Manuela Sellitto

Andrés Antonio González-Garrido

Joseph W Kable

Jean-Claude Dreher
email: dreher@isc.cnrs.fr

Laure Bottemanne

Vicarious Rewards Modulate the Drift Rate of Evidence Accumulation From the Drift Diffusion Model

Keywords: social cognition, motivation, decision making, drift diffusion models, drift rate, vicarious reward

Taking other people's interests into account is a fundamental ability allowing humans to maintain relationships. Yet, the mechanisms by which monetary incentives for close others influence perceptual decision-making processes remain elusive. Here, we compared perceptual decisions motivated by payoffs for oneself or a close relative. According to drift diffusion models (DDMs), perceptual decisions are made when sensory evidence accumulated over time -with a given drift rate -reaches one of the decision boundaries. We used these computational models to identify whether the drift rate of evidence accumulation or the decision boundary is affected by these two sources of motivation. Reaction times and sensitivity were modulated by three factors: the Difficulty (motion coherence of the moving dots), the Payoff associated with, and the Beneficiary of the decision. Reaction times (RTs) were faster for easy compared to difficult trials and faster for high payoffs as compared to low payoffs. More interestingly, RTs were also faster for self than for other-affecting decisions. Finally, using DDM, we found that these faster RTs were linked to a higher drift rate of the decision variable. This study offers a mechanistic understanding of how incentives for others and motion coherence influence decision-making processes.

INTRODUCTION

When playing at a shooting range in a fairground, we accumulate sensory evidence (about target movement) until we can shoot accurately, and win the prize. Now, if such decisions are made so that the prize goes to a close friend, will we process and use information in the exact same way? More precisely, how does motivational incentives for someone else influence the mechanisms engaged in making simple perceptual choices as compared to the same decisions associated with the same incentives, but for you?

In the last decades, the framework of sequential-sampling models, such as drift diffusion models (DDMs), has proven to be a powerful approach to explain the process of making a decision [START_REF] Vandekerckhove | Fitting the ratcliff diffusion model to experimental data[END_REF][START_REF] Ratcliff | The diffusion decision model: theory and data for two-choice decision tasks[END_REF][START_REF] Leite | Modeling reaction time and accuracy of multiple-alternative decisions[END_REF][START_REF] Summerfield | Building bridges between perceptual and economic decision-making: neural and computational mechanisms[END_REF][START_REF] Forstmann | Sequential sampling models in cognitive neuroscience: advantages, applications, and extensions[END_REF][START_REF] Ratcliff | Diffusion decision model: current issues and history[END_REF]. DDMs successfully capture the complex relationship between choice and reaction times (RTs) by decomposing these behavioral data into internal cognitive components of decision processing. In this framework, a decision reflects a decision variable drifting with a given rate (v), from an intermediate starting point (z) toward one of the decision boundaries at hands. Each boundary is separated from the starting point (z) of a given distance (a) and acts as a decision threshold for an option, so that the response of a decision is initiated when the decision variable reaches one of the boundaries. In the example of the shooting range, the decision variable would accumulate information about the position of the moving ducks over time, and when (relative) certainty about their position is reached, the decision of pulling the target is made.

Sensory encoding of information basically relies on the quality of the available evidence [START_REF] Ratcliff | The diffusion decision model: theory and data for two-choice decision tasks[END_REF]. A foggy weather would slow the rate at which the decision variable rises, as compared to clear climate conditions. Reliability of the decision depends on the distance between the starting point of the decision variable and the decision boundary; the decision rules are set by the read-out mechanisms [START_REF] Brainard | The psychophysics toolbox[END_REF][START_REF] Summerfield | Building bridges between perceptual and economic decision-making: neural and computational mechanisms[END_REF][START_REF] Oppenheimer | Information processing as a paradigm for decision making[END_REF][START_REF] Forstmann | Sequential sampling models in cognitive neuroscience: advantages, applications, and extensions[END_REF]. Reaching higher decision boundaries requires more evidence to be accumulated, thus leading to a better accuracy, but takes a longer time. Which of the evidence accumulation stage (drift of the decision variable) or the read-out mechanisms (distance between the starting point and the decision boundaries) would be adjusted differently based on vicarious information (the beneficiary of the decision)? How is the perceptual decision process modulated when the source of motivation concerns a close relative rather than oneself?

Here, we designed a new paradigm, enabling the use of DDMs to investigate the influence of the payoff associated with and the person affected by a perceptual decision (Figure 1). The participants performed a random dots task (left/right direction categorization) to win low or high payoffs, for themselves or for a close relative. We tested which of the DDM parameters are modified between other-affecting and self-affecting decisions: the drift rate of the decision variable (encoding) or the decision boundary (read-out; Figure 2)? Changes in the distance between the starting point and the decision boundary (a) would mean that people integrate beneficiary-related motivation through the read-out mechanisms, setting the decision rules prior to starting the evidence integration itself. Alternatively, a direct influence of self/other motivation on the decisional process could affect the drift rate of the decision variable, which is an index of the quality of evidence used for the decision. This would suggest that sources of motivation (payoff for self/payoff for other) are integrated together with the evidence for the choice alternatives into a single source of evidence during the accumulation process. Finally, a variation in the non-decision time would indicate that the beneficiary-related motivation acts on cognitive mechanisms outside of the decision process itself, such as primary encoding of the stimuli and motor execution.

MATERIALS AND METHODS

Participants

Forty healthy subjects were recruited by advertisements in the Lyon 1 Claude Bernard University students' mailing list. Subjects were screened using self-reports to exclude any psychiatric or neurological history, and current or previous substance abuse (except nicotine and festive alcohol consumptions). All participants gave written informed consent and received 20€ for their participation. This study was approved by the local research ethics committee (Comité de Protection des Personnes Sud-Est III); all methods were performed in accordance with the relevant guidelines and regulations. Two subjects were excluded, one for chance level performances and the other for technical problems, leaving 38 subjects for further analyses (15 females; mean age = 21.84, range = 18-34).

Stimuli

Random dots kinematograms (RDKs) were programmed using the MATLAB R Psychtoolbox [START_REF] Brainard | The psychophysics toolbox[END_REF][START_REF] Pelli | The videotoolbox software for visual psychophysics: transforming numbers into movies[END_REF]. The mask stimulus was a drifting random dots display of 2000 ms duration. Dots were white on a black background, with each frame composed of 50 white Gaussian blobs with a diameter of 2.85 mm. The stationary dots began to move with a speed of 2.7 • /s from their original locations, and each dot had a life duration of 500 ms. The motion of the dots was made by replotting dots corresponding to the previous ones at a determined spatial offset in the same direction so that all the dots moved in their directions at the same speed. During the experiment, RDKs appeared in a square centered on the screen (Dell, 19 , screen resolution set to 1,280 × 1,050, vertical refresh rate of 60 Hz), taking 30.8% of the screen, with participants at a distance of 60 cm.

Procedure

Before going to the laboratory, the volunteers were asked to choose a close relative for who they would be willing to play for, on half of the experiment. At their arrival, the participants sat in the experimental room, were informed, and gave their written consent. Their relationship with the chosen person was asked [seven participants chose one of their parents (mother or father), seven chose a sibling, eight chose their lover, three chose a friend, and two chose their roommate]. A few demonstration trials were shown, for them to see how the condition cue (Payoff and Beneficiary) was displayed. Subjects were trained and then finally completed the task. It lasted approximately 64 min, in four blocks of 16 min each. All were debriefed when the task was over.

Training

Before the task, subjects were trained to be familiarized with the design and timing. The training was composed of 10 trials of 15% coherently moving dots, which is the easy level of the task. To ensure that participants did not respond randomly, a sensitivity (d') criterion was set at d = 0.6 (i.e., 60% correct, which is higher than chance level). If subjects were below this criterion in the training session, they performed a second identical training. All of the included subjects eventually reached the criteria and subsequently performed the task.

Instructions

Participants were explained that they would perform a game in order to win money, either for themselves of for the close relative they chose. They were told that they would earn 10€ FIGURE 1 | Trials design. Each trial began with a cue, showing "me" or "him" (for self-and other-affecting decisions, respectively) and a full filled rectangle (high payoff) or a one-fifth filled rectangle (low payoff) on top of a square. The cue and the square were depicted in yellow or in blue, according to the beneficiary. Then, the first frame of the random dots kinematogram (RDK; stationary dots) appeared in the square for 1,000 ms. Following this, the moving dots were presented for 2,000 ms and the subject had to respond while the dots were moving. At the end of the 2,000 ms of dots motion, the payoff was presented. If the response was correct, a pile of coins proportional to the payoff was shown together with the value of payoff itself ("+2," "+10") above it. For incorrect responses and misses, a red-colored cross was displayed together with "+0" on top of it. Then, a new trial began and the cue of the upcoming trial was shown.

for doing the experiment and could win 2€ or 10€ more for themselves and also 2€ or 10€ for their relatives. The participants were asked to discriminate the left/right direction of coherently moving dots. They were instructed that they had to give one, and only one, response during the dots motion: if they gave more than one response or did not respond (miss), the program would consider it as incorrect. Money was not accumulated over trials, nor was such accumulation shown to the participants. They were told that one trial of each of the beneficiary condition (self and other) would be randomly selected (by a computer program) to determine their final payoffs. The payoff associated with the trial would be won by the beneficiary, if it was a correct trial. Participants were told (and believed) that the payoff for the other (as well as for themselves) would be sent after completing the experiment. In reality, the close relative received nothing and all participants received 20€ (as if the selected trial was won for himself and associated with a high payoff). This procedure (i) ensured that participants treated all decisions as equally relevant, both for themselves and their close relative; (ii) avoided any competition effects to arise between self and other interests. Also, accuracy was implicitly emphasized by telling the participants that, although they would have to adapt to the given 2 s to answer, time should not be a problem since the duration of the stimuli was chosen based on previous experimental results (pilot study).

Task Design

A square was always present in the middle of the screen. On top of this square appeared the cue, which indicated the beneficiary and payoff conditions of the forthcoming trial. The dots were displayed inside the area defined by the square. The square and the cue were colored yellow or blue, according to the beneficiary of the payoff associated with the trial. The color was used to emphasize the beneficiary of the trial and was counterbalanced between subjects.

Each trial began with the cue, which had a jittered duration from 800 to 1,200 ms and was used as inter-trial interval (ITI). The cue consisted in a word announcing the beneficiary of the decision ("him" for others-affecting decisions, "me" for selfaffecting decisions) to the left of a rectangle filled proportionally to the payoff associated with the decision (full filled rectangle for 10€, one-fifth filled rectangle for 2€). This cue remained on the screen during the entire subsequent trial. After the cue, the first frame of the RDK to come (a picture of stationary dots) was shown for 1,000 ms. Then, dots motion began and lasted for 2,000 ms, during which the subject had to respond. Motion coherence was either 13% (difficult) of 15% (easy), for all participants. At the end of the 2,000 ms of dots motion, the feedback illustrated the payoff for 500 ms. If the response was correct, a pile of coins proportional to the payoff (2 or 10€), was shown together with the value of payoff itself ("+2, " "+10"). For incorrect responses and misses, a red-colored cross was displayed together with "+0" above it. At the end of the trial, a new ITI was displayed, showing the cue for the trial to come.

A total of 104 trials per Beneficiary * Payoff * Difficulty condition were performed, leading to 832 trials per subject. The task was composed of 4 blocks, of 208 trials each. Each block included 26 trials of each of the 8 conditions. Difficulty levels, Payoffs, Beneficiaries, and dots direction were pseudo-randomized within each block and across participants. Randomization of dots direction was designed to avoid a bias toward one of the two (left or right) alternatives, constraining it to no more than three consecutive trials of the same dots direction.

It is to be noted that we actually ran a first experiment using another anonymous, randomly selected, participant as "the other." However, there was no main effect of the beneficiary on RT or on d' (Supplementary Table 1). Since we were aiming to characterize how others are taken into account into the perceptual decision-making process, and based on the literature showing that familiarity increase vicarious effects [START_REF] Mobbs | A key role for similarity in vicarious reward[END_REF][START_REF] Kawamichi | Activation of the reward system during sympathetic concern is mediated by two types of empathy in a familiarity-dependent manner[END_REF], we adapted our task with a close relative.

Statistical Analysis

Reaction times for corrects and RTs for errors were analyzed separately, and RTs were logarithmically transformed. logRT and sensitivity (d') normality distribution was ensured using Lilliefors tests. logRT and d' were then analyzed using three-way repeatedmeasures analyses of variances (rmANOVAs). The factors were as follows: "Beneficiary" (two levels: other vs. self), "Payoff " [two levels: high (10€) vs. low (2€)], and "Difficulty" [two levels: 13% motion coherence (difficult) vs. 15% coherence (easy)]. Beneficiary and Payoffs were overt factors, indicated by cues on each trial, but difficulty was not explicitly given to participants. During debriefing, we asked participants during debriefing how many difficulty levels they perceived. Most of them perceived two levels; only two of them thought there were more and one did not conscientiously perceived any. All post hoc analyses were performed using LSD Fisher tests. There was no effect of gender on behavior (Supplementary Table 2). Although there could be effects of sex hormone variations on decision making in young women, we did not record the phase of the menstrual cycle in our sample. All statistical analyses were performed using Statistica (STATISTICA R , Dell Inc., 2015), except for normality tests and DDM fitting, performed on MATLAB R .

Fitting the DDM to the Data

The DDM assumes that two-choice decisions are made by a noisy process that accumulates information over time from a starting point (z) toward one of two choice criteria or boundaries (here, corresponding to left and right response decision, respectively; Figure 2A). When one of the boundaries is reached, a response is initiated. The starting point and the decision boundaries are separated by distance (a). The evidence that drives the accumulation process, the drift rate (v), is derived from the representation of the stimulus. The better the quality of the evidence, the larger the drift rate toward the appropriate decision boundary, and the faster and more accurate the response (Figure 2C). The components of processing acting outside the decision process itself, such as encoding and response output, are combined in a single parameter: the non-decision time parameter (Ter). RT being the result of non-decision time added to the time it takes for accumulated evidence to reach one of the boundaries, and sensitivity coming from the reached boundary that determines which response is given, the model extracts the components of the decision process (values of drift rate, nondecision processes, and boundaries) from RT distribution and sensitivity data simultaneously.

For fitting the diffusion model to the data [START_REF] Ratcliff | Estimating parameters of the diffusion model: approaches to dealing with contaminant reaction times and parameter variability[END_REF][START_REF] Vandekerckhove | Fitting the ratcliff diffusion model to experimental data[END_REF], we used the MATLAB Diffusion Model Analysis Toolbox [DMAT [START_REF] Vandekerckhove | Diffusion model analysis with MATLAB: a DMAT primer[END_REF]]. The DMAT extracts the components of the decision process and their variability from RT distribution and sensitivity data from all trials for each condition. All trials, correct and error, are thus included in the DMAT parameter estimation. Parameters are estimated by maximizing a multinomial likelihood function. Left and right trials being equally distributed across the experiment (50% of trials for each direction, within each block), the underlying diffusion processes are supposed to be symmetric and no bias toward the left or right answer should arise. We ran a model where the starting point (z) was estimated independently from the decision boundary for the left and the right button presses separately. We then checked that z was not different between left and right responses using a one-way rmANOVA with response direction as factor. The analyses showed no effect of response direction (F 1,37 = 0.001; p = 0.971), ensuring that no bias emerged toward either the left or the right response. Consequently, we applied in all our models a starting point equal to half the distance between the left and right decision criteria (z = 1 /2 a). Each model was fitted to the data separately for each participant.

The first model we ran allowed all three parameters to vary [the boundary (a), the drift (v), and the non-decision time (Ter)]. The estimated parameter values did not follow a normal distribution; we thus used a decimal logarithmic transformation and ensured it normalized their distribution using Lilliefors tests (Supplementary Table 3) before we applied the threeway rmANOVA. The three factors were the Beneficiary of the decision, the Payoff associated with the decision and the Difficulty (dots coherence). The boundary (a) and the non-decision time (Ter) showed no effect of any factor. We thus ran a model where only the drift (v) was free to vary across conditions. Once again, we analyzed log(v) using the same three-way rmANOVA. In order to compare the goodness of fit of our models, we also ran the intermediate models (either the drift and the boundary or the drift and the non-decision time were allowed to vary) and compared the sum of the individual Bayesian Information Criterion (BIC) of the models.

Data Availability

The data used in the present paper will be available to any reader after publication. The datasets generated and/or analyzed during the current study will be available in the repository, on a permanent free-access web link.

RESULTS

Participants performed a random dots (left/right direction categorization) task to win low or high payoffs, for themselves or for a close relative. RTs and sensitivity (d') were collected and analyzed using three-way rmANOVAs, with "Beneficiary" (two levels: Other vs. Self), "Payoff " (two levels: High vs. Low), and "Difficulty" (two levels: Difficult vs. Easy) as factors.

Sensitivity (d')

Participants missed only one trial in the experiment. A main effect of task Difficulty was found; d' was better during Easy trials than during Difficult trials (d' Easy = 0.82; d' Difficult = 0.79; F 1,37 = 57.4; p = 0.0000001; Cohen's d = 0.362; Figure 3A). All interaction effects also reached significance, including the triple interaction effect (F 1,37 = 16.8; p = 0.000220). We consequently ran two-ways rmANOVAs for each difficulty level, keeping Beneficiary and Payoff as factors.

During Easy trials, d' was better for Self than for Other (d' Self = 0.83; d' Other = 0.80; F 1,37 = 16.2; p = 0.000276; Cohen's d = 0.305; Figure 4A) and better for Low than for High Payoffs (d' Low = 0.83; d' High = 0.81; F 1,37 = 11.5; p = 0.001683; Cohen's d = 0.266; Figure 4D). During Difficult trials, both Beneficiary (d' Self = 0.77; d' Other = 0.80; F 1,37 = 24.7; p = 0.000015; Cohen's d = 0.375) and Payoff (d' Low = 0.77; d' High = 0.81; F 1,37 = 30.0; p = 0.000003; Cohen's d = 0.465) were significant. The Beneficiary * Payoff interaction also reached significance (F 1,37 = 19.9; p = 0.000072). Sensitivity for Self-affecting decisions associated with a Low Payoff was lower than for Other-affecting ones (d' Self = 0.74; d' Other = 0.80; p < 0.000001; Cohen's d = 0.780) and lower than when associated with a High Payoff (Self: d' High = 0.80; Other: d' High = 0.81; p < 0.000001; Cohen's d = 0.816; Figure 5A).

Reaction Times

The results presented here come from analyses performed on logarithmically transformed RTs (decimal logarithm), for correct and error trials separately. For intelligibility, the mean values in the following paragraph are given as non-transformed RT, in milliseconds (ms). Difficulty had an effect on log RT from errors, with subjects being slower during Difficult than during Easy trials (RT Difficult = 1146 ms; RT Easy = 1110 ms; F 1,37 = 6.6; p = 0.0146; Cohen's d = 0.209). This was the only effect on RT from errors.

All the following results concern correct responses. We found a main effect of task Difficulty (Figure 3B) and a main effect of Beneficiary (Figure 3E) on log RT (for correct responses). That is, RTs were slower during Difficult than during Easy trials (RT Difficult = 1055 ms; RT Easy = 1033 ms; F 1,37 = 36.56; p < 0.001; Cohen's d = 0.144) and slower for Other than for Self (RT Other = 1054 ms; RT Self = 1035 ms; F 1,37 = 18.86; p < 0.001; Cohen's d = 0.125). The triple interaction effect was not significant (F 1,37 = 0.22; p = 0.645). However, both the Beneficiary * Difficulty and the Payoff * Difficulty interaction effects reached significance (F 1,37 = 37.10; p < 0.000001 and F 1,37 = 4.26; p = 0.0461, respectively). Given the main effect of Difficulty, we then ran separate two-way rmANOVA at each Difficulty levels, keeping Beneficiary and Payoff as factors.

RTs were slower for Other than for Self, during Easy trials only (RT Other = 1047 ms, RT Self = 1020 ms, F 1,37 = 32.6; p = 0.000002; Cohen's d = 0.180; Figure 4B). Payoff had an effect at both Difficulty level, but with opposite direction. During Easy trials, RTs were slower for High than for Low Payoffs (RT High = 1049 ms, RT Low = 1017 ms, F 1,37 = 23.5; p = 0.000022; Cohen's d = 0.203; Figure 4E), while during Difficult trials, they were faster for High

DDM Parameters

We started with the selection of the best-fitting model. The first model we ran allowed all three parameters [the boundary (a), the drift (v), and the non-decision time (Ter)] to vary. In this model ("full model"), the boundary (a) and the non-decision time (Ter) showed no effect of any of the three factors (Beneficiary, Payoff, and Difficulty). We thus applied a model where only the drift (v) was free to vary across conditions ("v free"). In order to compare the goodness of fit of our models, we also ran the intermediate models (either the drift and the boundary, "v free-a free, " or the drift and the non-decision time, "v free-Ter free, " were allowed to vary) and compared the sums of the individual BIC of the models. The model where only the drift (v) was allowed to vary showed a lower BIC than all other models (BIC sums: full model: 7.62 × 10 4 , v free: 7.30 × 10 4 ; v free-a free: 7.46 × 10 4 ; v free-Ter free: 7.45 × 10 4 ). To ensure that this reflected individual fits, we also compared the BICs of the models within each individual. Thirty-six of 38 subjects were best fitted with the model where only the drift is allowed to vary ("v free"); the two other subjects were best fitted with the addition of modulations of the boundary a ("v free-a free"). Furthermore, we ran the simulations of the data predicted by the model using the estimated parameter, for each subject (Supplementary Figure 1).

We subsequently applied a three-way (Beneficiary, Payoff, and Difficulty) rmANOVAs on the drift parameter (v) from the "v free" model. Note that log(v) values are negative, so that higher absolute values of log(v) actually mean lower drift rates (v) of the decision variables. Difficulty had a main effect on the drift rate (v), which was higher during Easy than during Difficult trials [log(v) Easy = -0.76; log(v) Difficult = -0.84; F 1,37 = 35.9; p = 0.000001; Cohen's d = 0.503; Figure 3D]. Beneficiary also had a main effect, v being higher during Self-than during Other-affecting decisions [log(v) Self = -0.78; log(v) Other = -0.82; F = 4.42; p = 0.0423; Cohen's d = 0.273; Figure 3F]. The Beneficiary * Payoff interaction also reached significance (F 1,37 = 6.28; p = 0.01673). For decision associated with a High Payoff, v was higher for Self than for Other During Easy trials, both Beneficiary and Payoff had a main effect: the drift (v) was higher for Self than for Other [log(v) Self = -0.70; log(v) Other = -0.81; F 1,37 = 19.8; p = 0.000076; Cohen's d = 0.587] and higher for Low than for High Payoffs [log(v) High = -0.79, log(v) Low = -0.73, F = 6.18; p = 0.017588; Cohen's d = 0.179].

DISCUSSION

Taking advantage of the DDM and the perceptual decisionmaking framework, we provided a mechanistic explanation of how others are integrated into the decisional process. Our results indicate that the beneficiary of the incentive associated with a decision modifies how decisions are performed. Decisions were faster for self than for others. As explained by the DDM, this was related to a higher drift rate (v) of the decision variable. In the present experiment, better sensitivity and faster RT were mirrored by higher drift rates. Higher drift rates have been found to explain shorter RT in tactile discrimination as well [START_REF] Mulder | Are accuracy and reaction time affected via different processes?[END_REF]. A change in the drift rate of the decision variable indicates a modification of the integration process itself, as branding does for economic value-based choices [START_REF] Philiastides | Influence of branding on preference-based decision making[END_REF]. Our result indicates that sensory evidence is integrated faster for self than for others. In the example of the shooting range, if we aim to reach a target to win a price for a close relative, the decision process would not differ in the amount of evidence we would accumulate before making the decision to shoot, but rather in the efficiency of accumulation of the sensory evidence.

It may be that participants tried to imagine their relative receiving the payoff, although not instructed to do so. This would have required higher cognitive demands and redirect part of the attentional load and neuronal energy from the evidence accumulation process. Using the Game Theory and Public Good Games, studies show that taking into account another person into a decision engages the processes of mentalizing (or the Theory of Minds) [START_REF] Frith | The role of social cognition in decision making[END_REF][START_REF] Stallen | The cooperative brain[END_REF]. It could also be that, when performing a self-affecting decision, more attentional resources are spent on the task (because of a higher motivation, due to direct self-benefit), thereby increasing the efficiency of evidence accumulation. In a study on value-based decision making combined with DDM, it has been suggested that, when choosing on behalf of another, a dual process takes place. Stimulus value integration, reflected in the drift rate (v), would be firstly computed based on selfpreferences and then adjusted to the other's inferred preferences [START_REF] Harris | Accounting for taste: a multi-attribute neurocomputational model explains the neural dynamics of choices for self and others[END_REF]. For others with similar preferences, RTs were longer and linked to a change in drift rate. Analogous mechanisms could have occurred during our experiment as well. The importance accorded to the evidence, reflected in the drift rate (v) of the decision variable, could have been initially lower during other-affecting decisions, or it could have been readjusted during the time of the decision. Alternatively, RTs for dissimilar others were also longer but associated with a higher decision boundary (a), which could have been implemented to overcompensate for an increased uncertainty about their preferences [START_REF] Harris | Accounting for taste: a multi-attribute neurocomputational model explains the neural dynamics of choices for self and others[END_REF].

Payoffs for others could have been integrated into the perceptual decision process through a change in the decision rules, outside of the mechanism of sensory evidence accumulation and change the distance between the starting point of the decision variable and the decision boundary. Other researchers also suggested that payoff can modify both stages, evidence accumulation and decision boundary. It postulates two processes, one for payoffs and another for stimulus information, and that on a given trial, attention is directed toward one of these information, never both [START_REF] Diederich | Modeling the effects of payoff on response bias in a perceptual discrimination task: bound-change, driftrate-change, or two-stage-processing hypothesis[END_REF][START_REF] Diederich | A further test of sequential-sampling models that account for payoff effects on response bias in perceptual decision tasks[END_REF]. Sequential-sampling models have previously been used to account for the effects of payoffs in a perceptual decision task with time constraints. These studies have reported changes in the distance from the starting point to the decision boundaries, a bias in the starting point of the decision variable, induced either by prior probabilities of being correct [START_REF] Leite | Modeling reaction time and accuracy of multiple-alternative decisions[END_REF][START_REF] Mulder | Bias in the brain: a diffusion model analysis of prior probability and potential payoff[END_REF] or by asymmetrical payoffs associated with the possible response alternatives [START_REF] Simen | Reward rate optimization in two-alternative decision making: empirical tests of theoretical predictions[END_REF][START_REF] Mulder | Bias in the brain: a diffusion model analysis of prior probability and potential payoff[END_REF]. These changes were characterized by a shift of the starting point of the decision variable closer to the decision boundary associated with the alternative having the higher probability or associated with the higher payoff. The starting point is then further from the other boundary (for the other alternative at hand) and the decision variable is less likely to reach it, establishing a bias and a change in response proportion.

In contrast, our experimental setup was designed to avoid response probability manipulations toward one of the (left or right) alternatives, in terms of probability (through trials randomization) and in terms of payoff (by assigning the same payoff to both response alternatives). We aimed to compare identical decisions made by the participants, either for themselves or for another person. It would be interesting to adapt our paradigm to asymmetrical alternatives, with the payoff going to one of the beneficiaries depending on the correct answer. Following our results, it could be expected that a bias toward the response associated with self-payoff would emerge. Finally, a variation in the non-decision time (Ter) would have indicated that the beneficiary-related motivation acts on cognitive mechanisms that are outside of the decision process itself, such as primary encoding of the stimuli and motor execution. Non-decision time is usually referred to as reflecting the early encoding of the stimulus of interest and the execution of the motor response, once the decision process is completed [START_REF] Brainard | The psychophysics toolbox[END_REF][START_REF] Frith | The role of social cognition in decision making[END_REF][START_REF] Ratcliff | The diffusion decision model: theory and data for two-choice decision tasks[END_REF][START_REF] Philiastides | Influence of branding on preference-based decision making[END_REF][START_REF] Stallen | The cooperative brain[END_REF], both external to the visuo-motor decision process in itself. Moreover, the non-decision time is thought to be necessary to account for speed-accuracy trade-offs [START_REF] Mulder | Are accuracy and reaction time affected via different processes?[END_REF], and it has been shown that speed-accuracy instructions also modulate the non-decision time [START_REF] Zhang | Dissociable mechanisms of speed-accuracy tradeoff during visual perceptual learning are revealed by a hierarchical driftdiffusion model[END_REF]. Variation in the non-decision time can mean that different strategies are applied [START_REF] Schuch | Task inhibition and response inhibition in older vs. younger adults: a diffusion model analysis[END_REF] and could include other components that influence the decision-making processes. However, the DDM cannot distinguish between different mechanisms within the non-decision time.

This study is a first step toward a better comprehension of how others influence decision-making processes. Altogether, our results suggest that the beneficiary affected by the decision is integrated together with the sensory evidence into the decision variable and affect the efficiency of the accumulation process during perceptual decision making. The present work provides further evidence of the strength of sequential-sampling models in a unified theory of choices [START_REF] Summerfield | Building bridges between perceptual and economic decision-making: neural and computational mechanisms[END_REF][START_REF] Polanía | Neural oscillations and synchronization differentially support evidence accumulation in perceptual and value-based decision making[END_REF][START_REF] Polanía | The precision of value-based choices depends causally on fronto-parietal phase coupling[END_REF], with outcomes that are self-interested or vicarious. However, while the main effect of beneficiary was significant on RT and drift rate (v), when analyzing difficulty levels separately, the effect was not present during difficult trials. This may be attributed to the fact that sensory evidence was too low for the drift to be modulated. Although the study of payoff per se was not our main goal, it is puzzling to observe that its effect was reversed between the easy and difficult level. Further studies are needed to confirm both results. A future direction would also be to specify how social distance to others changes perceptual decisions, as previously investigated using economic games where participants chose between selfish and generous alternatives [START_REF] Strombach | Social discounting involves modulation of neural value signals by temporoparietal junction[END_REF].

FIGURE 2 |

 2 FIGURE 2 | Drift diffusion models (DDMs) and hypotheses. (A) DDM main parameters. DDM assumes that two-choice decisions are made by a noisy process that accumulates information, with a given drift rate (v), over time. This process goes from the starting point (z) toward the decision boundary. When the boundary is reached, a response is initiated (with a button press, in usual experimental setups). The starting point and the boundary are separated by the distance (A). (B-D) Effects of boundary modulation, drift-rate changes, and non-decision time variation on response initiation. (B) Boundary modulation. A boundary increase (A+) leads decisions that require more sensory evidence, and thus a longer time, than when a lower boundary is set up (A-). (C) Drift-rate change. A drift rate increase (V+) produces faster sensory evidence accumulation than a lower one (V-), producing faster reaction times. (D) Non-decision time variation. A longer non-decision time (TER+) leads to slower decisions than a shorter one (TER-).

FIGURE 3 |

 3 FIGURE 3 | (A-C) Main effect of difficulty. Easy trials are green and on the left, Difficult trials are red and on the right. (A) Sensitivity (d') is worse, (B) reaction times (RTs) are longer, and (C) drift rate (v) is lower during Difficult trials than during Easy trials. (D-F) Main effects of beneficiary. Self-affecting trials are cyan and on the left; other-affecting trials are orange and on the right.(D) Sensitivity did not differ but there was (E) a faster RT and (F) a higher drift rate (v) for Self than for Others. Log RT, d', and log v are expressed in arbitrary units (a.u.). Bars represent the standard errors of the mean (SEM).

FIGURE 4 |

 4 FIGURE 4 | Effect of beneficiary and payoff for easy trials only. (A-C) Beneficiary. Self-affecting trials are cyan and on the left; Other-affecting trials are orange and on the right. During Easy trials, (A) sensitivity (d') is better, (B) RTs are faster, and (C) drift rate (v) is higher for Self than for Other. (D-F) Effect of payoff. Low Payoffs are in deep purple and on the left; High Payoffs are in light purple and on the right. (D) Sensitivity (d') is better, (E) RT is faster, and (F) v is higher for Low than for High Payoffs. Log RT, d', and log v are expressed in arbitrary units (a.u.). Bars represent the standard errors of the mean (SEM).

  than for Low Payoffs (RT High = 1045 ms, RT Low = 1065 ms, F 1,37 = 21.53; p = 0.000043; Cohen's d = 0.142).

  [log(v) Self = -0.76; log(v) Other = -0.83; p = 0.000078; Cohen's d = 0.385]. The Beneficiary * Difficulty and the Payoff * Difficulty interactions were significant (F 1,37 = 29.5; p = 0.0000004 and F 1,37 = 13.3; p = 0.000801, respectively). We consequently ran two-way rmANOVAs at each Difficulty level, keeping Beneficiary and Payoff as factors. During Difficult trials, Payoff had a main effect [log(v) High = -0.81, log(v) Low = -0.87, F 1,37 = 9.28; p = 0.004265; Cohen's d = 0.409; Figure 5C], but the Beneficiary * Payoff interaction was also significant (F 1,37 = 8.80; p = 0.005251). Payoff actually had an effect only for Self-affecting decisions, with a higher drift (v) for High than for Low Payoffs [log(v) High = -0.80, log(v) Low = -0.91; p = 0.000045; Cohen's d = 0.592].

FIGURE 5 |

 5 FIGURE 5 | Effect of payoff for difficult trials for self and close relative (other). (A-C) Effect of payoff for Self. (A) Sensitivity (d') is lower, (B) reaction times (RTs) are slower, and (C) drift rate (v) is lower for Low Payoffs than for High Payoffs. (D-F) Effect of payoff for Other. There is no difference in (D) sensitivity (d'), (E) RT, or (F) v between Low and High Payoffs. Log RT, d', and log v are expressed in arbitrary units (a.u.). Bars represent the standard errors of the mean (SEM).

Frontiers in Behavioral Neuroscience | www.frontiersin.org

July 2019 | Volume 13 | Article 142

ACKNOWLEDGMENTS

We thank Dr. Caroline Demily for medical screening of the participants.

FUNDING

This research has benefited from the financial support of IDEXLYON from the Université de Lyon (project INDEPTH) within the program Investissements d'Avenir (ANR-16-IDEX-0005) and of the LABEX CORTEX (ANR-11-LABX-0042) of the Université de Lyon, within the program Investissements d'Avenir (ANR-11-IDEX-007) operated by the French National Research Agency. This work was carried out within the framework of the LABEX ANR-11-LABEX-0042 of the Université de Lyon, within the program "Investissements d'Avenir" (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR). This work was also supported by grants from the Agence Nationale de la Recherche (ANR "Brain Choice" n • 14-CE13-0006 and ANR "Social-POMDP" n • 16-NEUC-0003-01) to J-CD.

ETHICS STATEMENT

All participants gave written informed consent and received 20€ for their participation. This study was approved by the local research ethics committee (Comité de Protection des Personnes Sud-Est III), all methods were performed in accordance with the relevant guidelines and regulations.

AUTHOR CONTRIBUTIONS

J-CD and LB designed the study and wrote the manuscript. LB collected the data and conducted the data analysis.

SUPPLEMENTARY MATERIAL

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fnbeh. 2019.00142/full#supplementary-material

Conflict of Interest Statement:

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Rohit Yadav

Iuliia Tkachenko

Alain Trémeau

Thierry Fournel
email: fournel@univ-st-etienne.fr

Estimation of Copy-sensitive Codes Using a Neural Approach

Keywords: Security and privacy → Authentication, • Computing methodologies → Neural networks copy-sensitive codes, authentication, estimation attack, neural networks for binarization, print-and-scan process

Copy sensitive graphical codes are used as anti-counterfeiting solution in packaging and document protection. Their security is funded on a design hard-to-predict after print and scan. In practice there exist different designs. Here random codes printed at the printer resolution are considered. We suggest an estimation of such codes by using neural networks, an in-trend approach which has however not been studied yet in the present context. In this paper, we test a state-of-the-art architecture efficient in the binarization of handwritten characters. The results show that such an approach can be successfully used by an attacker to provide a valid counterfeited code so fool an authentication system.

INTRODUCTION

Counterfeits is one of the main problems of these days. The number of counterfeited products (luxury goods, medicines, tickets, administrative documents) is predicted to increase three percent each year according to the association for packaging and processing technology. A big amount of security techniques exists such as hashing techniques, watermarking techniques, holograms and security printing techniques. However, most of these solutions are expensive in production or cannot be efficiently verified by nonspecialists without specific devices. The development of security elements that are based on the use of Measurable But Not Duplicable (MBND) characteristics [START_REF] Goldman | Non-counterfeitable document system[END_REF] that are formed during a production process, is a promising path for hardcopy document/packaging authentication. MBND can be physical characteristics (see for instance [START_REF] Schraml | Real or Fake: Mobile Device Drug Packaging Authentication[END_REF][START_REF] Wong | Counterfeit Detection Based on Unclonable Feature of Paper Using Mobile Camera[END_REF]), or some features of the printing process based either on the printer signature profile [START_REF] Adams | A study of the interaction of paper substrates on printed forensic imaging[END_REF][START_REF] Pollard | Model based print signature profile extraction for forensic analysis of individual text glyphs[END_REF][START_REF] Simske | High-resolution glyph-inspection based security system[END_REF] or on the use of Copy-Sensitive Graphical Codes (CSGC) [START_REF] Picard | Digital authentication with copy-detection patterns[END_REF][START_REF] Picard | Two dimensional barcode and method of authentication of such barcode[END_REF][START_REF] Tkachenko | Two-Level QR Code for Private Message Sharing and Document Authentication[END_REF]. These security elements which are cheap and easy to integrate, offers a user-friendly verification, compatible with standard devices for both production and verification. That is why they correspond to some commercial solutions for packaging protection. Nevertheless, the security aspects of these elements are not fully studied. The security of CSGC is based on the stochastic nature of Print-and-Scan (P&S) process. It can be easily shown that every time when an image is printed and scanned some information is lost in comparison with its digital version. This effect is called the information loss principle [START_REF] Picard | Digital authentication with copy-detection patterns[END_REF]. Additionally, each printer and scanner has its own signature [START_REF] Tchan | The development of an image analysis system that can detect fraudulent alterations made to printed images[END_REF]. Using these two properties, the authentication test can distinguish the original CSGC (printed once) from copied/counterfeited (printed several times). In this paper, we focus on the unclonability of CSGC and especially on the estimation attack of such codes using a neural approach. We use some random binary codes for our experiments. We show that a small amount of samples can be efficiently exploited in order to estimate the original structure of the digital CSGC. The rest of the paper is organized as follows. The authentication system is introduced in Section 2. We discuss possible attacks in Section 3. The decoding process using a neural network is depicted in Section 4. The description of constructed database and the experiments are presented in Section 5. Finally, we conclude in Section 6.

AUTHENTICATION SYSTEM

The authentication system using CSGC is illustrated in Fig. 1. The authority center creates the valuable document, puts the generated CSGC into this document and prints it using the dedicated printer. During the verification process, the document is scanned and the respective authentication test is applied to verify the authenticity. The generated CSGC is a binary black-and-white image (let call it I ), after being printed and scanned this CSGC is a grayscale image ( Ĩ = I + N P S , where N P S is a noise added by P&S process). An example of original (a black-and-white image) CSGC and its degraded (a grayscale image) CSGC versions are illustrated in Fig. 2. The authentication test can be performed as 1) a comparison of the binary CSGC I with an estimated binary code, here denoted as Î (that is obtained by binarization of grayscale image Ĩ during the authentication test) or as 2) a comparison of binary CSGC I with its degraded (graylevel) version Ĩ . It was shown theoretically [START_REF] Ho | Document authentication using graphical codes: impacts of the channel model[END_REF] that the second strategy is more efficient. The authors in [START_REF] Taran | Clonability of anti-counterfeiting printable graphical codes: a machine learning approach[END_REF] have tested two authentication strategies: i) using Hamming distance between binary original CSGC and binarized versions of printed CSGC, ii) using Pearson correlation between binary original CSGC and graylevel printed CSGC. Nevertheless, the results of ROC curves illustrate that both authentication strategies show the similar results in term of CSGC clonability. Therefore, the comparison of two binary images can give an idea about the attack efficiency. In general the authentication test can be formulated as a hypothesis test:

H 0 : d(I ; Î ) ≤ ϵ; H 1 : d(I ; Î ) > ϵ,
where d is a comparison function (for example, a distance between two images), ϵ is the distortion threshold that was calculated in advance by the authority center. Most of the attacks are produced between printing and scanning processes. An opponent needs to correctly predict I ′ -a binarized version of CSGC Ĩ that then will be re-printed and re-scanned using the same devices (in the case of the worst type attack) and the authentication test will process a grayscale counterfeited image Ĩ ′ . The comparison function d might be sensitive to distortions added during Print-and-Scan (P&S) process and must correctly discriminate CSGC printed ones and CSGC printed twice or counterfeited.

POSSIBLE ATTACKS

For counterfeiting, the opponent wants to create copies of CSGC codes as close as possible to original. For this the opponent can use different strategies depending on his/her practical skills. In this section, we discuss about tools that can be used to create counterfeited CSGC codes.

Uncontrolled duplication

The first most simple way to copy a document is the use of a copy machine or two consecutive P&S operations. However, when we use a copy machine we cannot control the image processing that is applied to the document during the copying process. This attack was explained and experimented in [START_REF] Tkachenko | Two-Level QR Code for Private Message Sharing and Document Authentication[END_REF][START_REF] Tkachenko | Printed document authentication using two level or code[END_REF]. Instead of using a copy machine, the attack can be performed by the use of a scanner and a printer (the same that were used for the original production in the worst case). In this case, the attack consists of two consecutive P&S operations. This attack can be performed by naive attacker and intuitively will have the same results as the unauthorized duplication using copy machine.

Smart attack

Here we suppose that the opponent have not only the same reproduction devices but also have several knowledge of image processing and experience in graphics tools. This attack consists also of two consecutive P&S operations, but in this case some basic image processing algorithms are applied between the two P&S operations.

The opponent can perform histogram equalization or application of sharpen enhancement of printed and scanned CSGC. These basic image processing techniques can improve the quality of CSGC, but the naive use of image processing techniques [START_REF] Tkachenko | Sensitivity of different correlation measures to print-and-scan process[END_REF] cannot help to create good quality counterfeits and thus cannot fool the authentication test.

The authors in [START_REF] Dirik | Copy detection pattern-based document protection for variable media[END_REF] propose the so-called "smart" attack: (a) an attacker may try to estimate the original CDP pixels utilizing inverse print-and-scan model; (b) then, s/he can generate genuine-like CDPs and copy CDP protected documents safely. In most experiments the CDP samples resist to such attacks. However, it was shown [START_REF] Baras | 2D bar-codes for authentication: A security approach[END_REF] that an attacker can produce a fake that successfully fools the detector with reasonable number of genuine goods. This authentication problem can be presented as an optimization game between the legitimate source and an attacker where each player tries to select the best P&S channel to minimize/maximize his authentication performance [START_REF] Ho | Document Authentication Using Graphical Codes: Reliable Performance Analysis and Channel Optimization[END_REF]. For P&S process simulation the lognormal and general Gaussian additive processes [START_REF] Baras | Towards a realistic channel model for security analysis of authentication using graphical codes[END_REF] are used. The conclusions after studying this minimax game [START_REF] Ho | Document authentication using graphical codes: impacts of the channel model[END_REF]: the opponent optimal parameters are close to the legitimate source parameters for both distribution families and the legitimate source can find a configuration which maximizes its authentication performance.

Data driven based approach

We can at the end imagine the situation, when an attacker uses devices (printer and scanner) from the same brand and constructs his/her own database of some printed-and-scanned codes as well as of their digital versions. In this case, s/he can estimate the structure of a printed CSGC by using some binarization methods. The use of some classical binarization methods does not give good results and the counterfeited codes cannot pass the authentication test [START_REF] Tkachenko | Exploitation of redundancy for pattern estimation of copy-sensitive two level QR code[END_REF]. Authors in [START_REF] Diong | Document authentication using 2D codes: Maximizing the decoding performance using statistical inference[END_REF] suggest to extract some statistics from the printed-and-scanned images then use 5 images in order to train some basic classifiers as LDA, SVM, QDA and naive Bayes. They showed that the use of supervised classification can significantly increase the quality of estimated (counterfeited) codes and the suggested authentication system will be affected by this attack. A deep neural network architecture (DNN) has been used in the very recently published paper [START_REF] Taran | Clonability of anti-counterfeiting printable graphical codes: a machine learning approach[END_REF]. In the present paper, we have adopted another type of neural architecture, an autoencoder, in the goal to retrieve a (graphical) code so far decoding CSGC, to study the same authentication system as in [START_REF] Diong | Document authentication using 2D codes: Maximizing the decoding performance using statistical inference[END_REF].

EFFICIENT LEARNING FOR DECODING

Auto-encoders are a type of feed-forward neural network which is trained to reconstruct the input as its output. The network has basically two parts: an encoder that learns an encoding function f and a decoder that learns the decoding function д. It has a hidden layer h that provides a useful compressed representation of the input which has been very useful in learning features and for dimensionality reduction [START_REF] Wang | Generalized autoencoder: A neural network framework for dimensionality reduction[END_REF]. The network basically takes an input x and minimizes the loss function L(x, д(f (x))).

In order to estimate the original code we make use of an existing auto-encoder based architecture called Selectional Auto-Encoder (SAE) [START_REF] Calvo-Zaragoza | A selectional auto-encoder approach for document image binarization[END_REF]. This SAE has previously been used in binarization of document image [START_REF] Calvo-Zaragoza | A selectional auto-encoder approach for document image binarization[END_REF] and has shown significant results. SAE are fully convolutional network without any fully connected layers. It consists of 5 layers of encoder and 5 layers of decoder. The hierarchy of layers in the encoder part of SAE consists of series of convolution and down-sampling operations till the hidden layer h, whereas in the decoder part it consists in series of convolution and up-sampling operations till reconstruction of the image to its original size (see an illustration in Fig. 3). In a binarization context, SAE is trained to output a selectional value for each pixel from an input image to decide whether that pixel belongs to foreground (black) or background (white). Since SAE performs an image to image processing the classification of each pixel is not computed independently, but also considering the neighbourhood pixels.

The network topology for SAE itself is based on a deep residual Encoder-Decoder Network (RED-Net) [START_REF] Mao | Image restoration using very deep convolutional encoder-decoder networks with symmetric skip connections[END_REF], which additionally consists of residual connection from its down-sampling layer to its corresponding up-sampling layer. Through these residual connections feature maps learned in the encoding layer are passed to its corresponding decoding layer which helps to recover better clean image through up-sampling. Residual connections have proven to be very effective and lead to better results while training deeper networks [START_REF] He | Deep residual learning for image recognition[END_REF]. Here, down-sampling is performed by convolution, and up-sampling is achieved using de-convolution. In addition, batch normalization followed by Relu activation is added after each convolution and de-convolution layers. The input and output windows of the network were set to 256 × 256 and size of kernel for convolution and de-convolution was set to 5 × 5. For all layers 64 feature maps were used. The weights of network were initialized using Xavier uniform initializer [START_REF] Glorot | Understanding the difficulty of training deep feedforward neural networks[END_REF] while training the network from scratch, otherwise the weights were initialized after pre-training on DIBCO database [START_REF] Pratikakis | ICFHR2016 handwritten document image binarization contest (H-DIBCO 2016)[END_REF]. The learning procedure was carried out using ways of stochastic gradient descent [START_REF] Bottou | Large-scale machine learning with stochastic gradient descent[END_REF] with learning rate of 0.001. The training of the model was done on a GeForce GTX 1080 card for 200 epochs, setting the batch size to 10. However, an early stopping strategy is applied if their is no decrements in the loss after 20 epochs.

Training a SAE consists of providing the input images and its corresponding binary ground-truth of the same size. According to the input size of the network, each image is cropped into several nonoverlapping chunks of size 256×256. Once SAE has been completely trained an image can be parsed through the network to obtain its binary version. The output chunks are then recombined to form the full image. This output is of the same size as the input image with restricted value in the range [0,1]. This is due to the use of sigmoid activation in the last layer of the network. After this step a global threshold is still required to obtain the binary values. The pixels whose selectional values are more than the global threshold are labeled as white otherwise as black. It has been shown that the choice of this global threshold does not impact the performance [START_REF] Calvo-Zaragoza | A selectional auto-encoder approach for document image binarization[END_REF].

We have used this implementation from [START_REF] Calvo-Zaragoza | A selectional auto-encoder approach for document image binarization[END_REF] which is available in GitHub1 .

EXPERIMENTS

In this section we describe our experiments and discuss the results that we obtained for some decoding methods presented in [START_REF] Diong | Document authentication using 2D codes: Maximizing the decoding performance using statistical inference[END_REF] and the decoding method using the SAE presented in Section 4.

Database description

In our database 2 , we have 100 random binary images with size of 100 × 100 dots with 48 -52% of black dots. The real size of printedand-scanned codes is 4 × 4 mm. We used a laser printer Xerox Phaser 6500 that has a true 600 dpi (dots per inch) resolution. The printing process was done dot per dot. For acquisition we used a high resolution scanner Epson Perfection V850 Pro with its highest resolution 9600 spi (samples per inch). The binary images were set in 600 ppi (pixels per inch), the grayscale images had size of 1600×1600 pixels after being printed and scanned with the defined resolutions. So one dot of the image is represented by a square of 16 × 16 pixels. We assume in this paper that the authority/authentication center and an opponent have the same printer and scanner. It is the worst case attack, as only the decoding can influence to authentication, but the physical process is the same. We divide our database into train and test bases. The train and validation database consists of 60 images, the test database consists of 40 images. Depending on the method, the number of samples used for training step changes, nevertheless, the number of test images will be kept the same all the time. We have varied the size of the training database from 60 images to 1 image. We used data augmentation by rotating the images to 90/180/270 degrees and by dividing each of them into four parts. That is why each image is represented by 13 images in the data augmentation setup. The sizes of train databases are presented in Table 2.

Estimation results

First of all, we implement and test the decoding methods proposed in [START_REF] Diong | Document authentication using 2D codes: Maximizing the decoding performance using statistical inference[END_REF]. The authors mentioned that the best results were obtained with features based on moments (F3 feature set) and with LDA (Linear Discriminant Analysis) classifier. That is why we tested our database only with LDA classifier, but we used all proposed feature vectors (F1-F5). The train base contains of 5 images (as in the reference paper), and we tested these decoding methods on 40 images of our test database. The results are illustrated in Table 1.

Decoding [START_REF] Diong | Document authentication using 2D codes: Maximizing the decoding performance using statistical inference[END_REF]. The training sets consist of 5 images.

We compare the 100 × 100 decoded CSGC with 100 × 100 digital codes and calculate the Bit Error Rate (BER) for each pair. According to our results the feature set F3 gives the best decoding results with mean BER equal to 14.70%. Then, we have tested the proposed decoding method based on autoencoders. To down-sample the parsed 1600 × 1600 binary output images obtained from our auto-encoders, we apply the majority vote strategy at each 16 × 16 module of the output binary image in order to consider it as black or a white pixel. The neural network methods are known to be efficient while the database is huge. Nevertheless, in this paper, we would like to find the minimal number of samples that can produce good estimation results. That is why we have tested our approach with 1 -60 images. In the same time, as our images are in high resolution, we obtain a quite big number of patches (see Table 2), that is enough to train our SAE. The results obtained using different size of trained database are presented in Table 3. We note that the better binarization results When we compare the results from Table 1 and Table 3, we note that the decoding with auto-encoder approach gives better results. We increase the decoding rate in average up to 91.25%. With classical thresholding the decoding rate is in average 65.35% and while using the decoding with feature set F3 and LDA, the decoding rate is in average 85.30%. That is why the use of neural network approaches can significantly increase the decoding rate of CSGC after P&S process.

Number of patches

Authentication test

In this section, we aim at study an impact of this estimation attack on the authentication test. The attack is as follows. An attacker scans the printed CSGC using the same scanner (as authentication center) and decodes the printed and scanned CSGC using either one of the tested classification methods (LDA with feature set F1 and F3) with 5 images in training base or an auto-encoder with 1 -60 images in training base. Then, s/he prints these counterfeited CSGC using the same printer. The authentication center verify the authenticity of CSGC by:

(1) decoding the printed CSGC using:

• classical thresholding with threshold th = 127,

• Otsu binarization method, (2) calculating the difference between the decoded CSGC and an original CSGC,

(3) comparing the obtained distance d with pre-calculated authentication threshold ϵ. We use the BER as authentication test as it is easy to implement and it can give us an idea about the efficiency of our attack and estimation accuracy as was explained in Section 2. The results of our decoding processes are presented in Table 4. We note that the best results are obtained for CSGC counterfeited using auto-encoder approach. The difference between the original and these counterfeited codes using thesholding and Otsu binarization for authentication is in average 3.05% and 2.78%, respectively. We plot the Receiver Operation Characteristics (ROC) curves for authentication using classical thresholding and Otsu's binarization in Fig. 4 and Fig. 5, respectively. By varying the authentication threshold ϵ, we compute the number of original (first print) and counterfeited (second print) codes that pass the authentication test. The percentage of accepted and rejected codes per attack are presented in Table 5. From this table we can conclude that if the opponent estimates the CSGC using classical thresholding, the counterfeited codes will not pass the authentication test. Let set the authentication threshold ϵ = 37.5. With this authentication threshold ϵ all 100% original codes pass the authentication test. With the classification strategy using LDA with F3 feature set 5% of counterfeited codes can pass this authentication test. The results using auto-encoder approach are better: while using 60 images with data augmentation, 55% of codes can pass the authentication test. While using 1 images with data augmentation, 62.5% of codes can pass the authentication test with the same authentication threshold ϵ. We suppose that it is due to global binarization using the same threshold which is not adapted to this kind of images. For authentication decoding using Otsu binarization, we have slightly different results as this binarizatoion threshold is adapted for each image.. The number of accepted and rejected codes per attack are presented in Table 5. If we chose the authentication threshold equal to ϵ = 28.5, all 100% of original codes can pass the authentication test, but also 17.5% of counterfeited codes using auto-encoder approach while using 60 images with data augmentation for training pass the authentication test. In comparison, there is no any image counterfeited using Otsu binarization or classification strategy using LDA with F3 feature set which can pass the authentication test with this ϵ. The obtained results show us that the use of decoding techniques based on auto-encoders can help an attacker to create the counterfeited CSGC that will fool the authentication test. 5: The percentage of accepted (A) and rejected (R) codes depending on authentication threshold ϵ for authentication using classical thresholding with th = 127 and using Otsu's binarization [START_REF] Diong | Document authentication using 2D codes: Maximizing the decoding performance using statistical inference[END_REF]

Printed

CONCLUSIONS

In this paper we achieve a more efficient estimation attack using a supervised approach based on neural networks, here an autoencoder. We obtain high decoding results while using quite small database (especially for neural network approaches). By training our neural network with 60 images of printed-and-scanned copy sensitive graphical code we obtain less then 10% as bit error rate. In future, we want to propose smarter authentication test and to test the proposed attacks with this smart authentication. The more realistic attacks need to be studied also. For example, the case when an attacker do not have the same printer-scanner as the authority center. In this case, an attacker needs to predict an impact of authentic P&S process.

Figure 1 :

 1 Figure 1: Considered authentication system using CSGC.

Figure 2 :

 2 Figure 2: Example of a) an original numeric CSGC before printing (I ) and b) its degraded version by P&S version ( Ĩ ).

Figure 3 :

 3 Figure 3: Binarization of CSGC using SAE architecture.

Figure 4 :

 4 Figure 4: ROC curve for LDA with F3 characteristics vector and all auto-encoder decoding for authentication test that use th = 127 for CSGC decoding.

Figure 5 :

 5 Figure 5: ROC curve for LDA with F3 characteristics vector and all auto-encoder decoding for authentication test that uses Otsu binarization for CSGC decoding.

Table 1 :

 1 Mean Bit Error Rate comparison for feature sets from

		method	BER	Std	Best case Worst case
		F1	17.14% 0.92%	15.57%	18.86%
		F2	16.72% 0.97%	14.75%	18.64%
	LDA	F3	14.70% 0.82% 12.97%	16.60%
		F4	16.07% 0.99%	14.31%	17.78%
		F5	16.72% 0.97%	14.75%	18.64%

Table 2 :

 2 Sizes of trained data sets.are obtained when we have bigger training database. The BER is 8.75%, when we use 60 images with data augmentation for training. Nevertheless, the binarization results obtained using 1 image with data augmentation are close to the results obtained using 5 images with data augmentation. The BER is 13.38%, when we use 1 image with data augmentation for training, and it is 12.41%, when we use 5 images with data augmentation for training. That means that the high decoding results can be obtained even with one CSGC image in training data base.

	Nb of images used Train database Train Validation
	60 im w/augm.	780 images	14410	50
	60 im	60 images	2890	50
	5 im w/augm.	65 images	1205	98
	5 im	5 images	245	98
	1 im w/augm.	13 images	241	98
	Nb of images used	BER	Std	Best case Worst case
	60 im w/augm.	8.75% 0.67%	7.49%	10.96%
	60 im	9.86% 0.87%	8.32%	12.25%
	5 im w/augm.	12.41% 0.99%	10.34%	14.70%
	5 im	12.91% 0.95	11.23%	15.03%
	1 im w/augm.	13.38% 0.93%	11.52%	15.57%

Table 3 :

 3 Mean Bit Error Rate comparison for auto-encoder binarization with different size of train base.

Table 4 :

 4 Mean Bit Error Rate obtained while applying a classical thresholding with th = 127 and an Otsu's binarization for authentication test.

https://github.com/ajgallego/document-image-binarization

The constructed database is publicly available: www.univ-st-etienne.fr/ graphical-code-estimation.