METHOD FOR PREDICTING A DENTAL SITUATION

Abstract

The invention relates to a method for predicting a future dental situation for a "current" patient, comprising the following steps: 1) acquisition of historical data relating to historical dental situations, each experienced, at a historical time, by a historical patient, the historical data relating to a historical dental situation comprising at least: said historical time; values ​​of tooth positioning parameters of said historical patient; 2) acquisition, at a "current" time, of data relating to a current dental situation experienced by said current patient, the set of data relating to said current dental situation, referred to as "current data", comprising at least: said current time; values ​​of tooth positioning parameters of said current patient;3) Statistical analysis of said historical and current data, so as to predict, at least at some future time, at least one future dental situation for the current patient; 4) Based on said future dental situation, evaluation of the benefit of orthodontic treatment. Abbreviated figure: no abbreviated figure;

Description

METHOD FOR PREDICTING A DENTAL SITUATION Technical Field The present invention relates to a method for predicting a dental situation and a method for determining, based on said prediction, an orthodontic device intended to correct a malposition of a patient's teeth. State of the art Typically, at the beginning of orthodontic treatment, the orthodontist determines the desired tooth position at the end of treatment, known as the "final setup." The final setup can be defined using an impression or a three-dimensional scan of the patient's teeth. The orthodontist then fabricates an orthodontic appliance adapted to this treatment. The orthodontic appliance is typically a bracket-type appliance with a metal archwire attached to the teeth. Alternatively, the orthodontic appliance can be a aligner. An orthodontic aligner typically comes in the form of a removable, one-piece appliance, usually made of a transparent polymer material, which has a channel shaped to accommodate several teeth of an arch, generally all the teeth of an arch. The shape of the channel is adapted to hold the aligner in position on the teeth, while simultaneously correcting the position of certain teeth. Treatment using aligners is advantageously less burdensome for the patient. In particular, the number of appointments with the orthodontist is limited. Furthermore, the pain is less than with a metal orthodontic wire attached to the teeth. The market for orthodontic aligners is therefore growing. In the case of orthodontic treatment using aligners, the shapes of the different aligners at various stages of treatment are typically determined at the beginning of the process. The desired tooth positioning at each of these stages is called the "intermediate setup." The orthodontist then has all the corresponding aligners made. Typically, there are around twenty aligners. At predetermined intervals, the patient changes aligners. Regardless of the orthodontic appliance used, the patient visits the orthodontist at regular intervals for a visual check-up. Depending on their diagnosis, the orthodontist may modify the orthodontic appliance. For example, if the orthodontic appliance consists of a metal archwire attached to the teeth, the orthodontist can adjust the tension exerted by the archwire. If necessary, they can also have a new, better-fitting orthodontic appliance made. In the case where the orthodontic appliance is a aligner, the orthodontist can take a new impression of the teeth, or, equivalently, a new three-dimensional scan of the teeth, and then order a new series of aligners. It is considered that on average, the number of aligners ultimately manufactured is around 45, instead of the 20 aligners classically planned at the beginning of treatment. The need to travel to the orthodontist for a check-up is a burden for the patient. The increased frequency of check-ups can also erode the patient's trust in their orthodontist. Finally, it results in an additional cost. Therefore, there is a need to limit the number of checkups at the orthodontist's office. Furthermore, there is a constant need to accelerate orthodontic treatments. Furthermore, apart from any orthodontic treatment, there is a need to better anticipate the evolution of the position of patients' teeth, particularly during the growth of children's teeth or the aging of the elderly. In the latter, aging leads in particular to a forward movement of the teeth. One object of the invention is to meet, at least partially, these needs. Summary of the invention The invention proposes a method for predicting a future dental situation for a patient, referred to as the "current patient," in particular for a current patient wearing orthodontic appliances, referred to as the "current orthodontic appliance," intended to correct a malposition of their teeth, said prediction method comprising the following steps: 1) acquisition of data, referred to as "historical data," relating to past dental situations, referred to as "historical dental situations," each experienced at a specific moment, referred to as the "historical moment," by a patient, referred to as the "historical patient," the historical patient possibly being undergoing orthodontic treatment, referred to as the "historical orthodontic treatment," during which they are fitted with orthodontic appliances, referred to as the "historical orthodontic appliance,"The complete set of historical data relating to a historical dental situation, comprising at least: - said historical moment; - values ​​of context parameters at said historical moment, the context parameters comprising: - preferably, if the historical patient has a historical orthodontic appliance, - parameters of said historical orthodontic appliance, in particular relating to the class and / or conformation of the historical orthodontic appliance; - preferably, parameters on the environment of the historical orthodontic treatment to which the historical dental situation belongs, such as a pain coefficient and / or a cost and / or a duration and / or a number of appointments with the orthodontist and / or a probability of success associated with said historical orthodontic treatment; - parameters of tooth positioning of said historical patient; - preferably other anatomical parameters besides tooth positioning parameters.such as the arrangement and / or structure of bone tissue (particularly of the jaws) and / or alveolus tissue and / or soft tissue (particularly the gums and / or frenula and / or tongue and / or cheeks) of the historical patient; - preferably, functional parameters of the historical patient, in particular neurofunctional parameters, such as ease of breathing, swallowing, or closing the mouth; - preferably, the age and / or sex and / or an identifier of said historical patient; 2) acquisition, at a given time, referred to as the "current time," of data relating to a dental situation experienced by said current patient, referred to as the "current dental situation," the set of data relating to said current dental situation, referred to as "current data," comprising at least: - preferably, said current time; - values ​​of context parameters at said current time, the context parameters comprising: - preferably,If the current patient has a current orthodontic appliance: - parameters of said current orthodontic appliance, in particular relating to the class and / or conformation of the current orthodontic appliance; - preferably, parameters on the environment of the current orthodontic treatment to which the current dental situation belongs, referred to as "current orthodontic treatment", such as a pain coefficient and / or cost and / or duration and / or number of appointments with the orthodontist and / or probability of success associated with said current orthodontic treatment; - tooth positioning parameters of said current patient; - preferably other anatomical parameters besides tooth positioning parameters, such as the arrangement and / or structure of bone tissue (particularly of the jaws) and / or alveolus tissue and / or soft tissue (particularly the gums and / or frenula and / or tongue and / or cheeks) of the current patient; - preferably,Functional parameters of the current patient, in particular neurofunctional parameters such as ease of breathing, swallowing, or closing the mouth; preferably, the age and / or sex and / or an identifier of said current patient; 3) statistical analysis of said historical and current data, so as to predict, at least at one future time, at least one future dental situation for the current patient; 4) based on said future dental situation, assessment of the benefit of orthodontic treatment for the current patient or, if the current patient has current orthodontic appliances, reassessment of the current orthodontic treatment, preferably by an orthodontist, and, based on said reassessment, possible modification of the current patient's orthodontic treatment, for example, modification or change of the current orthodontic appliance and / or modification of an appointment schedule with an orthodontist. The ability to predict future dental situations constitutes a considerable advantage compared to the situation prior to the invention. In general, it is becoming possible to predict the evolution of tooth position, whether or not orthodontic treatment is involved. For example, it is becoming possible to predict how a child's teeth will move during their growth, allowing for early intervention to correct an unfavorable situation. Similarly, teeth tend to shift, especially as the patient ages. Thanks to the invention, it becomes possible to predict this shift, allowing for early intervention to correct an unfavorable situation. The ability to predict future dental situations is a particularly significant advantage when the current patient is undergoing orthodontic treatment. Indeed, until the present invention, during an examination, the orthodontist could only perceive the most visible anomalies, for example, significant detachment of the aligner in certain areas. Their ability to anticipate problems was therefore limited. Furthermore, the orthodontist could misinterpret a situation. For example, they might consider a detachment of an aligner to be an anomaly, when in fact this detachment was only temporary, or would remain limited. Advantageously, the prediction made by the method according to the invention allows it to anticipate a future situation that visual observation alone cannot reveal. It can therefore, for example, choose not to modify the current orthodontic appliance even if it perceives a detachment. Conversely, it can modify the current orthodontic appliance even if it does not perceive a detachment, or only a very slight one. As will be seen in more detail later in the description, the effectiveness of orthodontic treatment is considerably improved. The current orthodontic appliance may be a splint. A method according to the invention is particularly well suited to determining the most suitable times to change the splint worn by a current patient. In step 3), preferably, for at least one, preferably for each of said future dental situations, and / or for at least one, preferably for each of said future times, if the current patient is fitted with a current orthodontic appliance, values ​​are determined, at said future times, of parameters of said current orthodontic appliance; and / or values ​​of parameters for the positioning of the teeth of the current patient at said future times (in particular at a target future times);and / or preferably, a difference in the value of one or more parameters for the positioning of the teeth of the current patient with the value of said positioning parameter(s) in a dental situation constituting a target at said future time; and / or a cost for said future dental situation to occur; and / or a pain coefficient for said dental situation to occur; and / or a probability that the predictions relating to the parameters of the current dental appliance if the current patient is fitted with such an appliance and / or to the positioning parameters of said teeth of said current patient, and / or said cost and / or said pain coefficient will conform to reality. Preferably, in step 3), we determine several future dental situations, for the same future time, and / or at least one future dental situation, for several different future times. Preferably, several statistical analyses are performed, modifying the future time each time, in order to predict future dental situations up to a target future time, for example up to an intermediate or final setup. This cycling makes it possible to predict an evolution of the position of the teeth and / or a "potential orthodontic treatment" up to the target future time. Preferably, one or more potential orthodontic treatments are determined to achieve, at a target future time, a specific target future dental situation or a target future dental situation falling within a specific range of dental situations. Preferably, first and second potential orthodontic treatments are determined, leading, at the target future time, to extreme dental situations for at least one tooth positioning parameter of the current patient. The "extreme" situations correspond to minimum and maximum limits for said positioning parameter, that is to say, limits below and above which, respectively, the dental situation at the target future time is considered unacceptable. Represented on the same graph, the curves showing the temporal evolution of the value of the positioning parameter for these first and second potential orthodontic treatments define an area, called the "biozone," which advantageously allows for the easy identification of abnormal tooth positioning drift. It is sufficient, at any given moment, to measure the value of the positioning parameter and verify whether, at that moment, it falls within the biozone. The starting moment of the potential orthodontic treatment(s) can be, in particular, the current moment or an initial moment corresponding to the beginning of current orthodontic treatment with an orthodontic appliance worn by the current patient. Preferably, several potential orthodontic treatments are determined by modifying at least one constraint each time. Advantageously, the orthodontist can thus assess the impact of a change in a constraint. For example, he can change the constraint of the diameter of the metal arch and observe the effect of this change on the potential orthodontic treatment. Preferably, the process includes an optimization operation of the constraints according to at least one optimization criterion, an operation in which a succession of statistical analyses is implemented by modifying each time one or more of said constraints for the same future time, until an optimal dental situation is found with regard to the optimization criterion, following at least one optimization rule. Preferably, by implementing a series of statistical analyses, several potential orthodontic treatments corresponding to the application of different constraints are established, until an optimal potential orthodontic treatment is found with regard to the optimization criterion following at least one optimization rule. Preferably, the optimization criterion is chosen from the group formed by a pain coefficient, a cost, a deviation from a desired value for a positioning parameter, a duration, a number of orthodontic appointments, a number of aligners, a probability of success, or a combination of these criteria, each criterion being able to be associated with the current orthodontic treatment or with a dental situation of said current orthodontic treatment, for example, said current dental situation or with a target future time. Definitions A "current patient" is a person for whom the method according to the invention is implemented to predict a future dental situation, regardless of whether that person has a malposition of the teeth or not. The patient is said to be "current" for the sake of clarity, to distinguish it from a "historical" patient. By "dental situation" we mean a situation relating to the position of the teeth. A "category" of patients groups all patients according to physiological data, for example groups all patients in a particular age group and / or of the same sex. A "class" of orthodontic appliances defines a set of comparable orthodontic appliances. For example, a class of orthodontic appliances may group together all orthodontic appliances that are active aligners made of the same material, or all orthodontic appliances with brackets equipped with the same metal archwire. The "context parameters" are the parameters useful for evaluating a dental situation. They include, in particular, the parameters of the positioning of the teeth of the patient in question and, where applicable, the parameters of the orthodontic appliance in question. The "parameters of the orthodontic appliance" include intrinsic parameters, such as the material(s) that constitute the said orthodontic appliance or resting shape parameters, for example the shape of a splint or the diameter of an orthodontic arch. They also include application parameters. In one embodiment, the parameters of the orthodontic appliance are general parameters that identify the class of the orthodontic appliance. A "shape parameter" is a parameter useful for determining the shape of an orthodontic appliance. For example, x, y, and z are shape parameters in a Cartesian Oxyz coordinate system. The values ​​of these shape parameters allow us to define the position of a point on the orthodontic appliance in space, preferably a point on the surface of the orthodontic appliance. A shape parameter can also be a diameter of an orthodontic archwire, a material thickness, or a dimension, for example. An "application parameter" is a parameter useful for determining how the orthodontic appliance operates in the dental situation under consideration. The position of the orthodontic archwire attachment points on the teeth or the tension of the orthodontic archwire are examples of application parameters. The length of time the orthodontic appliance has already been worn at the time under consideration is also an application parameter. A "positioning parameter" is a parameter useful for determining the position of a tooth. For example, the abscissa, often denoted x, the ordinate, often denoted , and the height, often denoted z, are positioning parameters in a Cartesian Oxyz reference frame. The radial coordinate, often denoted r or p, and called the radius, the angular coordinate, also called the polar angle or azimuth, and often denoted t or Θ, and the height, often denoted h, are positioning parameters in a cylindrical reference frame. The values ​​of these positioning parameters allow us to define the position of a point in space. The parameters used to determine the shape of an orthodontic appliance may be the same as or different from the parameters used to determine the position of the teeth. For clarity, these parameters have been designated differently, as "shape parameters" and "positioning parameters", respectively. Constraints are parameters whose values ​​are not free. We distinguish: "non-adjustable" constraints, in particular the positioning parameters of the teeth of the current patient at the present moment or parameters relating to the current patient, such as his age or sex, and "adjustable" constraints, for which the orthodontist or the current patient can set ranges of variation, at the present moment and / or at one or more future moments. Examples of adjustable constraints include a range of acceptable positions for the current patient's teeth at a future time, a maximum treatment cost, a maximum pain coefficient during treatment, or an average pain coefficient during current orthodontic treatment. In particular, when seeking an orthodontic appliance better suited to orthodontic treatment, by modifying or replacing the current orthodontic appliance, the parameters of the current orthodontic appliance, for example the shape of a splint, can also be adjustable constraints. The "acquisition conditions" of an image specify the position and orientation in space of an image acquisition device relative to the patient's teeth or a model of the patient's teeth, and preferably the calibration of this image acquisition device. Acquisition conditions are said to be "virtual" when they correspond to a simulation in which the acquisition device would be in said acquisition conditions (theoretical positioning and preferably calibration of the acquisition device). A "set-up" classically corresponds to a positioning of the teeth that the treatment aims to achieve at a certain point in the treatment, in particular at the end of the treatment ("final set-up") or at a predetermined intermediate stage of the treatment ("intermediate set-up"), for example at a time planned to change the aligner or modify the tension of the orthodontic arch. The "calibration" of an acquisition device consists of the set of calibration parameter values. A "calibration parameter" is an intrinsic parameter of the acquisition device (unlike its position and orientation) whose value influences the acquired image. Preferably, the calibration parameters are chosen from the group formed by the aperture, exposure time, focal length, and sensitivity. By "image," we mean a two-dimensional image, like a photograph. An image is made up of pixels. An "acquirable" ("preview") image is the image that the acquisition device can record at a given moment. For a camera or a phone, it is the image that appears on the screen when the photo or video acquisition application is in operation. A "discriminating information" is a characteristic information that can be extracted from an image {"image feature"), classically by computer processing of that image. Discriminatory information can have a variable number of values. For example, edge information can be 1 or 0 depending on whether a pixel belongs to a boundary or not. Brightness information can take on a large number of values. Image processing allows the extraction and quantification of discriminatory information. "Metaheuristic" methods are known optimization methods. They are preferably chosen from the group formed by: - ​​evolutionary algorithms, preferably chosen from: evolutionary strategies, genetic algorithms, differential evolution algorithms, distribution estimation algorithms, artificial immune systems, Shuffled Complex Evolution path recomposition, simulated annealing, ant colony algorithms, particle swarm optimization algorithms, tabu search, and the GRASP method; - the kangaroo algorithm, - the Fletcher and Powell method, - the noise method, - stochastic tunneling, - random restart hill climbing, - the cross-entropy method, and - hybrid methods between the metaheuristic methods mentioned above. "Comprising" or "comprising" or "presenting" should be interpreted in a non-restrictive manner, unless otherwise indicated. Brief description of the figures. Other features and advantages of the invention will become apparent upon reading the detailed description that follows and upon examination of the accompanying drawing in which: - Figure 1 shows a flowchart illustrating the implementation of a prediction method according to the invention, - Figure 2 (2a to 2e) shows examples of graphical representations providing predictions obtained by implementing a method according to the invention for the value of a tooth positioning parameter, as a function of time, - Figure 3 shows a flowchart illustrating the implementation of a method for easily acquiring historical or current data, - Figure 4 shows an example of an initial reference model, - Figure 5 (5a-5d) illustrates a process for determining tooth models in a reference model, - Figure 6 (6a-6d) illustrates the acquisition of an updated image using a retractor.an operation of cutting out this image, and the processing of an updated image allowing the contour of the teeth to be determined, - figure 7 schematically illustrates the relative position of reference marks 12 of a retractor 10 on updated images 14i and 142, according to the directions of observation represented by dashed lines, - figure 8 represents, on an acquired image, a reference map established for a reflection information. Detailed description Step 1) is a historical data acquisition step. It must start before step 3), but preferably continues during and after step 3). Each historical situation corresponds to a situation in which a historical patient found themselves, and for which historical data were collected. The number of historical situations for which historical data are acquired is preferably greater than 1,000, preferably greater than 10,000, preferably greater than 100,000, preferably greater than 500,000. This improves the accuracy of the statistical analysis. Historical situations may concern different classes of orthodontic appliances. The number of historical situations relating to the same class of orthodontic appliances is preferably greater than 1,000, preferably greater than 10,000, preferably greater than 100,000, preferably greater than 500,000. The number of historical situations relating to the same category of patients is preferably greater than 1,000, preferably greater than 10,000, preferably greater than 100,000, preferably greater than 500,000. Preferably, all historical data is recorded in a computer database. Of course, the current patient may have experienced historical situations, and therefore may have been a "historical patient" himself. Step 2) is a step of collecting current data relating to the current situation experienced by the current patient and which is relevant for the statistical analysis of step 3). Current data preferably allows us to determine the category to which the current patient belongs. If the current patient wears a current orthodontic appliance, the current data allows the parameters of this appliance to be determined, but also, preferably, the class of this appliance. In step 1) and / or step 2), the acquisition of historical or current data, respectively, can be carried out by any means. It may in particular result from the implementation of a data acquisition process comprising the following steps: a) creation of a three-dimensional digital reference model of at least part of an arch, preferably of at least one arch of a patient (current or historical), or "initial reference model" and for each tooth, definition, from the initial reference model, of a three-dimensional digital reference model of said tooth, or "tooth model"; b) acquisition of at least one two-dimensional image of the patient's arches, called the "updated image", under real acquisition conditions;c) analysis of each updated image and creation, for each updated image, of an updated map relating to discriminating information; d) optionally, determination, for each updated image, of coarse virtual acquisition conditions approximating said real acquisition conditions; e) search, for each updated image, by deformation of the initial reference model, of an updated reference model corresponding to the positioning of the teeth during the acquisition of the updated image, the search being preferably carried out using a metaheuristic method, preferably evolutionary, preferably by simulated annealing, and f) collection of data relating to the updated reference model and preferably, if the patient wears orthodontic appliances, relating to said orthodontic appliance. Depending on whether this process is implemented in step 1) or step 2), the data collected will be historical or current data, respectively. The manufacture of the updated reference model is advantageously possible without special precautions, in particular because the actual positioning of the teeth is measured with an updated reference model which results from a deformation of the initial reference model so that it corresponds to the observations provided by the updated images, i.e. so that the updated images are views of the deformed initial reference model. Such a data acquisition process, illustrated in Figure 3, therefore allows, from one or more simple images of the teeth, taken without precise pre-positioning of the teeth in relation to the image acquisition device, for example from a photograph taken by the patient, to accurately assess the position of the teeth at the time of step b). This assessment can also be carried out remotely, from simple photographs taken by a mobile phone, without the patient having to travel, in particular to the orthodontist. If the patient wears orthodontic appliances, this evaluation advantageously allows for the acquisition of numerous data enabling the establishment of correlations between parameters of the orthodontic appliance, its behavior, and tooth configurations. In step a), an initial reference model of the arches, or a part of the patient's arches, is created with a 3D scanner. Such a model, called a "3D" model, illustrated in figure 4, can be observed from any angle. The initial reference model can be prepared from measurements taken on the patient's teeth or on a physical model of their teeth, for example a plaster model. In the initial reference model, a part corresponding to a tooth, or "tooth model", is delimited by a gingival border which can be decomposed into an internal gingival border (on the side of the inside of the mouth relative to the tooth), an external gingival border (oriented towards the outside of the mouth relative to the tooth) and two lateral gingival borders. In step b), an updated image of a part of an arch, an arch or the arches is taken using an image acquisition device, preferably a mobile phone. Preferably, a dental retractor is used in step b), as shown in Figure 6a. The retractor typically consists of a support with a rim extending around an opening and arranged so that the patient's lips can rest on it while allowing the patient's teeth to be seen through said opening. In step c), each updated image is analyzed so as to produce, for each updated image, an updated map relating to at least one discriminating information. An updated map represents discriminating information in the reference frame of the updated image. For example, Figure 5b is an updated map of the tooth contour obtained from the updated image of Figure 5a. The discriminating information is preferably chosen from the group consisting of contour information, color information, density information, distance information, brightness information, saturation information, reflection information, and combinations of these. A person skilled in the art knows how to process an updated image to reveal the discriminating information. In the optional step d), the actual acquisition conditions during step b are roughly determined.In other words, we determine at least the relative position of the image acquisition device at the moment it took the updated image (position of the acquisition device in space and orientation of this device). Step d) advantageously limits the number of tests on virtual acquisition conditions during step e), and therefore considerably speeds up step e). Preferably, one or more heuristic rules are used. For example, preferably, conditions corresponding to a position of the image acquisition device behind the teeth or a distance from the teeth greater than 1 m are excluded from virtual acquisition conditions that could be tested in step e). In a preferred embodiment, as illustrated in Figure 7, registration marks shown on the updated image, and in particular registration marks 12 of the spreader, are used to determine a substantially conical region of space delimiting virtual acquisition conditions that can be tested in step e), or "test cone". Specifically, we preferably have at least three non-aligned reference marks 12 on the spacer 10, and we precisely measure their relative positions on the spacer. The registration marks are then located on the updated image, as described previously. Simple trigonometric calculations allow us to determine approximately the direction in which the updated image was taken. Step d) only allows for a rough assessment of the actual acquisition conditions. However, step d) allows us to determine a limited set of virtual acquisition conditions likely to correspond to the actual acquisition conditions, and, within this set, virtual acquisition conditions that constitute the best starting point for step e) described below. The objective of step e) is to modify the initial reference model until we obtain an updated reference model that corresponds to the updated image. Ideally, the updated reference model is therefore a digital three-dimensional reference model from which the updated image could have been taken if this model had been real. We therefore test a succession of reference models "to be tested", the choice of a reference model to be tested preferably depending on the level of correspondence of the reference models "to be tested" previously tested with the updated image. This choice is preferably made by following a known optimization process, in particular chosen from metaheuristic optimization processes, preferably evolutionary, in particular in simulated annealing processes. Preferably, step e) includes - a first optimization operation to search for virtual acquisition conditions that best correspond to the real acquisition conditions in a reference model to be tested determined from the initial reference model, and - a second optimization operation to search, by testing a plurality of said reference models to be tested, for the reference model that best corresponds to the positioning of the patient's teeth during the acquisition of the updated image in step b). Preferably, a first optimization operation is performed for each test of a reference model to be tested during the second optimization operation. Preferably, the first optimization operation and / or the second optimization operation, preferably the first optimization operation and the second optimization operation implement a metaheuristic method, preferably evolutionary, preferably a simulated annealing. Preferably, step e) comprises the following steps: e1) defining a reference model to be tested as the initial reference model, then, e2) following the subsequent steps, testing virtual acquisition conditions with the reference model to be tested in order to closely approximate said real acquisition conditions; e21) determining virtual acquisition conditions to be tested; e22) creating a two-dimensional reference image of the reference model to be tested under said virtual acquisition conditions to be tested; e23) processing the reference image to create at least one reference map representing, at least partially, said discriminating information; e24) comparing the updated and reference maps in order to determine a value for a first evaluation function.said value for the first evaluation function depending on the differences between said updated and reference maps and corresponding to a decision to continue or stop the search for virtual acquisition conditions that approximate said real acquisition conditions more accurately than said virtual acquisition conditions to be tested determined at the last occurrence of step e21); e25) if said value for the first evaluation function corresponds to a decision to continue said search, modification of the virtual acquisition conditions to be tested, then resumed at step e22); e3) determination of a value for a second evaluation function, said value for the second evaluation function depending on the differences between the updated and reference maps in the virtual acquisition conditions that best approximate said real acquisition conditions and resulting from the last occurrence of step e2).said value for the second evaluation function corresponding to a decision to continue or stop the search for a reference model approximating the tooth positioning during the acquisition of the updated image with greater accuracy than said reference model to be tested used in the last occurrence of step e2), and if said value for the second evaluation function corresponds to a decision to continue said search, modification of the reference model to be tested by moving one or more tooth models, then resumed in step e2). In step e1), it is determined that the reference model to be tested is the initial reference model during the first execution of step e2). In step e2), one begins by determining virtual acquisition conditions to be tested,that is to say, a virtual position and orientation that can correspond to the actual position and orientation of the acquisition device when capturing the updated image, but also, preferably, a virtual calibration that can correspond to the actual calibration of the acquisition device when capturing the updated image. The image acquisition device is then virtually configured in the virtual acquisition conditions to be tested in order to acquire a reference image of the reference model to be tested under these virtual acquisition conditions. The reference image therefore corresponds to the image that the image acquisition device would have taken if it had been placed, relative to the reference model to be tested, and optionally calibrated, in the virtual acquisition conditions to be tested (step e22)). If the updated image was taken when the position of the teeth was exactly that in the reference model to be tested, and if the virtual acquisition conditions are exactly the real acquisition conditions, then the reference image is exactly superimposable on the updated image. The differences between the updated image and the reference image result from errors in the evaluation of the virtual acquisition conditions (if they do not exactly correspond to the real acquisition conditions) and from tooth displacements between step b) and the reference model to be tested. To compare the updated and reference images, we compare the discriminating information on these two images. More precisely, we create, from the reference image, a reference map representing the discriminating information (step e23)). The updated and reference maps, both relating to the same discriminating information, are then compared and the difference between these two maps is evaluated by means of a score. For example, if the discriminating information is the outline of the teeth, one can compare the average distance between the points of the outline of the teeth that appears on the reference image and the points of the corresponding outline that appears on the updated image, the score being higher the smaller this distance. Preferably, the virtual acquisition conditions include the calibration parameters of the acquisition device. The score is higher the closer the tested calibration parameter values ​​are to the calibration parameter values ​​of the acquisition device used in step b). For example, if the tested aperture is far from that of the acquisition device used in step b), the reference image will have blurred and sharp regions that do not correspond to the blurred and sharp regions of the updated image. If the discriminating information is the tooth contour, the updated and reference maps will therefore not represent the same contours, and the score will be low. The score could be, for example, a correlation coefficient. The score is then evaluated using a first evaluation function. The first evaluation function determines whether the cycling on step e2) should be continued or stopped. The first evaluation function can, for example, be equal to 0 if the cycling should be stopped or equal to 1 if the cycling should continue. The value of the first evaluation function may depend on the score achieved. For example, it may be decided to continue the cycle at step e2) if the score does not exceed a first threshold. For example, if an exact match between the updated and reference images leads to a score of 100%, the first threshold could be, for example, 95%. Of course, the higher the first threshold, the better the accuracy of the evaluation of the virtual acquisition conditions if the score manages to exceed this first threshold. The value of the first evaluation function may also depend on scores obtained with previously tested virtual acquisition conditions. The value of the first evaluation function can also depend on random parameters and / or the number of cycles of step e2) already performed. In particular, it is possible that despite repeating the cycles, it may not be possible to find virtual acquisition conditions that are sufficiently close to the actual acquisition conditions for the score to reach the first threshold. The first evaluation function may then lead to the decision to stop the cycling even though the best score obtained has not reached the first threshold. This decision may result, for example, from a number of cycles exceeding a predetermined maximum number. A random parameter in the first evaluation function can also allow further testing of new virtual acquisition conditions, even if the score appears satisfactory. The evaluation functions classically used in metaheuristic optimization processes, preferably evolutionary, particularly in simulated annealing processes, can be used for the second evaluation function. If the value of the first evaluation function indicates that it is decided to continue the cycling on step e2), the tested virtual acquisition conditions (step e25) are modified and a cycle (step e2) is started again, consisting of producing a reference image and a reference map, then comparing this reference map with the updated map to determine a score. The modification of virtual acquisition conditions corresponds to a virtual movement in space and / or a change in orientation and / or, preferably, a change in the calibration of the acquisition device. This modification can be random, provided, however, that the new virtual acquisition conditions to be tested always belong to the set determined in step d). The modification is preferably guided by heuristic rules, for example by favoring modifications which, according to an analysis of previous scores obtained, appear most favorable for increasing the score. The cycling on e2) is continued until the value of the first evaluation function indicates that it is decided to exit this cycling and proceed to step e3), for example, if the score reaches or exceeds said first threshold. The optimization of the virtual acquisition conditions in step e2) is preferably performed using a metaheuristic method, preferably evolutionary, preferably a simulated annealing algorithm. Such an algorithm is well known for nonlinear optimization. If the cycling process was stopped at step e2) without a satisfactory score being obtained, for example, without the score reaching the first threshold, the process can be stopped (failure situation) or resumed at step c) with new discriminating information and / or with a new updated image. The process can also be continued with the virtual acquisition conditions corresponding to the best score achieved. A warning can be issued to inform the user of the error in the result. If we left the cycle at step e2) when a satisfactory score could be obtained, for example because the score reached, or even exceeded, the said first threshold, the virtual acquisition conditions correspond substantially to the real acquisition conditions. Preferably, the virtual acquisition conditions include the calibration parameters of the acquisition device. The procedure thus allows the values ​​of these parameters to be evaluated without needing to know the nature of the acquisition device or its settings. Step b) can therefore be carried out without any special precautions, for example by the patient himself using his mobile phone. In addition, the search for the actual calibration is carried out by comparing an updated image with views of an initial reference model under virtual acquisition conditions that are being tested. Advantageously, it does not require the updated image to show a calibration standard gauge, that is, a gauge whose characteristics are precisely known to determine the calibration of the acquisition device. The updated images are not used to create a completely new, updated three-dimensional model, but only to modify the initial, very accurate reference model. A completely new, updated three-dimensional model created from simple photographs taken without special precautions would be, in particular, too imprecise for a comparison with the initial reference model to lead to conclusions about tooth movement. Differences may remain between the determined virtual acquisition conditions and the real acquisition conditions, especially if teeth have moved between steps a) and b). The correlation between the updated and reference images can then be further improved by repeating step e2), the reference model to be tested being modified by moving one or more tooth models (step e3)). The search for the reference model that best approximates the positioning of the teeth during the acquisition of the updated image can be carried out like the search for virtual acquisition conditions that best approximate the real acquisition conditions (step e2)). In particular, the score is evaluated using a second evaluation function. This second evaluation function determines whether the cycling on steps e2) and e3) should be continued or stopped. For example, the second evaluation function can be equal to 0 if the cycling should be stopped or equal to 1 if the cycling should continue. The value of the second evaluation function depends preferably on the best score obtained with the reference model to be tested, i.e. the differences between the updated and reference maps, in the virtual acquisition conditions that best approximate said real acquisition conditions. The value of the second evaluation function may also depend on the best score obtained with one or more previously tested reference models. For example, it may be decided to continue the cycling if the score does not exceed a second minimum threshold. The value of the second evaluation function may also depend on random parameters and / or the number of cycles of steps e2) and e3) already carried out. If the value of the second evaluation function indicates that it is decided to continue the cycling on steps e2) and e3), the reference model to be tested is modified and a cycle (steps e2) and e3)) is started again with the new reference model to be tested. The modification of the reference model to be tested corresponds to a displacement of one or more tooth models. This modification can be random. The modification is preferably guided by heuristic rules, for example by favoring modifications which, according to an analysis of previous scores obtained, appear most favorable to increase the score. Preferably, we look for the displacement of a tooth model that has the strongest impact on the score, modify the reference model to be tested by moving this tooth model, and then continue the cycle through steps e2) and e3) to optimize the score. We can then search, among the other tooth models, for the one that has the strongest impact on improving the score, and again search for the optimal displacement of this other tooth model on the score. We can continue in this way with each tooth model. Next, it is possible to repeat the cycle on all tooth models and continue in this way until a score above the second threshold is obtained. Of course, other strategies can be used to move one or more tooth models into the reference model to be tested and search for the maximum score. The cycling on steps e2) and e3) is continued until the value of the second evaluation function indicates that it is decided to exit this cycling and continue to step f), for example if the score reaches or exceeds said second threshold. The search for a reference model with cycling on steps e2) and e3) to search for the positions of the tooth models that optimize the score is preferably carried out using a metaheuristic method, preferably evolutionary, preferably a simulated annealing algorithm. Such an algorithm is well known for nonlinear optimization. If the cycling process was stopped at steps e2) and e3) without a satisfactory score being obtained, for example without the score reaching the second threshold, the process can be stopped (failure situation) or resumed at step c) with new discriminating information and / or with a new updated image. If it is decided to restart the process at step c) from another discriminating information and / or another updated image because the first or second threshold was not reached, the choice of the new discriminating information and / or the new updated image can depend on the scores obtained previously, in order to favor the discriminating information and / or the updated image which, in light of these scores, appear the most promising. New discriminating information, obtained for example by combining other discriminating information already tested, can be used. If necessary, the patient may also be asked to acquire one or more new, updated images. Preferably, instructions are provided to guide the positioning of the acquisition device for capturing this new, updated image. For example, the patient may be instructed to take a photograph of the right side of their lower arch. If we have left the cycle on steps e2) and e3) without a satisfactory score being obtained, a warning may be issued to inform the user of the error in the result. If we have left the cycling on steps e2) and e3) when a satisfactory score has been obtained, for example because the score has reached, or even exceeded, the said second threshold, the virtual acquisition conditions correspond substantially to the real acquisition conditions and the tooth models in the reference model obtained (called "updated reference model") are substantially in the position of the patient's teeth at the time of step b). The cycling on steps e2) and e3) advantageously improves the evaluation of the calibration parameters of the acquisition device in step b). At the end of step e), the updated reference model corresponds substantially to the updated image. It is then possible to take precise measurements of tooth positioning and / or the shape of the orthodontic appliance in order to acquire historical or current data. In step 3), all statistical analysis methods can be used. Advantageously, statistical analysis allows for the establishment of correlations between historical data, and in particular between parameter values ​​of the orthodontic appliance (if worn) and its behavior, without requiring the analytical development of each correlation. Statistical analysis is preferably implemented by a computer program. It involves analyzing historical data to predict the value of one or more contextual parameters at a future time, based on a set of constraints imposed for this prediction, including current data. Statistical analysis allows for the prediction, at a future time—preferably any future time—of at least one parameter related to the positioning of the current patient's teeth, for example, the theoretical position of any point on a tooth. More specifically, statistical analysis makes it possible to build, from historical data, a predictive model that can forecast how the value of certain parameters will evolve according to "input data". Preferably, the historical data includes context parameter values ​​relating to historical dental situations experienced by the current patient. Preferably, the statistical analysis assigns a weight to these values ​​that is higher than that of context parameter values ​​relating to historical dental situations experienced by other patients. Thus, for example, if the current patient is undergoing orthodontic treatment, analyzing the historical data of other orthodontic treatments—for example, 1000 other similar orthodontic treatments—might lead to an estimate that the displacement of the centroid of one of the patient's teeth along the x-axis (Ox) in the month following the current time should be 60 pm. If analyzing the historical data of the current patient alone leads to an estimate of this displacement at 50 pm, statistical analysis could, for example, estimate this displacement at 55 pm. In this example, the weight of the patient's historical data is therefore 1000 times greater than that of the historical data of other patients. The input data are values ​​that fix the values ​​of certain parameters. The values ​​of some parameters can only be input data. These parameters thus constitute non-adjustable constraints. For example, the prediction is necessarily made from the position of the teeth of the current patient at the current time. The values ​​of the tooth positioning parameters of the current patient at the current time are therefore input data. Similarly, if the current patient is undergoing orthodontic treatment, the prediction is based on the current dental situation in which an orthodontic appliance is worn on the teeth in their present position. The value of certain parameters of the orthodontic appliance at the present time, for example, the position of the attachment points, can therefore also be imposed. The class of the current orthodontic appliance or its intrinsic parameters are other examples of non-adjustable constraints. Parameters that are not non-adjustable constraints can be fixed or only allowed to vary within fixed ranges. They constitute adjustable constraints, notably by the orthodontist and / or the patient. For example, the total duration of orthodontic treatment can be fixed at 6 months. A pain coefficient measuring the maximum pain during orthodontic treatment can also be fixed. In a preferred embodiment, the future time is an "objective" future time, i.e., corresponding to a predetermined time in the treatment, in particular corresponding to an intermediate or final setup, and a range for the possible values ​​of a tooth positioning parameter is imposed at this future time. This positioning parameter is then an adjustable constraint. A parameter is an adjustable constraint only if, for statistical analysis, it is decided to limit the range of its possible values. Otherwise, it is a free parameter. Parameters that are not constraints are therefore free to vary. If the ranges of possible values ​​for the adjustable constraints are sufficiently wide and if the adjustable constraints are not too numerous, statistical analysis will make it possible to predict at least one future dental situation that respects the constraints. Otherwise, simple trials will allow, by relaxing certain constraints, at least one prediction to be obtained. Many parameters can be adjustable constraints. Statistical analysis therefore often makes it possible to determine several "potential orthodontic treatments" to improve the current patient's dental situation. Simple trials can limit the ranges of possible values ​​for the adjustable constraints in order to limit the number of potential orthodontic treatments. Preferably, if the current patient is undergoing orthodontic treatment, the statistical analysis should only use historical data on dental situations related to orthodontic appliances of the same class as the current orthodontic appliance. This improves the accuracy of the prediction. Preferably, the statistical analysis uses only historical data on dental situations relating to historical patients in the same category as the current patient. This improves the accuracy of the prediction. A future moment can be, in particular, more than one week, more than two weeks, more than three weeks, more than five weeks, more than eight weeks, or more than ten weeks later than the current moment. The prediction is more precise the closer the future moment considered is to the current moment. Preferably, a future dental situation is determined for a future time corresponding to an intermediate or final set-up. When statistical analysis makes it possible to determine several future dental situations for the same future time, it preferably selects at least one, preferably two, future dental situations corresponding to extreme dental situations, that is to say, situations corresponding to acceptable limit values, at that future time, for an adjustable constraint. The adjustable constraint can be in particular a positioning parameter of a tooth for which the orthodontist and / or the patient have fixed a range of possible values. Preferably, at least one future dental situation is determined for several different future times. When determining at least one future dental situation for several different future times, the different future times may be separated by more than 3 days, more than one week or more than 2 weeks, and / or less than 2 months, or less than one month. Preferably, at least one of the future time points is a "target" future time point. Statistical analysis thus allows us to predict a potential orthodontic treatment up to the target future time point. By setting adjustable constraints, it is possible to predict several potential orthodontic treatments and therefore measure the impact of a choice on the adjustable constraints. The results of the statistical analysis can be presented in any form. Preferably, the difference between a future dental situation for a future time and a prediction of the anticipated dental situation, for said future time, at a time prior to the current time, for example at the beginning of treatment, is presented. This presentation of the difference is particularly useful when the future time corresponds to an intermediate or final setup. Preferably, the difference between a potential orthodontic treatment and a corresponding prediction of the anticipated orthodontic treatment at a time prior to the current time is presented, for example at the beginning of treatment. This presentation of the difference allows visualization of whether the treatment has proceeded and will proceed in accordance with the initial prediction. Preferably, several future dental situations are presented, at different future times, on the same graphic representation. Preferably, a graphical representation is established based on the results of the statistical analysis, presenting a prediction of the temporal evolution of at least one contextual parameter. The temporal evolution may include, in particular: - a parameter of the current orthodontic appliance; and / or - a parameter of the positioning of the teeth of the current patient, for example, the temporal evolution of the displacement of a point on a tooth; and / or - a probability that the future dental situation will occur at a given future time; and / or - a deviation from a dental situation constituting a target at a given future time; and / or - a predictable cost for the future dental situation to occur at a given future time; and / or - a pain coefficient for the dental situation to occur at a given future time. The time scale is preferably linear.A graphical representation allows, for example, the immediate perception of the dynamics of the action of the orthodontic appliance. In particular, the observation that the curve of a positioning parameter increases or decreases less rapidly as time passes can be interpreted as meaning that the orthodontic appliance is losing its effectiveness. Such a curve is particularly simple to understand, which makes its use possible by the current patient himself. In a preferred embodiment, the graphical representation includes indications of whether the evolution is satisfactory or unsatisfactory. For example, the curve may change color if the slope is considered abnormal. It is thus possible to determine, for example, the point at which any delay in adapting the treatment will be detrimental. Preferably, the graphic representation can be displayed on a mobile phone. In particular, it is viewable by the patient. Advantageously, the patient can thus decide for themselves, at the most opportune moment, whether to take steps to modify or change their orthodontic appliance, or to make an appointment with the orthodontist. In one embodiment, the number of parameters whose evolution is represented graphically is less than 10, preferably less than 5, preferably less than 4, preferably less than 3, preferably less than 2. In one embodiment, the number of tooth points for which the evolution of one or more parameters is represented graphically is less than 10, preferably less than 5, preferably less than 4, preferably less than 3, preferably less than 2. Decision-making is thus facilitated. Preferably, a report is established based on the result of the statistical analysis, providing - diagnostic information and / or recommendations for applying a new orthodontic treatment to the current patient or for modifying an orthodontic treatment applied to the current patient and / or - a score representative of the effectiveness of a treatment applied to the current patient and / or of potential alternative orthodontic treatments. The report may specify, in particular, how to modify the tension of the arc of the current orthodontic appliance or how to manufacture a new splint. Preferably, several potential orthodontic treatments are determined which, starting from the current dental situation, will achieve a desired tooth positioning, and then said potential treatments are presented to the patient and / or the orthodontist so that they can choose one of said potential orthodontic treatments. Preferably, the modification of adjustable constraints is repeated within the framework of an optimization. At each optimization cycle, one or more of said adjustable constraints are modified, then - the resulting future dental situation is evaluated until an optimal dental situation is found with regard to an optimization criterion, following at least one optimization rule, and / or - preferably, the potential orthodontic treatment obtained is evaluated until an optimal orthodontic treatment is found with regard to an optimization criterion, following at least one optimization rule. Of course, all known optimization methods can be implemented. More specifically, to perform an optimization, some adjustable constraints are classically fixed, others are variable within a range that is fixed. For optimizing a future dental situation, the optimization criterion could be, for example, a pain coefficient or a cost associated with that situation. The objective of the optimization could be, for example, to minimize the pain coefficient at a future time. An initial statistical analysis is then performed with a first pain coefficient, and it is examined whether the result is acceptable. If the result is acceptable, the pain coefficient is reduced, and it is examined whether the new result is acceptable. Constraints are thus modified until the lowest pain coefficient that achieves an acceptable result is determined. For the optimization of orthodontic treatment, the optimization criterion could be, for example, a deviation from a desired value for a positioning parameter at a target future time, such as at the end of treatment. The optimization criterion could also be an average pain coefficient evaluating, on average, the pain until the end of treatment, or a total treatment cost. At each optimization cycle, it is then necessary to predict a potential orthodontic treatment, measure the optimization criterion for this potential orthodontic treatment, for example by averaging the pain coefficients associated with each future dental situation of the potential orthodontic treatment, and then modify one or more adjustable constraints while respecting the ranges within which these variable constraints can vary. By comparing the values ​​of the optimization criterion obtained for the different cycles, we can thus search for the optimal potential orthodontic treatment. The optimization rule may be, for example, to minimize or maximize the value of the optimization criterion. Optimization is preferably carried out by a computer, with the orthodontist or patient only specifying adjustable constraints, for example, a maximum value or an acceptable range for the adjustable constraints. For example, the orthodontist may impose a maximum cost, a maximum duration, a maximum pain coefficient, a maximum number of appointments or a maximum number of aligners. He may also specify, depending on the objective of the orthodontic treatment, the range of acceptable values ​​for one or more context parameters, and in particular positioning parameters (range P on figure 2, described below). Through statistical analysis of historical data, the computer and / or the orthodontist and / or the current patient then search for one or, preferably several, future dental situations, preferably one or, preferably several, potential orthodontic treatments that can meet these adjustable constraints. In one embodiment, if the imposed adjustable constraints do not allow the determination of a potential orthodontic treatment respecting these constraints, the orthodontist modifies them, then renews the statistical analysis and optimization. He repeats these operations until he has found at least one potential orthodontic treatment. For example, if the patient wants their treatment to last less than 3 months, an adjustable constraint related to pain or cost can be at least partially lifted. To best explore the different possible treatments, it is also possible to remove the constraint related to one or more tooth positioning parameters at a target future time. For example, in Figure 2a, described below, the T3 curve could only be generated because the constraint that, at the target future time tf, the value of the positioning parameter x must be within the range P was removed. In contrast, this constraint was not removed in the example in Figure 2c. Optimization can also be partially manual. In step 4), the orthodontist analyzes the results obtained in step 3) and may determine an orthodontic treatment or modify a current orthodontic treatment based on these results and, preferably, on the current patient's preferences. The predictive capability offered by the invention makes it possible, in particular, to determine orthodontic treatment based on constraints such as the cost of treatment, the number of appointments with the orthodontist, the shape or adjustment of the orthodontic appliance, pain, treatment duration, or the probability of success. The orthodontist may consider the situation acceptable and decide not to implement orthodontic treatment for the current patient or not to modify an orthodontic treatment the current patient is undergoing. Alternatively, they may decide to fabricate an orthodontic appliance, modify the current orthodontic appliance possibly worn by the current patient, or replace it.The orthodontist can, in particular, adjust the tension of an orthodontic archwire on the existing appliance and / or replace an orthodontic archwire on the existing appliance and / or fabricate a new orthodontic aligner to replace the existing appliance. In one embodiment, the existing orthodontic appliance is an aligner, and a second aligner, fabricated based on the results of the statistical analysis in step 3, is sent to the patient. The orthodontic appliance is thus well-suited to the actual treatment. The orthodontist can also advantageously decide to modify the initially planned treatment, particularly by modifying the intermediate setups. In the case of orthodontic treatment using aligners, the process allows for limiting the number of aligners manufactured. The aligners can be manufactured throughout the treatment, allowing them to be perfectly adapted to the actual situation at the time they need to be used. Finally, the cost and duration of treatment are reduced. Examples Figure 2a shows three potential orthodontic treatments T1, T2, and T3, corresponding to three different sets of constraints. For each potential orthodontic treatment, a future dental situation was evaluated, using statistical analysis, at times t1, t2, and tf. The x-axis represents time. The y-axis represents the value of a context parameter x (e.g., the position of a point on a tooth along the x-axis). The range P is a constraint imposed on x at time tf. It specifies the range of acceptable positions for this point at the future target time tf, corresponding, for example, to the end of treatment with the current orthodontic appliance. The limits of this range correspond to extreme dental situations acceptable for the value of x at time tf. Initially, the orthodontist may choose not to impose the P range. The three potential orthodontic treatments T1, T2, and T3 may, for example, differ in their perceived pain values, corresponding, for instance, to three possible settings of the orthodontic Tare tension. For example, a pain coefficient measuring perceived pain might be 200, 150, and 100 for the potential orthodontic treatments T1, T2, and T3, respectively. Starting from the current time ta, statistical analysis, performed for each of the future times t1, t2, and tf, and at each of these future times for the three pain coefficient values, allows us to predict the orthodontic treatment based on the pain coefficient. For example, we observe that if the patient accepts a pain coefficient of 200 (curve T1), the target for the considered context parameter will be reached as early as time t3. It will be reached at time U with the pain coefficient of T2.Figure 2a shows that the treatment objective will not be achieved with the current orthodontic appliance if the current patient wishes to apply the pain coefficient of T3. In agreement with the current patient, the orthodontist can then choose to lengthen the duration of treatment or widen the P range or modify the current orthodontic treatment, for example by changing the current orthodontic appliance, which will possibly result in additional costs. The curve T in Figure 2a represents the initially planned treatment at the initial time t0. At the current time ta, a significant difference Δχ can be observed by examining the patient's teeth between the actual position xa and the initially planned position x* at time ta. Without the prediction according to the invention, the orthodontist would likely have decided to modify the treatment, for example, by changing the orthodontic appliance. If the current orthodontic appliance corresponds to the curve T2, the orthodontist can advantageously determine that the delay will be made up without needing to modify the treatment. Conversely, as shown in Figure 2b, at the current time ta, the orthodontist can observe a small difference Δχ between the actual position xa and the initially planned position x* at time ta. Without the prediction according to the invention, the orthodontist would likely have decided not to modify the treatment.If the current orthodontic appliance corresponds to the T2 curve, it can be advantageous to observe that the gap will increase and that the objective will not be achieved if the treatment is not modified. Statistical analysis thus makes it possible to accurately predict the behavior of an orthodontic appliance based on the value of its parameters and the configuration of the teeth in which it is placed, but also to simulate alternative treatments, for example by modifying the constraints. The curves corresponding to the potential orthodontic treatments T1, T2, and T3 also allow, at each future time point, visualization of the gap between the predicted future dental situation if one of these potential orthodontic treatments is applied and the dental situation constituting the objective at that future time point (curve T). In particular, at time tf, Figure 2a allows visualization of the gap between the objective for the value of the considered context parameter, Xf, and the corresponding values ​​xi, X2, and X3 for the predicted future dental situations with the constraints associated with the potential orthodontic treatments T1, T2, and T3. The orthodontist can also decide to impose the range P as a constraint to be respected. The optimization then leads to a graphical representation like that of Figure 2c. In one embodiment, as shown in Figure 2d, a potential orthodontic treatment, referred to as "optimal," is determined from the initial time t0, for example at the beginning of treatment. This treatment is defined for a given parameter, for example a positioning parameter, and extreme potential orthodontic treatments are determined, corresponding to minimum and maximum limits considered acceptable for said positioning parameter. These potential orthodontic treatments are represented by the curves Topt, Tmax, and Tmm, respectively, in Figure 2d. The curves Tmax and Tmin thus define an envelope providing, at any time until the future target time tf, a tolerance relative to the Topt curve corresponding to the optimal treatment. At the final time tf, for example at the end of treatment or at an intermediate setup, this tolerance corresponds to the range P of accepted final positions.The area, hatched in figures 2d and 2e, which extends between the two curves Tmax and Tmin, is called a "biozone". In figure 2d, the curve Tr represents the actual evolution of the value of the parameter considered, in this case the position xA. At any given moment, it is very easy to check if the position x is within the biozone. If so, the treatment proceeds normally. Otherwise, it is necessary to correct the treatment accordingly. In the example in Figure 2d, the x position moved out of the biozone at time ti, the anomaly was detected at time t2 and the treatment was modified at time t3. The modification brought the curve Tr back into the biozone, from time t4. The biozone is a particularly effective tool for quickly verifying whether a treatment is proceeding as planned. In the example in Figure 2e, the method according to the invention is used outside of orthodontic treatment, with the current patient's teeth being normally positioned. The optimal Topt curve corresponds to a "normal" evolution for the current patient, who is an elderly person. The Tmax and Tmin curves define the biozone boundary. The actual position x is monitored. Each measurement of the position x is compared, at the corresponding time, to the biozone. The position x moved out of the biozone at time ti, the anomaly was detected at time t2 and a treatment was applied from time t3. The modification made it possible to bring the curve Tr back into the biozone, from time t4. As is now clear, the method according to the invention makes it possible to optimize orthodontic treatment, while improving the information provided to the patient. Of course, the invention is not limited to the embodiments described and represented above. In particular, the patient is not limited to a human being. Specifically, a method for monitoring tooth positioning according to the invention can be used for another animal. The invention is not limited to the context of orthodontic treatment applied to the current patient. Prediction of the evolution of tooth position is also possible even when the patient is not undergoing any treatment, for example, for monitoring purposes.

Claims

CLAIMS 1. A method for predicting a future dental situation for a patient, referred to as the "current patient", said prediction method comprising the following steps: 1) acquisition of data, referred to as "historical data", relating to past dental situations, referred to as "historical dental situations", each experienced, at a time, referred to as the "historical time", by a patient, referred to as the "historical patient", the set of historical data relating to a historical dental situation comprising at least: - said historical time; - values ​​of context parameters of said historical time, the context parameters comprising tooth positioning parameters of said historical patient;2) acquisition, at a given moment, referred to as the "current moment", of data relating to a dental situation experienced by said current patient, referred to as the "current dental situation", the set of data relating to said current dental situation, referred to as the "current data", comprising at least: - preferably, said current moment; - values ​​of context parameters at said current moment, the context parameters comprising tooth positioning parameters of said current patient; 3) statistical analysis of said historical data and said current data, so as to predict, at least one future moment, at least one future dental situation for the current patient;4) depending on the said future dental situation, assessment of the benefit of orthodontic treatment or, if the current patient has an orthodontic appliance, referred to as "current orthodontic appliance", reassessment of the orthodontic treatment of said current patient, and, depending on said reassessment, possible modification of the orthodontic treatment of the current patient.; 2. A method according to the immediately preceding claim, wherein the context parameters at said historical moment comprise: - if the historical patient is fitted with an orthodontic appliance, referred to as the "historical orthodontic appliance", - at least one parameter of said historical orthodontic appliance relating to the class and / or conformation of the historical orthodontic appliance; and / or - at least one parameter on the environment of the orthodontic treatment to which the historical dental situation belongs, referred to as the "historical orthodontic treatment", chosen from a pain coefficient, a cost, a duration, a number of appointments with an orthodontist, and a probability of success associated with said historical orthodontic treatment; and / or - at least one functional parameter of the historical patient; and / or - at least one anatomical parameter of the historical patient other than the parameters of the positioning of his teeth;and / or - the age and / or sex and / or an identifier of said historical patient.; 3. A method according to any one of the preceding claims, wherein the context parameters at said current time comprise: - if the current patient is fitted with a current orthodontic appliance, - at least one parameter of said current orthodontic appliance relating to the class and / or conformation of the current orthodontic appliance; and / or - at least one parameter on the environment of the current orthodontic treatment to which the current dental situation belongs, referred to as "current orthodontic treatment", chosen from a pain coefficient, a cost, a duration, a number of appointments with an orthodontist and a probability of success associated with said current orthodontic treatment; and / or - at least one functional parameter of the current patient; and / or - at least one anatomical parameter of the current patient other than the parameters of the positioning of his teeth; and / or - the age and / or sex and / or an identifier of said current patient.

4. A method according to any one of the preceding claims, wherein, in step 3), several future dental situations are determined, for the same future time, and / or at least one future dental situation is determined, for several different future times.

5. A method according to any one of the preceding claims, wherein, in step 3), for at least one, preferably for each of said future dental situations, and / or for at least one, preferably for each of said future times, the following are determined: - if the current patient is fitted with a current orthodontic appliance, values, at said future time, of parameters of said current orthodontic appliance; and / or - values ​​of tooth positioning parameters of said current patient at said future time; and / or - a deviation from a dental situation constituting a target at said future time; and / or - a cost for said future dental situation to be achieved; and / or - a pain coefficient for said dental situation to be achieved;and / or - a probability that the predictions relating to said parameters of said current orthodontic appliance and / or to the positioning parameters of said teeth of said current patient, and / or to said cost and / or to said pain coefficient are in accordance with reality.; 6. A method according to any one of the preceding claims, wherein, in step 3), several of said statistical analyses are performed, modifying said future time each time, so as to predict future dental situations up to an objective future time, and thus constitute a "potential orthodontic treatment" up to said objective future time.

7. A method according to the immediately preceding claim, in which several potential orthodontic treatments are determined, by modifying a constraint each time.

8. A method according to the immediately preceding claim, wherein first and second potential orthodontic treatments are determined leading, for at least one tooth positioning parameter of the current patient, to extreme dental situations for said future objective time, an extreme dental situation corresponding to a minimum or maximum limit for said tooth positioning parameter of the current patient.

9. Method according to the immediately preceding claim, wherein the time evolution of the value of said positioning parameter for the first and second potential orthodontic treatments is represented on the same graph.

10. A method according to any one of the four immediately preceding claims, wherein the starting time of the potential orthodontic treatment(s) is the current time or an initial time corresponding to the start of a current orthodontic treatment with an orthodontic appliance worn by the current patient.

11. A method according to any one of the preceding claims, comprising a constraint optimization operation as a function of at least one optimization criterion, an operation in which a succession of steps is implemented 3) modifying each time one or more of said constraints, until an optimal dental situation is found with regard to an optimization criterion, following at least one optimization rule.

12. A method according to the immediately preceding claim, wherein the optimization criterion is chosen from the group formed by a pain coefficient, a cost, a deviation from a desired value for a positioning parameter, a duration, a number of appointments with the orthodontist, a number of aligners, a probability of success or a combination of these criteria, each criterion being able to be associated with the current orthodontic treatment or with a dental situation of said current orthodontic treatment.

13. A method according to any one of the preceding claims, wherein, in step 1) or 2), to acquire said historical or current data, respectively, the following steps are carried out: a) creation of a digital three-dimensional reference model of at least a part of an arch, preferably of at least one arch of a patient, or "initial reference model" and for each tooth, definition, from the initial reference model, of a digital three-dimensional reference model of said tooth, or "tooth model"; b) acquisition of at least one two-dimensional image of the patient's arches, called "updated image", under real acquisition conditions; c) analysis of each updated image and creation, for each updated image, of an updated map relating to discriminating information;d) optionally, determination, for each updated image, of coarse virtual acquisition conditions approximating said actual acquisition conditions; e) search, for each updated image, by deformation of the initial reference model, of an updated reference model corresponding to the positioning of the teeth during the acquisition of the updated image, the search being preferably carried out using a metaheuristic method, preferably evolutionary, preferably by simulated annealing, and f) collection of data relating to the updated reference model and relating to the current orthodontic appliance by the patient.

14. A method according to the immediately preceding claim, wherein step e) comprises the following steps: e1) defining a reference model to be tested as the initial reference model and then, e2) following the subsequent steps, testing virtual acquisition conditions with the reference model to be tested in order to closely approximate said real acquisition conditions; e21) determining virtual acquisition conditions to be tested; e22) creating a two-dimensional reference image of the reference model to be tested under said virtual acquisition conditions to be tested; e23) processing the reference image to produce at least one reference map representing, at least partially, said discriminating information;e24) comparison of the updated and reference maps so as to determine a value for a first evaluation function, said value for the first evaluation function depending on the differences between said updated and reference maps and corresponding to a decision to continue or stop the search for virtual acquisition conditions approximating said real acquisition conditions more accurately than said virtual acquisition conditions to be tested determined at the last occurrence of step e21); e25) if said value for the first evaluation function corresponds to a decision to continue said search, modification of the virtual acquisition conditions to be tested, then resumed at step e22);e3) determination of a value for a second evaluation function, said value for the second evaluation function depending on the differences between the updated and reference maps in the virtual acquisition conditions best approximating said real acquisition conditions and resulting from the last occurrence of step e2), said value for the second evaluation function corresponding to a decision to continue or stop the search for a reference model approximating the positioning of the teeth during the acquisition of the updated image more accurately than said reference model to be tested used in the last occurrence of step e2), and if said value for the second evaluation function corresponds to a decision to continue said search, modification of the reference model to be tested by moving one or more tooth models, then resumed at step e2).;