FR3131407A1 - Method for characterizing the movement of mobile entities and associated computer program product - Google Patents

Abstract

Method for characterizing the movement of mobile entities and associated computer program product The present invention relates to a method (100) for characterizing the movement of mobile entities, such as pedestrians, over areas of an environment. The method (100) comprises a learning phase (110) comprising the reception (121), (122) of an adjacency matrix and of a database comprising, for several successive instants, pairs of data. The learning phase further includes training a model as a function of the database and the adjacency matrix, the model providing, from a number of entity(ies) in each zone, a respective set of parameter(s) characterizing the movement of the entities in the environment. The method further comprises an exploitation phase (120) comprising the reception (131), for each zone, of a number of mobile entity(ies), and the application (134), to the number of mobile entity(ies) received for each zone, from the model trained to obtain a respective set of parameter(s) characterizing the movement of the mobile entities and associated with said numbers of mobile entity(ies). Figure for the abstract: Figure 3

Description

Method for characterizing the movement of mobile entities and associated computer program product

The present invention relates to a method for characterizing the movement of mobile entities in an environment.

The present invention also relates to a computer program product comprising software instructions capable of implementing such a characterization process.

The present invention relates to the field of movement of mobile entities in a predetermined environment.

By “mobile entities” we mean things, or beings, capable of moving in the environment. For example, mobile entities are pedestrians, cyclists, motorcyclists, car drivers, robots, drones, or even animals.

By “environment” we mean a space, for example predefined, in which mobile entities are able to move. For example, the environment is a station hall, an airport, a metro hall, a parking lot, or a forest.

In the field of characterizing the movement of mobile entities in an environment, it is known to use a simulator to predict a scenario of the evolution of the movements of mobile entities in the environment. To carry out such a simulation of the movement of mobile entities in the environment, it is nevertheless necessary to calibrate the simulator so that the predicted scenario is as realistic as possible. The calibration of the simulator is, for example, carried out using a set of parameters characterizing the movement of mobile entities in the environment.

Determining this set of parameters is particularly complex since these parameters generally vary over time and depending on the situation. Furthermore, if the set of parameters is not well defined, the scenario predicted by the simulator is unrealistic. In such a case, the predicted scenario is unusable.

We know from the article “ Density-based evolutionary framework for crowd model calibration” by J. Zhong, N. Hu, W. Cai, M. Lees, and LB Luo a method for determining a set of calibration parameters d a simulator and the use of the simulator to characterize the movement of mobile entities. The method in said article uses evolutionary algorithms in an approach to optimizing the coefficients of a model to approximate the real behavior of a crowd.

However, this method requires knowledge of a prior model capable of providing an acceptable set of parameters. In addition, this method requires a significant number of simulations, by the simulator, to converge the evolutionary algorithms towards a satisfactory solution making it possible to subsequently generate a good set of calibration parameters.

Thus, the method of art is sometimes too complex and/or too slow to use.

There is therefore a need to simplify and make faster the characterization of the movement of mobile entities in the environment.

For this, the invention proposes a method for characterizing the movement of mobile entities in an environment, simpler and quicker to operate.

For this purpose, the invention relates to a method of characterization for the movement of mobile entities, such as pedestrians, over areas of an environment, the method comprising a learning phase comprising the following steps implemented by a computer:

- reception of an adjacency matrix indicating the possible movements between two adjacent zones,

- reception of a database comprising, for each of a plurality of successive instants, a pair of data, each pair of data comprising a number of mobile entity(ies) in each zone and a set of parameter(s) characterizing the movement of mobile entities in the environment,

- training a model according to the database and the adjacency matrix, the model being configured to provide, from a number of mobile entity(ies) in each zone, a game respective parameter(s) characterizing the movement of mobile entities in the environment,

the method further comprising an exploitation phase comprising the following steps:

- reception, for each zone, of a number of mobile entity(ies), and

- application, to the number of mobile entity(ies) received for each zone, of the trained model to obtain a respective set of parameter(s) characterizing the movement of the mobile entities in the environment and associated with said entity numbers mobile(s).

According to particular embodiments, the method comprises one or more of the following characteristics, taken in isolation or in all technically possible combinations:

- the process further comprises, during the exploitation phase, the following steps:

- detection of an anomaly in the set of parameter(s) obtained, and

- if the anomaly is detected in the parameter set(s), implementation of a corrective action in the environment;

- the method comprises, during the exploitation phase, a step of predicting the movements of the mobile entities in the environment, from the set of parameter(s) obtained, to obtain a predicted scenario;

- the method further comprises, following the prediction step, the following steps:

- detection of an anomaly predicted from the predicted scenario, and

- if the predicted anomaly is detected, implementation of a corrective action in the environment;

- during the exploitation phase, the reception stage includes the following sub-stages:

- obtaining information on mobile entities in the environment from at least one sensor, and

- for each zone, determination of the number of mobile entity(ies) in the zone by processing the information obtained;

- the training stage includes the following sub-stages:

- for each zone, calculation, over a sliding time window of successive instants, of an average number of mobile entity(ies) in the zone,

- calculation of at least one set of averaged parameter(s), over the sliding time window, from the set of parameter(s) characterizing the movement of the mobile entities in the environment,

- application, to the model, of a supervised learning algorithm based on the average number of mobile entity(ies) in each zone, at least one set of averaged parameter(s) and of the adjacency matrix;

- the method further comprises, between the sub-step of calculating at least one set of averaged parameter(s) and the application sub-step, a sub-step of normalizing the average number of entities (s) mobile(s) of each zone to obtain a normalized vector of number of mobile entity(ies) of which an algebraic norm is preferably equal to one,

during the application step, the learning algorithm is applied to the model from the normalized vector, the at least one set of averaged parameter(s) and the adjacency matrix;

- the respective set of parameter(s) obtained during the exploitation phase comprises at least one parameter chosen from a group consisting of:

- an average speed of mobile entities in the environment,

- a maximum throughput of mobile entities at one or more points in the environment,

- an average flow of mobile entities at one or more points in the environment,

- a frequency of arrival near the environment, of transport vehicles,

- for at least a first and a second point in the environment, a proportion of the pedestrians at the second point who have previously passed through the first point, and

- for at least a first point in the environment, a second point in the environment and at least one path between the first and second points, a proportion of pedestrians taking said path among the pedestrians going from the first to the second point;

- The zones are numbered,

the adjacency matrix comprising a plurality of rows, a plurality of columns, and a coefficient for each row and each column,

each coefficient being equal to a predefined value if a movement is possible from the zone whose number is equal to the column of the coefficient, towards the zone whose number is equal to the row of the coefficient;

The present invention also relates to a computer program product comprising software instructions which, when executed by a computer, implement such a characterization method.

Other characteristics and advantages of the invention will appear on reading the following description of embodiments of the invention, given by way of example only and with reference to the appended drawings in which:

, there is a schematic view of an environment in which mobile entities are able to move,

, there is a schematic view of a calculator suitable for implementing a characterization method according to the invention, and

, there is a flowchart of the characterization process implemented by the computer of the .

In reference to the , we describe an environment 10 comprising a plurality of zones Z _i in which mobile entities, such as pedestrians, are likely to move.

In the remainder of the description, the mobile entities will be considered to be pedestrians without loss of generality. The elements described below are in fact applicable to other mobile entities such as cyclists, motorcyclists, car drivers, robots, drones, or even animals.

For example, environment 10 is a train station hall or a metro station.

In the example illustrated on the , environment 10 includes thirteen zones respectively named Z ₁ to Z ₁₃ . The movement of pedestrians in zones Z _i is, for example, free. In other words, pedestrians are capable of moving from any first zone Z _i to each second adjacent zone Z _j .

For example, on the , zones Z ₁ , Z ₃ , Z ₇ correspond to entrances to environment 10. In this same example, zones Z ₅ and Z ₆ correspond to train or metro platforms through which pedestrians are obliged to pass to enter the train or metro. It is clear that areas of congestion are likely to appear.

The environment 10 further comprises at least one sensor capable of obtaining information on pedestrians in the environment 10, and preferably in the zones Z _i . Optionally, the at least one sensor comprises a plurality of cameras, each pointed towards one or more zones Z _i and capable of obtaining images of pedestrians in said zone(s) Z _i .

On the , a calculator 20 is shown.

The calculator 20 is preferably a computer.

More generally, the calculator 20 is an electronic calculator capable of manipulating and/or transforming data represented as electronic or physical quantities in registers of the calculator 20 and/or memories, into other similar data corresponding to physical data in memories, registers or other types of display, transmission or storage devices.

As shown on the , the computer 20 comprises a display unit 22 and a data processing unit 24.

The display unit 22 is for example a computer monitor connected to the processing unit 24. The display unit 22 is capable of displaying, to a user, information from the unit treatment 24.

The processing unit 24 is connected to the display unit 22 and comprises a processor 26 and a memory 28. The processing unit 24 is for example connected to the sensor(s) described above. The memory 28 preferentially stores a computer program product 30 comprising software instructions which, when executed by the processor 26, implement a method 100 for characterizing the movement of pedestrians in the environment 10.

Alternatively, the computer program product is stored on an unrepresented information medium. The information medium is a medium readable by the computer 20, usually by the processing unit 24. The readable information medium is a medium adapted to memorizing electronic instructions and capable of being coupled to a bus of a computer system.

For example, the information medium is a floppy disk or a flexible disk (of the English name " floppy dis c " ), an optical disk, a CD-ROM, a magneto-optical disk, a ROM memory, a RAM memory, EPROM memory, EEPROM memory, magnetic card, optical card or USB key.

The operation of the computer 20 will now be described with reference to the representing a flowchart of different phases of the method 100 for characterizing pedestrian movement.

The method 100 comprises a learning phase 110 and an operating phase 120.

The learning phase 110 is for example implemented prior to implementation of the operating phase 120 in environment 10.

The learning phase 110 aims to carry out machine learning (from English machine learning ) of a model from so-called labeled data which are pairs of data comprising each of the input data of the model and the data corresponding outputs. The aim of learning is therefore to modify the model so that when it receives the input data of a pair of data, it provides the associated output data in the labeled data.

The learning phase 110 includes a first step 121 of receiving an adjacency matrix A indicating the possible movements between two adjacent zones. In the aforementioned example in which movement between the zones is free, the adjacency matrix A indicates for each zone Z _i the other zones Z _j which are adjacent to it, that is to say contiguous. Preferably, the zones Z _i are numbered and the adjacency matrix A is a square matrix comprising, for each zone Z _{i ,} a row and a column. In this example, for each row i and for each column j, the adjacency matrix A includes a coefficient A _{i , j} equal to one if the zones Z _i and Z _j are adjacent, or equal to zero if the zones Z _i and Z _j are not adjacent.

In environment 10 shown on the , the adjacency matrix A is as follows:

We note that the adjacency matrix A is then a symmetric matrix since, if a first zone Z _i is adjacent to a second zone Z _j , then the second zone Z _j is also adjacent to the first zone Z _i .

According to an alternative embodiment, movements between the zones are constrained. In other words, from at least one zone Z _i , pedestrians are able to move towards only part of the zones Z _j adjacent to said zone Z _i .

Such a case is for example observable if environment 10 is an airport. It is in fact no longer possible to go back after passing through customs.

Thus, the adjacency matrix A is not symmetric. In the aforementioned example, the coefficient A_{i , j} corresponding to the passage of a first zone Z_ilocated before customs, towards a second zone Z_jlocated after customs, is equal to one. In this same example, the coefficient A_{j , i} corresponding to the reverse passage is equal to zero.

Then, the learning phase 110 includes a second step 122 of receiving a database. The database includes, for each of a plurality of successive moments, T_k a pair of data. Each pair of data includes on the one hand a number of pedestrian(s) in each zone Z_i, and on the other hand a set of parameters characterizing the movement of pedestrians in environment 10. The numbers of pedestrian(s) in each zone are for example grouped in the form of a vector. Analogously, the set of parameters forms, for example, a vector.

The set of parameters includes for example one or more parameters chosen from a group consisting of:

• an average speed of movement of pedestrians in environment 10,
• a maximum flow of pedestrians at one or more points in the environment 10,
• an average flow of pedestrians at one or more points in the environment 10,
• a frequency of arrival near environment 10, of transport vehicle(s), and
• for at least a first and a second point in the environment, a proportion of the pedestrians at the second point who have previously passed through the first point, and
• for at least a first point in the environment, a second point in the environment and at least one path between the first and second points, a proportion of pedestrians taking said path among the pedestrians going from the first to the second point.

Then, the learning phase 110 includes a step 123 of training a model according to the database and the adjacency matrix A. The model is configured to provide, from a number of pedestrians (s) in each zone Z _i , a respective set of parameters characterizing the movement of pedestrians in environment 10.

The model is for example a neural network. According to this example, the neural network comprises an input layer comprising a neuron for each zone Z _i of the environment 10, one or more hidden layers comprising a plurality of neurons each, and an output layer comprising a neuron for each parameter from the parameter set. Additionally, the neural network includes connections from each neuron in one layer to a neuron in a subsequent layer and, for each connection, an adjustable weight.

In particular, the model is preferably a graph neural network ( Graph Neural Network ) or a graph convolutional network ( Graph Convolutional Network ). Such networks include a plurality of hidden layers each comprising as many neurons as the input layer. In addition, these networks are capable of receiving the adjacency matrix A and of only including connections for possible movements according to the adjacency matrix A. In other words, with these networks, a connection between a first neuron n _i of a hidden layer and a second neuron n _j of the next hidden layer, only exists on the condition that a movement between a first respective zone Z _i and the second respective zone Z _j is possible, according to the matrix d adjacency A. Thus, the GNN and GCN networks include a lower number of connections than a classic deep neural network, and consequently fewer adjustable weights, thus making it possible to accelerate the learning of the neural network and to stabilize neural network learning.

The training step 123 optionally includes a first sub-step 124 of calculating, for each zone Z _i , an average number of pedestrian(s) in the zone Z _i . For this purpose, during the first calculation sub-step 124, for each zone Z _i , the average number of pedestrian(s) is for example calculated over a sliding time window. The sliding window includes for example a predefined number N of successive instants T _k . The sliding window is applied to the numbers of pedestrian(s) of the data pairs in the database. The predefined number N of successive instants T _k is for example equal to five, ten, fifteen, or twenty.

For example, for each zone Z _i , a first average number is calculated by averaging the numbers of pedestrian(s) in said zone Z _i , for each of the first N instants (T _k ) _{k = 1,… ,N} of the database. Then, for each zone Z _i , a second average number is calculated by averaging the numbers of pedestrian(s) in said zone Z _i , for N successive instants (T _i ) _{i= 2,… , N+1} between the second instant T ₂ and the N+1-th instant T _N+1 of the database. Then, for each zone Z _i , the calculation is preferably iterated until the sliding window reaches the last instant T _D for which the database includes a pair of data.

We then understand that for any instant T _k and for each zone Z _i , the number of pedestrian(s) in the zone Z _i contributes to N averaged numbers of pedestrian(s) in said zone Z _i .

Analogously, the training step 123 comprises a second calculation sub-step 125 of at least one set of parameters averaged over the sliding time window. The calculation of the or each set of averaged parameters is analogous to that of the average number of pedestrian(s) in each zone Z _i .

Preferably, the same sliding time windows are applied for calculating the average number of pedestrian(s) in each zone Z_iduring the first calculation sub-step 124 and for calculating the sets of average parameters during the second calculation sub-step 125.

Optionally, the first 124 and second 125 calculation sub-steps are carried out simultaneously by the processing unit 24.

The training step 123 advantageously comprises a sub-step 126 of normalizing the average number of pedestrian(s) in each zone Z _i , to obtain a normalized vector of which an algebraic norm is preferably equal to one. The normalization substep 126 is also called the standardization substep.

The algebraic norm of a vector including components is for example defined by the following equation:

Or is the transposed operator,

is the square root function,

is the i-th component of the vector .

To this end, for each sliding window, the average numbers of pedestrian(s) are for example grouped into an average vector . The average vector is then normalized, to obtain a normalized vector for example according to the following equation:

The training step optionally further comprises a sub-step 127 of application, to the model, of a supervised learning algorithm from the or each normalized vector VN, the or each set of averaged parameters and the adjacency matrix A.

The supervised learning algorithm is for example a stochastic gradient descent algorithm.

During the application substep 127, the supervised learning algorithm modifies the weights of the model so that, when a normalized vector VN is provided as input to the model, the model provides a set of parameters at its output as close as possible to the set of averaged parameters corresponding to said normalized vector VN. The adjacency matrix A makes it possible to limit the number of weights to be modified by the supervised learning algorithm.

After the training step 123, the model is said to be trained and the learning phase 110 ends.

The operating phase 120 is for example implemented following the learning phase 110, or several hours, days, or months after the learning phase 110.

The operating phase 120 includes a third reception step 131 during which, for each zone Z _i , a number of pedestrian(s) in the zone Z _i is received.

Optionally, the third reception step 131 includes a sub-step 132 for obtaining information(s) from the at least one sensor present in the environment 10.

When the at least one sensor includes cameras, during the obtaining substep 132, the images captured by the cameras are obtained by the processing unit 24.

Then, the third reception step 131 optionally comprises a sub-step 133 of determining a number of pedestrian(s) in each zone Z _i by processing the information obtained during the obtaining sub-step 132.

When the information is images, the determination of the number of pedestrian(s) in each zone Z _i is for example carried out by application of an image processing algorithm known per se. Such an algorithm is based, for example, on artificial intelligence tools such as models from machine learning. The images are then VCA data (from English, Video Content Analysis ).

Then the operating phase 120 includes a step 134 of application, to the number of pedestrian(s) received for each zone Z _i , of the model trained during the learning phase 110, to obtain a respective set of parameters characterizing the movement of pedestrians in the environment 10.

The set of parameters obtained during application step 134 then depends on the numbers of pedestrian(s) received.

Optionally, the operating phase 120 includes a first step 135 of detecting an anomaly in the set of parameters. The anomaly is, for example, the fact that one of the parameters in the parameter set exceeds a predefined threshold.

For example, when the set of parameters includes the average speed of pedestrians in environment 10, if the average speed is greater than a first predefined value such as 10 km/h, then an anomaly is detected indicating that the pedestrians are running instead of to walk. Such an anomaly is, for example, characteristic of an abnormal crowd movement.

In the same example, if the average speed is less than a second predefined value such as 2 km/h, then an anomaly is detected indicating an overall congestion of the environment 10 preventing the peaceful movement of pedestrians.

According to another example, when the set of parameters includes the maximum flow of pedestrians at a point in the environment 10, if this flow is less than a third predefined value such as 100 pedestrians per minute, then an anomaly is detected indicating that an element blocks the aforementioned point of environment 10.

According to yet another example, when the set of parameters includes the frequency of arrival near the environment 10 of transport vehicles, if this frequency is less than a fourth predefined value, then an anomaly is detected indicating a problem of circulation of transport vehicles. Such a problem is, for example, likely to create congestion in environment 10 because pedestrians risk not being extracted from environment 10 quickly enough by transport vehicles.

It is clear that the predefined threshold(s) are likely to change over time, and in particular over the course of the day or the year.

Optionally, the operating phase 120 includes, if an anomaly is detected during the first determination step 135, a first step 136 of implementing a corrective action in the environment 10.

The corrective action is for example, an opening of a new zone Z _i in environment 10, an extension of an already existing zone Z _i or an opening of a passage between two zones Z _i not yet adjacent.

The first implementation step 136 includes, for example, the emission of an alert to an operator, via the display unit 22. The operator is then able to implement one of the actions of aforementioned correction.

Alternatively, the first implementation step 136 comprises for example sending an actuation command in environment 10 to perform one of the aforementioned corrective actions, autonomously.

As a variant or optional addition, following the application step 134, the operation phase 120 includes a step 137 of predicting the movement of pedestrians in the environment 10. The prediction step 137 includes, for example, simulation of the movement of pedestrians in the environment 10, by a simulator included in the memory 28 of the processing unit 24, from the set of parameters obtained by application of the trained model to the number of pedestrian(s) in each zone Z _i .

We then understand that the parameters of the set of parameters are input quantities of the simulator making it possible to predict, as faithfully as possible, the evolution of the movement of pedestrians in environment 10. In other words, these parameters are calibration parameters of the simulator.

During prediction step 137, a predicted scenario is determined. The predicted scenario describes the evolution of pedestrian movement in environment 10 over a predefined duration.

The predefined duration is for example equal to five minutes, ten minutes, thirty minutes, one hour, two hours, or five hours.

It is clear that the longer the predefined duration, the less realistic the predicted scenario. Indeed, after a long period of time, the situation in environment 10 has evolved such that the parameters of the parameter set have become obsolete.

The predicted scenario includes an evolution of quantities simulated by the simulator.

The simulated quantities are for example the position of each pedestrian in environment 10, or the density of pedestrians in each zone Z _i

Following the prediction step 137, the exploitation phase 120 advantageously comprises a second step 138 of detecting a predicted anomaly from the predicted scenario.

The second detection step 138 is analogous to the first detection step 135 with the exception that the predicted anomaly is detected in the simulated quantities rather than in the parameters of the parameter set.

If a predicted anomaly is detected during the second detection step 138, then the exploitation phase 120 advantageously comprises a second implementation step 139 similar to the first implementation step 136.

During the second implementation step 139, the corrective action is implemented in the environment 10 in a preventive manner. In other words, the corrective action(s) implemented during the second implementation step 139 are intended to prevent the predicted anomaly(s) detected from occurring in the environment 10.

Then, the operating phase 120 is for example repeated with the reception 131 of new numbers of pedestrian(s) in the zones Z _i .

Thus, the method according to the invention makes it possible to characterize the movement of pedestrians in environment 10 in a simple and realistic manner.

With the first 124 and second 125 optional calculation sub-steps, temporal dynamics of pedestrians are taken into account. In other words, taking into account several pairs of data for each input of the model learning makes it possible to account for a temporal evolution of pedestrian movement.

With the optional normalization step 126, or standardization, learning is accelerated since all the vectors used for training the model are comparable.

With the optional training sub-step 127 taking into account the adjacency matrix A, the learning of the model is accelerated. In addition, for a fixed number of data pairs, learning the model from the adjacency matrix A is of better quality than without the use of the adjacency matrix A.

In addition, the use of the adjacency matrix A makes it possible to account for the spatiality of environment 10 and takes advantage of the knowledge of the distribution of zones Z _i in environment 10.

The optional sub-steps of obtaining 132 and determining 133 make it possible to receive the number of pedestrian(s) in each zone Z _i in a simple and substantially inexpensive manner.

The optional prediction step 137 in combination with the application step 134 makes it possible to faithfully report an evolution of the movement of pedestrians in environment 10 and therefore to predict potential future anomalies.

The optional detection steps 135, 138 and implementation 136, 139 ensure the proper movement of pedestrians in environment 10.

Claims (9)

Method (100) for characterizing the movement of mobile entities, such as pedestrians, in zones (Z_i) of an environment (10), the method (100) comprising a learning phase (110) comprising the following steps implemented by a computer (20):

• reception (121) of an adjacency matrix (A) indicating the possible movements between two adjacent zones (Z _i ),
• reception (122) of a database comprising, for each of a plurality of successive instants (T _k ), a pair of data, each pair of data comprising a number of mobile entity(ies) in each zone (Z _i ) and a set of parameter(s) characterizing the movement of the mobile entities in the environment (10),
• training of a model according to the database and the adjacency matrix (A), the model being configured to provide, from a number of mobile entity(ies) in each zone ( Z _i ), a respective set of parameter(s) characterizing the movement of the mobile entities in the environment (10),

the method further comprising an exploitation phase (120) comprising the following steps:

• reception (131), for each zone (Z _i ), of a number of mobile entity(ies), and
• application (134), to the number of mobile entity(ies) received for each zone (Z _i ), of the model trained to obtain a respective set of parameter(s) characterizing the movement of the mobile entities in the environment ( 10) and associated with said numbers of mobile entity(ies),

during the exploitation phase (120), the reception step (131) comprises the following sub-steps:

• obtaining information about mobile entities in the environment (10) from at least one sensor, and
• for each zone (Z _i ), determination of the number of mobile entity(ies) in the zone (Z _i ) by processing the information obtained.

. Method (100) according to claim 1, wherein the method further comprises, during the operating phase (120), the following steps:

• detection (135) of an anomaly in the set of parameter(s) obtained, and
• if the anomaly is detected in the set of parameters, implementation (136) of a corrective action in the environment (10).

Method (100) according to claim 1 or 2, further comprising, during the exploitation phase (120), a step (137) of predicting the movements of the mobile entities in the environment (10), from the game of parameter(s) obtained, to obtain a predicted scenario. Method (100) according to claim 3, further comprising, following the prediction step (137), the following steps:

• detection (138) of an anomaly predicted from the predicted scenario, and
• if the predicted anomaly is detected, implementation (139) of a corrective action in the environment (10).

Method (100) according to any one of the preceding claims, in which the training step (123) comprises the following substeps:

• for each zone (Z _i ), calculation (124), over a sliding time window of successive instants (T _k ), of an average number of mobile entity(ies) of the zone (Z _i ),
• calculation (125) of at least one set of averaged parameter(s), over the sliding time window, from the set of parameter(s) characterizing the movement of the mobile entities in the environment (10),
• application (127), to the model, of a supervised learning algorithm based on the average number of mobile entity(ies) in each zone (Z _i ), of the at least one set of parameter(s) ) averaged(s) and the adjacency matrix (A).

Method (100) according to the preceding claim, further comprising, between the calculation sub-step (125) of at least one set of averaged parameter(s) and the application sub-step (127), a sub-step (126) of normalizing the average number of mobile entity(ies) of each zone (Z _i ) to obtain a normalized vector ( ) number of mobile entity(ies) for which an algebraic norm is preferably equal to one,
during the application step (127), the learning algorithm is applied to the model from the normalized vector ( ), the at least one set of averaged parameter(s) and the adjacency matrix (A). Method (100) according to any one of the preceding claims, in which the respective set of parameter(s) obtained during the exploitation phase (120) comprises at least one parameter chosen from a group consisting of:

• an average speed of the mobile entities in the environment (10),
• a maximum flow rate of mobile entities at one or more points in the environment (10),
• an average flow rate of mobile entities at one or more points in the environment (10),
• a frequency of arrival near the environment (10), of transport vehicles,
• for at least a first and a second point in the environment, a proportion of the pedestrians at the second point who have previously passed through the first point, and
• for at least a first point in the environment, a second point in the environment and at least one path between the first and second points, a proportion of pedestrians taking said path among the pedestrians going from the first to the second point.

Method (100) according to any one of the preceding claims, in which the zones (Z _i ) are numbered,
the adjacency matrix (A) comprising a plurality of rows, a plurality of columns, and a coefficient (A _i,j ) for each row and each column,
each coefficient (A _i,j ) being equal to a predefined value if movement is possible from the zone (Z _j ) whose number is equal to the column of the coefficient (A _i,j ), towards the zone (Z _i ) whose number is equal to the coefficient line (A _i,j ). Computer program product comprising software instructions which, when executed by a computer, implement the characterization method (100) according to any one of claims 1 to 8.