "The use of non-human primates in research") and all our experimental protocols were approved by Kyoto University (WRC-2017KS009A).

Subjects a. Human participants

One hundred and thirty-eight children (63 girls and 75 boys) and forty adults (20 women and 20 men) took part in this study. Children were pupils in a kindergarten and primary school in Strasbourg, France. Twenty children were enrolled for each age group (3-year-old, 4-yearold, 5-year-old, 7-year-old, 8-year-old, 9-year-old and 10-year-old) except for the group of 8year-olds, which was composed of 18 children (Table 1). Their participation was voluntary and subject to parental consent. Drawings from kindergarten children (3-, 4-, 5-year-olds) were collected in 2018 and drawings from primary school children in 2019. This means that children who were 6 years old in 2019 could not be tested because they have already been involved when they were 5 years old in 2018.

The adults tested were 21 to 60 years old (Table 1). Beyond the age effect (children versus adults), experienced and naive sub-samples were tested in adults to assess the effect of experience on the indices studied. Twenty adults were considered to be naive in drawing since they never took drawing lessons and did not draw as a hobby. These participants were researchers and students of the research institute where the authors worked (naive adults: 30.8±10.54 years-old). Twenty experts in drawing were also enrolled, including art school students and professional illustrators (expert adults: 30.4±11.12 years-old). For both groups, naive and expert, we accepted all ages but made sure to retain the same number of men and women. Participation was voluntary. Table 1. Groups, sex and test condition of human participants. For each group of participants, half of the subjects began testing with the free condition instructions; the other half with the self-portrait condition. The choice was made randomly.

b. Chimpanzees

Five female chimpanzees (Pan troglodytes) between 10 and 22 years of age were tested at the Kumamoto Sanctuary of the Wildlife Research Center of Kyoto University in Japan (Table 2). Individuals belonged to the same social group of 6 individuals (5 females and 1 male) and lived in a 300m 2 enriched and wooded enclosure. All had experienced behavioral and cognitive tests during "participant observation" [START_REF] Matsuzawa | The 40th anniversary of the Ai Project: the commemorative gift is a silk scarf painted by Ai the chimpanzee[END_REF][START_REF] Matsuzawa | Cognitive Development in Chimpanzees[END_REF], in which the experimenters interacted directly with the subject during test sessions and were present in the daily lives of the chimpanzees.

Chimpanzees had already been familiarized with touchscreens in previous experimental procedures.

Participants groups

Gender Free => Self-portrait Self-portrait => Free 2, Supplementary materials Figure S9). Two consecutive points (i and j) in the drawing d determined a step or a vector of a length L(i,j). We then calculated the step lengths S on Excel with latitude x and longitude y (in pixels).

Step lengths between 0 and 10 pixels were removed since they often corresponded to very short, inactive movements such as imprecise lines or finger sideslips and caused inaccuracies.

We then determined whether the step length frequency distribution of a drawing followed a power law (y = a*x µ ) or an exponential law (y = a.e x* l ) using the Maximum Likelihood Method [START_REF] Edwards | Revisiting Lévy flight search patterns of wandering albatrosses, bumblebees and deer[END_REF]. To achieve this, we calculated the exponent of the distribution (Equation 1 for power law and Equation 2 for exponential law) in order to determine the In chimpanzees, drawing sessions lasted on average five minutes during which each individual drew less than one minute (mean = 49±17.7 seconds). However, given that chimpanzees were stimulated by the experimenters and often distracted by their environment, drawing duration was only analyzed in humans. The duration of each drawing was measured in seconds and corresponded to the elapsed time between the first and the last point of the drawing.

c. The use of color

The color of each point has also been recorded by our drawing software. Since the subjects had access to 10 different colors, we defined first a color index ranging from 1 to 10 and corresponding to the number of colors used. We then considered the number of times a subject changed the color used. This second color index can be equal or higher to the number of colors used, as the same color can be used several times.

d. The meaning of drawings in children

When asked about the meaning of their drawing, a child can say what they intended to draw before drawing (internal representativeness) but also what they see once their drawing is finished (fortuitous meaning; 16). If a child remembers the first meaning of their drawing three days later, we can consider this consistency in their answer to be evidence of a real intention to represent the object in question at the outset. This part of the study concerns the three youngest groups of children (between 3 and 5 years old), for whom representative, decipherable and readable drawing (external representativeness) was not systematic.

Each child was questioned immediately after drawing and three days later (LM or MP showed him his drawing again) about the meaning of their drawing in the self-portrait and free conditions. We chose to not question children before and after their drawing to not disturb them, influence them and their choices, especially the youngest ones who, for some, were initially intimidated by the exercise. Besides, drawing sessions did not last long and children could give the same meaning to their drawing just to match what they had announced, even if plans changed along the way (they did not have the necessary graphic skills to achieve their drawing or at the end, the drawing had no real representational purpose per se). Answers were recorded and coded 1 when the child gave us the same answer at the end of the test session and three days later (for example, "me" for the self-portrait condition) and 0 when the child gave us two different answers. First, we analyzed children's answers for the self-portrait condition. This allowed us to determine whether children were able to understand and follow an instruction, and also indicated their ability to represent something when asked to do so, regardless of whether they could produce a figurative drawing on their own under the free condition. We then compared the answers given by children three days after their drawing in the self-portrait condition with those given three days after drawing in the free condition. This comparison allowed us to determine whether the type of test condition affected the meaning (or the memory thereof) that children had given to their production.

e. Statistics

The multicollinearity of our different indices was tested using a VIF test for each model.

As no index had a VIF superior to 4 (VIFmax=2.71), we concluded that there was no collinearity between our variables [START_REF] Dormann | Collinearity: a review of methods to deal with it and a simulation study evaluating their performance[END_REF]. This means that the spatial index, the color used and the time taken to draw are not dependent on each other.

The indices were analyzed in two different ways. First, we compared human participants and chimpanzees by taking only the free condition drawings into account. The sex factor was excluded as all chimpanzees were female. In a second step, we compared gender, test condition and groups within the groups of human participants. No influence of condition order was found (Wilcoxon test, W < 303, p > .05207) meaning that data did not significantly differ whether the person first drew under free or self-portrait conditions.

Each index was studied through Generalized Linear Models GLM (dependent variable ~ explanatory variables). Individual (IDs) was added as a random factor when considering the meanings of drawings in children. We first selected the most efficient model to explain the variability of the studied index, using the variables group, gender, test condition, gendercondition interaction and/or group-condition interaction. The model selection was carried out by a dredge (package MuMin; 65) which is a forward procedure (from the null to complete model). After the dredge, we selected the one with the lowest AIC (model selection; 65). When the AIC difference of the first two best models did not exceed two [START_REF] Burnham | Multimodel inference: understanding AIC and BIC in model selection[END_REF], they were compared using an Anova (anova function (glm1, glm2, test: "F" or "Chisq")). When the difference was not significant (p > .05), the simplest model was preferred to respect the parsimony principle.

For each selected model, the probability distribution was adapted to the dependent variable and the conditions of application (normality and homoscedasticity of residuals) were graphically verified. All analyses were performed in R. 3.5.0 (66) and for all tests, the significance threshold was set to a = .05.

Supplementary materials Results

1. The spatial index µMLE S3. Results of the generalized linear model carried out to compare the number of colors used. (a) between chimpanzees and humans (compared to chimpanzees) and (b) among humans (free condition compared to self-portrait condition and boys/men compared to girls/women). Table S10.

Estimate

Fig 1 .

 1 Fig 1. Boxplots of the spatial index µ MLE for each group, i.e. chimpanzees and humans (children and adults). Since the condition factor is not present in the selected model, all drawings were studied without distinction of conditions. Each boxplot depicts the median (bold bar), 25-75% quartiles (box), mean (cross) and outliers (points).

Fig 3 .

 3 Fig 3. (a) Boxplots of the number of colors used by chimpanzees and humans for each condition and for each sex. (b) Boxplots of the number of color changes by chimpanzees and humans for each condition and sex. Boxplots depict the median (bold bar), 25-75% quartiles (box), mean (cross) and outliers (points).

Fig 4 .

 4 Fig 4. Percentages of answers given by children of 3, 4, 5 years old to the question "What did you draw?" for the self-portrait condition and for the free condition.

3 .

 3 Experimental design a. Human participantsHabituation phase: each participant (children and adults) was invited to try a touchscreen tablet (iPad Pro, 13-Inch, version 11.2.2, capacitive screen reacting to the conductive touch of human fingers), then draw on it with their fingers and understand how it worked, notably to change the color used (Fig.5A, Supplementary Video file S7). The drawing with fingers was preferred to allow the inclusion of some chimpanzees and youngest children who have not yet mastered the use of a pencil. A panel consisting of 10 different colors was displayed on the bottom of the screen, and the participant could select one color for their drawing by clicking on one of them. When they clicked on a different color in the panel, any subsequent drawing production was in that color. Children were habituated the day before the tests to avoid overstimulation. Adults were tested immediately after discovering the tablet. Testing phase: each child was individually tested at school, during school time, in their classroom for 3-year-olds, and in the staff room for the older children. The experimenter (LM or MP) stayed during the test but kept their distance during drawing in order to avoid influencing the child. Adults were also tested individually in a room at the research institute for naive participants or at the art school for the experts. Contrary to children, adult participants were left alone in the room. A camera recorded the hand movements of all participants while drawing, in case we needed to control for any problem during the session (interruption of the drawing, involuntary tracings, etc.). No time limit was applied. the chimpanzee's behavior when drawing. Chimpanzees drew on two consecutive days in October 2017, and 12 drawings were collected (Table

Fig 5 .Fig 6 .

 56 Fig 5. Procedure set up for (a) human participants and (b) chimpanzees. All drew with their fingers and were filmed during the drawing sessions.

Figure S8 .

 S8 Figure S8. Examples of drawings by 3-year-old children, in free and self-portrait conditions.

Table 2 . Name and year of birth for each chimpanzee and the number of drawings completed for each test session.

 2

Table S1 .

 S1 Results of the generalized linear model realized to compare the spatial fractal index

	µMLE. (a) between chimpanzees and humans (compared to chimpanzees) and (b) among humans
	(compared to 3-year-old children).
			Estimate	Std. Error	t value	Pr(>|t|)
	a	Intercept	1.50	0.04	34.91	< 0.0001
		3-year-old children	0.22	0.05	4.51	< 0.0001
		4-year-old children	0.28	0.05	5.73	< 0.0001
		5-year-old children	0.34	0.05	6.85	< 0.0001
		7-year-old children	0.37	0.05	7.47	< 0.0001
		8-year-old children	0.28	0.05	5.55	< 0.0001
		9-year-old children	0.34	0.05	6.82	< 0.0001
		10-year-old children	0.33	0.05	6.60	< 0.0001
		Naive adults	0.23	0.05	4.63	< 0.0001
		Expert adults	0.20	0.05	4.10	< 0.0001
	b	Intercept	1.72	0.03	71.72	< 0.0001
		4-year-old children	0.06	0.03	1.79	0.07
		5-year-old children	0.12	0.03	3.43	< 0.001
		7-year-old children	0.14	0.03	4.33	< 0.0001
		8-year-old children	0.05	0.03	1.58	0.11
		9-year-old children	0.11	0.03	3.37	< 0.001
		10-year-old children	0.10	0.03	3.05	0.002
		Naive adults	0.01	0.03	0.19	0.85
		Expert adults	-0.02	0.03	-0.61	0.54
		2. The drawing duration

Table S2 .

 S2 Results of the generalized linear model to study drawing duration among humans (compared to 3-year-old children, and free condition compared to self-portrait condition).3. The use of colors a. Number of colors used Table

  Table with data used for the analysis, see "Data table" excel file.

Acknowledgments

We thank the school director and the teachers who gave us access to their classrooms, proving their interest in our research project. We are grateful to all the participants and to the parents of all the children, who accepted with enthusiasm to contribute to our study. Thanks also to Sarah Piquette, who provided help regarding the ethical components of this project. We are also grateful to Naruki Morimura and Fumihiro Kano, who helped us with data collection in chimpanzees.

Each participant (child and adult) was tested in two conditions. This choice of drawing tasks was made in order to assess a possible difference in results between a non-specific task (free drawing) and a specific one (self-portrait).

Free condition: "Draw what you want". The experimenter explained to the subject that they could draw whatever they wanted, with no further instructions. The experimenter systematically asked each child up to and including the age of five to say what they had drawn when they had finished their drawing (in older children, it was always obvious what has been drawn). The same question was asked three days later to monitor the consistency of the answer.

Self-portrait condition: "Draw yourself". The experimenter instructed the subject to draw themselves. Again, the experimenter systematically asked each child up to and including the age of five what they had drawn, and repeated the question three days later to monitor the consistency of the answer.

In each participant group, half of the subjects began the test with the free condition instructions, the other half started with the self-portrait condition. The choice was made randomly. To ensure adequate levels of concentration, none of the children drew under both conditions the same day. A total of 356 drawings were collected in humans (Table 1, Supplementary materials Figure S8).

b. Chimpanzees

Each female or mother-daughter duo was isolated during lunch time in a testing room using a system of trapdoors and tunnels. Once inside the room, they were provided with fruit and vegetables and asked to sit down. The experimenter (SH) presented a resistive touch screen (1947L 19-Inch Rear-Mount Touch monitor) to the chimpanzee and encouraged her to draw on it using her fingers (Fig. 5B, Supplementary Video file S7). Each individual was free to approach and use the touchscreen. There was no time limitation. In the case of mother-daughter duos, some fruit juice was given to the chimpanzee who did not draw to avoid disruptions. The touch screen was connected to a computer that was controlled by a second experimenter (MP), who directly recorded the data for the drawing. Since chimpanzees have a color recognition quite similar to that of humans [START_REF] Matsuzawa | Colour naming and classification in a chimpanzee (Pan troglodytes)[END_REF][START_REF] Matsuno | Color classification by chimpanzees (Pan troglodytes) in a matching-to-sample task[END_REF], they also had the opportunity to use colors. A color gradient was displayed on the right-hand side of the screen, and the subject could select a color for her drawing by clicking on it. When she clicked a different color of the panel then any subsequent drawing appeared in that color. Each test session was videotaped in order to analyze distribution log-likelihood (Equation 3 for power law and Equation 4 for exponential law),

where n is the total number of step lengths and Smin is the minimum step length.

(1) Maximum estimate of the power law exponent µMLE:

(2) Maximum estimate of the exponential law exponent lMLE: The model retained (power or exponential) was that with the lowest AIC, considering a minimum difference of 2 between the two AICs [START_REF] Burnham | Multimodel inference: understanding AIC and BIC in model selection[END_REF].

All the drawings produced by our 10 groups of participants (chimpanzees, 7 grades of children, naive and expert adults) followed a power law (lowest AIC, see Supplementary data Table S10). The Maximum Likelihood Estimate of the power law exponent µ MLE was then used to draw conclusions on the efficiency of the representation for each drawing. This index is comprised of values between 1 and 3 [START_REF] Bartumeus | Animal search strategies: a quantitative random-walk analysis[END_REF][START_REF] Viswanathan | Optimizing the success of random searches[END_REF]. The higher the index, the more the line was considered to be directed, well planned and efficient [START_REF] Viswanathan | Optimizing the success of random searches[END_REF]. S4. Results of the generalized linear model to compare the number of color changes. (a) between chimpanzees and humans (compared to chimpanzees) and (b) among humans (free condition compared to the self-portrait condition and boys/men compared to girls/women).

b. The drawing duration

The meaning of drawings in children

Table S5. Results of the generalized linear model carried out to study the consistency of the answer for the self-portrait condition among the three youngest categories of children (compared to the 3-year-old children and the response rate « me » immediately compared to « me » after three days).

Estimate


D Caurant

Anne-Marie Lejus

Jeanine Théry

Daniel Vivien

Elaboration and devitrification study of glasses in the

Al2O3 -La2O3 system