Method and device for the automatic localization of condylar points in a patient model

Abstract

A method for locating the condylar points (2) of a patient (1), comprising a step of obtaining (S1) a bi-condylar axis (3); a step of recording (S2) left and right mandibular kinematics when said patient performs at least one left (12) and right (11) lateral movement of their mandible (5); a step of determining (S3) a left and right condylar point on said axis (3), by determining a point minimizing a measure of movement in the left and right mandibular kinematics. Figure for the abstract: Fig. 2

Description

Title of the invention: Method and device for the automatic localization of condylar points in a model of a patient FIELD OF THE INVENTION

[0001] The present invention relates to an automatic method and a device for precisely determining the location of condylar points in a digital model of a patient, including the facial mass.

[0002] This determination is important in order to allow precise modeling of the patient's facial mass, and in particular of his face and, above all, of its kinematics. The term "face" can be understood here as including all the cutaneous, osteoarticular, neuromuscular parts, the dental arches, etc. of the front hemisphere of the patient's head.

[0003] For example, precise knowledge of the face and its kinematics can allow optimal adjustment of articulators or other tools used in dentistry.

[0004] A mechanical articulator has long been used as an essential tool in laboratory procedures in different fields of dentistry, such as orthodontics, denture design, maxillofacial, or orthognathic surgery, etc., to aid in both diagnosis and treatment planning. A mechanical articulator is a physical instrument that facilitates the reproduction of the relationship between the jaws and the base of the skull, as well as the mandibular articulation.

[0005] With technological advances, the articulator is moving from a mechanical device to its digital equivalent, a "virtual articulator" (VA). A virtual articulator is a computer tool that can reproduce the relationship between the jaws and simulate the movement of the jaws.

[0006] For this type of tool, it is clear that there is a need to improve knowledge of the kinematics of the patient's face, and not just their static anatomy.

[0007] Among the essential joints of the human face are the temporomandibular joint, which allows movement of the mandible.

[0008] This articulation comprises a mandibular condyle (hereinafter abbreviated to simply "condyle") which is the rounded eminence at the end of the mandibular bone and which articulates with the mandibular fossa via the articular disc.

[0009] The condyles, left and right, form a bi-condylar axis which passes through these two condyles, respectively left and right.

[0010] In the existing literature, different bi-condylar axes could be defined, for example the hinge axis, the kinematic axis, or anatomical axes.

[0011] The location of the condyles is therefore essential in order to be able to determine a bi-condylar axis allowing in particular the modeling of mandibular kinematics.

[0012] Historically, the study of mandibular kinematics is carried out by taking cutaneous points (i.e. on the surface of the face) as reference.

[0013] For example, a practitioner can, by palpation, feel the bony outgrowths corresponding to the mandibular condyles.

[0014] Other techniques for locating condyles rely on statistical conventions.

[0015] Indeed, the general location of the condyles is known, but their actual position on an individual patient may vary and the condyles may lack precise visual indicators. Thus, several definitions of the condylar point may be used.

[0016] Thus, mechanical articulators, proposed in the past, were based on distinct locations of the condyles.

[0017] [Fig.7] illustrates some locations of the condyles established by the state of the art: - Guichet Point PI, corresponding to the Denar® articulator by N. Guichet, in 1960 - Gy point if P2, corresponding to the Dentatus® articulator - Monson Point P3 - Duminil Point P4

[0018] For example, the Duminil condylar point P4 can be located 9.5 mm forward from the angle of the tragus PT and 7.5 mm vertically downward from a straight line formed between the ectocanthion PO and the angle of the tragus.

[0019] In another example, to ensure the transfer of models of the dental arches by referencing them in relation to the bi-condylar axis, systems such as facial bows with ear tips have become the norm. The positioning of these same tips in the auditory canal will make it possible to deduce the location of the condyles and therefore that of their mechanical representation during assembly on the articulators.

[0020] Yet another technique is to use pointing styluses and look for the place where it only moves in rotation during mandibular movements.

[0021] Still other methods of locating the condyles are described in the prior art. For example, we can cite the thesis of Mathilde Bapelle, “Posterior determinants of mandibular kinematics: literature review and analysis of Modjaw@ recordings”, Human Medicine and Pathology. 2020. dumas-02976829.

[0022] However, all of these methods are based on the determination of a cutaneous condylar point, i.e. located on the surface of the face. However, the condyles are subcutaneous (i.e. under the skin) and it is important to precisely locate these points in order to obtain a good model of the mandibular kinematics.

[0023] A poor approximation of a condylar point can lead to poor modeling of mandibular kinematics. This poor modeling can then lead to poor parameterization of an articulator, or any other simulation tool.

[0024] It can also induce a misinterpretation of mandibular kinematics, and thus cause the determination of dyskinesia that does not exist.

[0025] We therefore understand the need to improve the precision in determining the location of the condylar points. Summary of the invention

[0026] According to a first aspect, the invention provides a method for locating the condylar points of a patient, comprising - a step of obtaining a bi-condylar axis; - a step of recording left or right mandibular kinematics when said patient performs at least one left or right lateral movement of his mandible, - a step of determining a left, respectively right, condylar point on said axis, by determining a point minimizing a measure of movement in the left, respectively right mandibular kinematics.

[0027] Thus, the method makes it possible to determine condylar points which are not constrained by the surface of the face, but are as close as possible to the true location of the condyles.

[0028] Furthermore, as seen previously, different cutaneous condyles have been proposed in the literature. The method makes it possible to free oneself from these subjective choices and to base oneself on the patient's kinematics and not on the anatomy.

[0029] The method makes it possible to free oneself from the patient's anatomy by basing itself solely on the kinematic behavior of the mandible.

[0030] Furthermore, the method is agnostic on the determination of an initial bi-condylar axis: whatever the type of bi-condylar axis chosen, the method will make it possible to optimize the location of the condylar points on this axis.

[0031] Still other advantages will appear in the description which follows.

[0032] According to different implementations, this method may comprise one or more of the following characteristics, taken individually or in combination: - said bi-condylar axis is obtained from right and left cutaneous condylar points; - a measure of movement of a point is calculated as the sum of the movements of this point during said lateral displacement; - the said movement of a point is determined by the distance between the co- ordinates of said point in two successive samples of said mandibular kinematics; - said point minimizing said movement measurement is sought by dichotomy starting from two exploration points and comparing said movement measurement to the two exploration points and to a midpoint of said exploration points; - at each iteration of the dichotomy search, if the movement measure of said midpoint is less than the movement measure of a single exploration point, then said midpoint replaces said single exploration point;

[0033] if the movement measurement at said midpoint is less than the movement measurement of the two exploration points, then a first new midpoint is determined between a first exploration point and said midpoint and a second new midpoint between the second exploration point and said midpoint, and

[0034] if the sum of movement of one of said first new midpoint and said second new midpoint is less than the sum of movement of said midpoint, then said midpoint replaces the opposite exploration point,

[0035] otherwise, said first and second new midpoints replace said exploration points; - said exploration points include at least one cutaneous condylar point; - said condylar points are used to configure an articulator.

[0036] According to another aspect, the invention proposes a computer program comprising instructions adapted for the implementation of a method as previously described when said program is deployed on an information processing platform.

[0037] According to another aspect, the invention provides a device for locating the condylar points of a patient, comprising - means for recording left or right mandibular kinematics when said patient performs a left or right lateral movement of his mandible, - processing means for determining a left, respectively right, condylar point on a previously obtained bi-condylar axis, by determining a point minimizing a movement measurement in the left, respectively right mandibular kinematics. BRIEF DESCRIPTION OF THE FIGURES

[0038] Other characteristics and advantages of the invention will now be described in the following description of different implementations in connection with the attached figures. - [Fig.l] illustrates a face of a patient on which different elements have been positioned for understanding embodiments of the invention. - [Fig.2] diagrams a functional architecture of a device according to one embodiment of the invention. - [Fig.3] illustrates a flowchart of a method according to one embodiment of the invention. - [Fig.4] illustrates a flowchart of a step of the method according to an embodiment of the invention - [Fig.5] illustrates a step of the method according to one embodiment of the invention. - Figures 6a, 6b, 6c, 6d, 6e, 6f illustrate examples of the progress of a step of the method according to an embodiment of the invention. - [Fig.7] illustrates different condylar points proposed in the state of the art.

[0039] DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

[0040] The proposed method is based on the search for condylar points on a bi-axis condylar based on mandibular kinematics.

[0041] In [Fig.l] a face 1 of a patient is illustrated.

[0042] The mandible 5 is schematically represented in dotted lines. This articulates with the mandibular fossa at the level of the condyles 2 via the articular disc.

[0043] More precisely, the temporomandibular joint, abbreviated TMJ, is a di-arthrosis (or synovial, of the bi-condylar type) which unites the mandibular fossa of the temporal bone with the condyle of the mandible by means of a fibrocartilaginous articular disc and closed by an articular capsule.

[0044] This temporomandibular joint is described in more detail in the scientific literature to which the following Wikipedia page can form an access point:

[0045] https: / / fr.wikipedia.org / wiki / Articulation_temporo-mandibulaire

[0046] The invention aims to locate the condylar points 2.

[0047] As seen previously, it is known and customary to determine cutaneous condylar points, 4, that is to say located on the surface of the skin of the face.

[0048] As can be seen, however, in [Fig.l], there is a substantial gap between the sought condylar points 2 and the cutaneous condylar points 4. This gap is notably linked to the particular anatomy of patient 1. Furthermore, as illustrated in [Fig.7], numerous cutaneous points are described in the literature without there being any consensus.

[0049] In order to best estimate the condylar points, a device and a method are proposed, illustrated by Figures 2 and 3 respectively.

[0050] The method comprises a step of obtaining SI of a bi-condylar axis 3.

[0051] This step can be implemented in different ways and the method described does not does not depend on a particular implementation. On the contrary, whatever the bi-condylar axis provided, the method will make it possible to optimize the estimation of the location of the condylar points on this axis.

[0052] For example, cutaneous condylar points 4, right and left, can be obtained, for example by palpation. These cutaneous condylar points then make it possible to determine the bi-condylar axis 3 as being the axis passing through these two cutaneous condylar points.

[0053] Another example of implementation is described by French patent FR3027205B1. This document describes a method for modeling the mandibular kinematics of a patient.

[0054] Generally speaking, therefore, the bi-condylar axis is the axis passing through two chosen condylar points, these not necessarily being cutaneous points.

[0055] These may, for example, be condylar points obtained from specific reference parameters such as the sagittal plane, for example.

[0056] From an axis, we can choose points arbitrarily far from a center.

[0057] A step S2 consists of recording left, respectively right, mandibular kinematics when the patient performs at least one left, respectively right, lateral displacement of his mandible (5).

[0058] To do this, the device 20, illustrated in [Fig.2], may comprise a camera 21 substantially oriented towards the face 1 of the patient. This camera may be a normal optical camera, or an infrared camera. It may also be a stereoscopic camera, such as in patent FR3027205B1 for example.

[0059] Other means, in particular sensors, may also be used in addition to or instead of a camera. For example, IMU inertial markers may be positioned on the patient's face.

[0060] Preferably, patient 1 performs two distinct lateral movements, one to his right 11, one to his left 12. These movements could be repeated in order to average the acquired data and avoid aberrant measurements. Generally speaking, the lateral movement may have to be judged clinically relevant by the clinician in order to be exploited.

[0061] According to one embodiment, these lateral movements, or diduction, can be defined as mandibular movements, asymmetrical, eccentric, with a horizontal component.

[0062] In particular, these may be movements moving away from the median sagittal plane. (also called "lateralization") but also which approaches the median sagittal plane (also called "medialization"). Thus, in this embodiment, the laterality movement can account for medial displacements (on the non-working side, for example on the way out), as well as the centrifugal (outward) and centripetal (return) phases of the movement.

[0063] Through experimentation, it has been found that it is preferable to break down the movement of the mandible into two separate movements, one to the right and the other to the left. This breakdown ensures the determination of the natural, resting position of the mandible and also allows better control of the movement by the patient.

[0064] Lateral movements can go all the way without going beyond it, in order to remain in pure laterality. Other implementations are obviously possible, particularly in the case of occlusal or articular pathologies where there is no contact on the working side for example.

[0065] The patient can be guided in his movement by the instructions of a practitioner or operator standing at his side and manipulating the device 20. He can also be guided by the device 20 itself which can then have an appropriate human-machine interface to provide visual (screen, etc.) or audio instructions.

[0066] Recording mandibular kinematics includes capturing a video stream, i.e. a sequence of digital images at a predefined rate in number of images per second.

[0067] The digital images can then be processed (by the processing means 22) in order to determine a model of an area encompassing the mandible 5, associating with points of this area location sequences over time.

[0068] According to the proposed method, it is considered that the condylar points 2 sought are located on the bi-condylar axis.

[0069] Knowing the mandibular kinematics, recorded at step S2, we can therefore know the displacement of each point of this axis, over time.

[0070] Different types of systems can be used to enable the tracking of jaw movements in real time. Some have been mentioned previously, such as camera tracking from the company Modjaw, but we can also cite, for example, electromagnetic systems, systems based on ultrasound, systems using inertial sensors IMUs (for "Inertial Motion Unit" in English).

[0071] Step S3 consists of automatically determining the condylar points 2 by determining the points of the bi-condylar axis minimizing a measure of movement in the mandibular kinematics.

[0072] More precisely, step S3 can determine: - a right condylar point on the bi-condylar axis 3 by determining a mid point minimizing a measure of movement in the right mandibular kinematics, and, - a left condylar point on the bi-condylar axis 3 by determining a point minimizing a measure of movement in the left mandibular kinematics.

[0073] A movement measurement makes it possible to associate a value with all or part of the points of the bi-condylar axis. Step S3 searches for the minima taken by this value, which correspond to the two condylar points sought.

[0074] Different definitions and expressions of a measure of motion can be used.

[0075] According to one embodiment, the measurement of movement of a point can be defined as the sum of the movements of this point during the lateral displacement.

[0076] If the displacement is sampled over time, the measurement of the movement of a point can be expressed as the sum of the movements of this point between two successive samples of the mandibular kinematics. These samples can, for example, correspond to the images of the captured digital image sequence (corresponding to a video stream).

[0077] The movement of a point between two samples can be seen as the distance between the coordinates of this point in these two samples.

[0078] Thus, for any point P of the bi-condylar axis,

[0079] [Math.l] S(P)=L b ^(P,.tP t )

[0080] In this expression P; represents the 3D coordinates of point P in sample i, i.e. for example in image number i in the captured image sequence comprising n images. d() is a distance measure between two points.

[0081] [Fig.5] illustrates this step S3 and illustrates the values ​​of the movement measurement S(x) for x representing the coordinate of the point considered on the bi-condylar axis, between two points A and B located on either side of a condylar point.

[0082] During a lateral movement, the mandible performs a rotational movement around the condylar points. We can therefore assume that the movement is minimal at these points, and that the further we move away, to one side or the other, from each condylar point, the greater the movement becomes.

[0083] Also, each condylar point corresponds to the local minimum of the curve S(x) between two points A, B, framing this condylar point. In order to reduce the problem to a search for a local minimum, it is preferable to be interested in each condylar point independently of the other.

[0084] For each condylar point, we therefore seek the point with coordinates xmin located between the points A, B with respective coordinates xA, xB, having the value S(xmin) minimizing the function S(x).

[0085] In the following, we will describe the procedure for one condylar point. The procedure is obviously the same, mutatis mutandis, for the other condylar point.

[0086] The determination of the exploration points A, B can be carried out in different ways. They must both be on either side of the condylar point sought.

[0087] For example, one of the two exploration points may be a cutaneous condylar point (or any other arbitrarily chosen point). The other exploration point may be the midpoint between the two cutaneous condylar points, or any other point located on the bi-condylar axis at a predetermined distance (for example a few centimeters) in the direction of the other cutaneous condylar point (or other). This predetermined distance is chosen (by the user or automatically) so that whatever the anatomy of the patient, there is assurance that the condylar point sought is framed by the two exploration points.

[0088] Thus, the left condylar point 2 can be sought between the cutaneous condylar point 4 and, for example, the middle of the two cutaneous condylar points 4, or another point located on the bi-condylar axis 3 determined to be on the other side of the left condylar point.

[0089] According to one embodiment of the invention, step S3 can be implemented by a dichotomous method from the pair of initial exploration points A, B.

[0090] [Fig.4] represents a flowchart of a possible implementation of this dichotomous method.

[0091] Step S31 consists of determining the two initial exploration points A, B as previously described. These two exploration points define an exploration interval.

[0092] The following steps aim to update the exploration points A, B in order to iteratively reduce the interval [A; B]. This method can be interrupted when the search interval is lower than a predefined threshold determining a desired precision.

[0093] At each iteration of the dichotomous method, the movement measurement is compared at the two exploration points and at a midpoint M of said exploration points.

[0094] Step S32 comprises the determination of this midpoint M. It should be noted that the method can be generalized to any other point of the open segment ]A; B[.

[0095] Step S33 comprises comparing the motion measurements S(A), S(B), S(M) of the three points concerned.

[0096] Three situations can arise, represented by figures 6a, 6b, 6c.

[0097] If the movement measurement at the midpoint M is less than the measurement of movement of a single exploration point A, B, then this midpoint M replaces this exploration point (S34, S35);

[0098] More precisely, in a first case illustrated by [Fig.6c], if S(M)<S(B), et S(M)> S(A), then, in a step S34, the exploration point B is replaced by the midpoint M. The new exploration interval becomes [A; M] and the method loops back to step S32 for a new iteration in which the midpoint M becomes the exploration point B.

[0099] In a second case illustrated by [Fig.6b], if S(M)<S(A), et S(M)> S(B), then, in a step S35, the exploration point A is replaced by the midpoint M. The new exploration interval becomes [M; B] and the method loops back to step S32 for a new iteration in which the midpoint M becomes the exploration point A.

[0100] In a third case, illustrated by [Fig.6a], the movement measure S(M) at the midpoint (M) is less than the movement measure of the two exploration points. That is to say, we have both S(M) <S(A) et S(M)<S(B).

[0101] In this case, the method continues to step S36.

[0102] It should be noted that only these three cases are possible. By construction, in fact, it it is impossible that the movement measure at the midpoint is not less than at least the movement measure of one of the two exploration points A, B.

[0103] In this step S36, a first new midpoint MA is determined between a first exploration point A and the midpoint (M) and a second new midpoint (MB) between the second exploration point B and the midpoint M.

[0104] Again, 3 situations can arise which are tested in step S37:

[0105] If the sum of movement of one of the first new midpoint MA and the second new midpoint MB is less than the sum of movement of the midpoint M, then the midpoint M replaces the opposite exploration point (i.e. the interval centered on the new midpoint whose sum of movements is less than that of the midpoint is chosen).

[0106] More precisely, in a first case illustrated by [Fig.6f], the sum of movements S(MA) of the first new midpoint MA is less than the sum of movements S(M) of the midpoint M, then, in a step S38a, this midpoint M replaces the opposite exploration point B. For the next iteration, we consider the exploration interval [A; M] (centered on the point MA).

[0107] In a second case, illustrated by [Fig.6e], the sum of movements S(MB) of the first new midpoint MB is less than the sum of movements S(M) of the midpoint M, then, in a step S38b, this midpoint M replaces the opposite exploration point A. For the next iteration, we consider the exploration interval [M; B] (centered on the point MB).

[0108] In the third case, illustrated by [Fig.6d], the sum of movements of none of the new midpoints, MA, MB, is not less than the sum of movement of the midpoints M, then, in a step S38c, these new midpoints replace the exploration points A, B. For the next iteration, we therefore consider the exploration interval [MA; MB].

[0109] The method stops when the exploration interval (or the distance between the two exploration points) is less than a predefined threshold corresponding to a desired precision (step S39). This threshold can be defined by a user or automatically determined from the precision of the input data.

[0110] The condylar point sought can then be the midpoint of this last exploration interval.

[0111] A pseudo-code in Python language can be provided for a possible implementation of this method:

[0112] def exploration (A: point3d, B: point3d, P:mn)-> point3Dd:

[0113] while (distance(A,B) <P):

[0114] M=middle(A,B)

[0115] if (S(M)>S(A)):

[0116] B=M

[0117] elif (S(M)>S(B))

[0118] A=M

[0119] else:

[0120] MA=middle(A,M)

[0121] MB=middle(B,M)

[0122] If (S(MA) <s(m)):

[0123] B=M

[0124] Elif (S(MB) <s(m)):

[0125] A=M

[0126] else:

[0127] A=MA

[0128] B=MB

[0129] return middle(A,B)

[0130] In this pseudo-code the function "midpoint" returns the midpoint of 2 points. The points belong to a point3D type. The keywords "while", "if", "elif", "else", "return", "def" correspond to those of the Python language.

[0131] As previously stated, this same process can be iterated for the left condylar point and the right condylar point. The process is identical, only the initial exploration interval is modified (i.e. the two exploration points). Each process will thus search for the unique local minimum of the function S(X) on the segment [A; B] corresponding to the left condylar point, respectively the right condylar point, research.

[0132] The condylar points thus determined can be used for subsequent treatments.

[0133] This provides more precise modeling of mandibular kinematics that can be used in different ways.

[0134] For example, this modeling can make it possible to configure a virtual articulator 23, or any other digital simulation tool.

[0135] One of the advantages of virtual articulators compared to mechanical articulators of previous generations is that they can have greater precision because they are less constrained by physical aspects.

[0136] Indeed, the mechanical articulators are positioned at the level of the surface of the face and therefore an approximation of the condyles via the cutaneous condyles may be sufficient in this context.

[0137] But the transition to digital technology allows for greater precision in modeling, and therefore makes it necessary to better determine the different parameters allowing modeling, including therefore the condylar points.

[0138] As seen previously, the proposed method makes it possible to overcome the anatomical particularities of each patient, by allowing the determination of a bi-condylar axis based on mandibular kinematics alone. This axis is also universal in the sense that it does not depend on a choice of a particular cutaneous condylar point (Guichet point, Gy si point, Monson point, Duminil point, etc.), and is less subject to human errors when determining these points by the practitioner.

[0139] It can be validly used to allow the repositioning of other characteristic elements of the “face” or the skull, whether they are other characteristic points, or axes, planes, etc. (sagittal plane, Frankfurt plane, Camper plane, axio-orbital plane, etc.)

[0140] Of course, the present invention is not limited to the examples and the embodiment described and shown, but is defined by the claims. It is in particular susceptible of numerous variants accessible to those skilled in the art.

Claims

Claims

1. Method for locating the condylar points (2) of a patient (1), comprising - a step of obtaining (SI) a bi-condylar axis (3); - a step of recording (S2) a left, respectively right, mandibular kinematics, when said patient performs at least one left (12), respectively right (11), lateral displacement of his mandible (5), - a step of determining (S3) a left, respectively right, condylar point on said axis (3), by determining a point minimizing a measure of movement in the left, respectively right, mandibular kinematics.

2. Method according to the preceding claim, in which said bi-condylar axis is obtained from right and left cutaneous condylar points (4).

3. Method according to one of the preceding claims in which a measurement of movement of a point is calculated as the sum of the movements of this point during said lateral displacement.

4. Method according to the preceding claim, wherein said movement of a point is determined by the distance between the coordinates of said point in two successive samples of said mandibular kinematics.

5. Method according to one of the preceding claims, in which said point minimizing said movement measurement is sought by dichotomy starting from two exploration points and comparing said movement measurement at the two exploration points and at a midpoint of said exploration points.

6. Method according to the preceding claim, in which, at each iteration of the dichotomy search, - if the movement measurement at said midpoint (M) is less than the movement measurement of a single exploration point (A, B), then said midpoint (M) replaces said single exploration point (S34, S35); - if the movement measurement at said midpoint (M) is less than the movement measurement of the two points exploration, then, a first new midpoint (MA) is determined (S36) between a first exploration point (A) and said midpoint (M) and a second new midpoint (MB) between the second exploration point (B) and said midpoint (M), and - if the sum of movement of one of said first new midpoint (MA) and said second new midpoint (MB) is less than the sum of movement of said midpoint (M), then said midpoint (M) replaces the opposite exploration point (B or A, respectively), - otherwise, said first and second new midpoints (MA, MB) replace said exploration points (A and B, respectively).

7. Method according to one of claims 5 or 6, wherein said exploration points comprise at least one cutaneous condylar point.

8. Method according to one of the preceding claims, wherein said condylar points (2) are used to parameterize an articulator (23).

9. Computer program comprising instructions adapted for implementing a method according to one of the preceding claims when said program is deployed on an information processing platform.

10. Device for locating the condylar points (2) of a patient (1), comprising - means (21) for recording left, respectively right, mandibular kinematics, when said patient performs a left (12), respectively right (11), lateral displacement of his mandible (5), - processing means (22) for determining a left, respectively right, condylar point on a previously obtained bi-condylar axis (3), by determining a point minimizing a measure of movement in the left, respectively right, mandibular kinematics.

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