A digital method and system for determining jaw relationships

Abstract

The application discloses a kind of digital determination method and system of jaw position relation, it is related to stomatology digital technology field, comprising: obtaining the three-dimensional data of patient and mandibular three-dimensional motion trajectory;According to three-dimensional data and mandibular three-dimensional motion trajectory, reference coordinate system is constructed;Simulated three-dimensional motion trajectory is constructed based on mandibular three-dimensional motion trajectory, and simulated plane is constructed based on three-dimensional data and reference coordinate system;The intersection of simulated three-dimensional motion trajectory and simulated plane is calculated;According to the density distribution of intersection point, determine the optimal point, and obtain the position of mandible according to the three-dimensional reconstruction of optimal point.The application applies three-dimensional data acquisition, three-dimensional data registration and fusion technology, without the assistance of intraoral physical support, occlusal record material or old denture, through individual mandibular three-dimensional motion trajectory feature analysis, the position relationship of three-dimensional reconstruction edentulous maxilla and mandible of patient is realized, and the direct digital determination of the jaw position relationship of edentulous patient is realized.

Description

Technical Field

[0001] This invention relates to the field of digital technology in oral medicine, and more specifically to a digital method and system for measuring jaw position relationships. Background Technology

[0002] Currently, it is routinely used in clinical practice. Recording the jaw position relationship in edentulous patients is a crucial step in the fabrication of complete dentures, directly impacting their success. Determining and recording the jaw position relationship involves two steps: first, determining the vertical and horizontal distances; second, recording the jaw position relationship using occlusal recording material. However, the jaw position relationship recorded after the occlusal recording material has hardened may not be the same as the one determined by the dentist. This could be due to uneven occlusal contact between the upper and lower occlusal pads causing mandibular occlusal deviation, or the patient developing a protruding bite due to prolonged tooth loss. If the jaw position record deviates significantly, it needs to be re-determined and recorded, a complex process dependent on the dentist's experience. After completing and verifying the jaw position record, the positional relationship of the upper and lower jaws within the edentulous patient's mouth can be transferred to the dental laboratory for the design and fabrication of the complete denture. The determination and recording of the jaw position relationship in conventional complete dentures relies on the clinician's clinical skills, patient guidance and control, and the dimensional stability of the occlusal recording material. The development of clinical digital technologies and intelligent diagnostic and treatment equipment aims to reduce clinical procedures and reliance on experience, thereby providing patients with efficient, precise, and automated dental restoration treatments. With further research, the determination and recording of jaw relationships are expected to break through conventional methods, enabling direct digital measurement of jaw relationships.

[0003] Electronic Gothic arches can determine the centric relationship using sensors and display it on a computer screen, but clinicians still need to rely on occlusal recording materials and the position displayed on the computer screen to assist in recording the jaw relationship. The ARCUSdigma mandibular motion tracker can record protrusion and lateral movements, automatically calculate and analyze the centric relationship position, and display it on the screen to assist doctors in intraoral procedures. The creation of occlusal records for edentulous patients. In the Jaw Relation module of the Zebirs electronic facebow, by analyzing the trajectories of the patient's multiple opening and closing movements, protrusion movements, and lateral movements, the system can automatically determine the position with the highest repeatability of mandibular movements, and then record this position using occlusal recording materials. Wenjun She et al. used JT-3D to study the habitual opening and closing movement trajectories of edentulous patients, determining the location of the trajectory point 2 mm above the sagittal plane in the resting jaw position, and using occlusal recording materials to refer to this position for auxiliary analysis. Record the positional relationship between the upper and lower jaws within the mouth.

[0004] In recent years, Lee et al. attached tracking targets to the upper and lower anterior teeth to record the mandibular opening and closing motion trajectories of patients with severe wear, analyzed the changes in vertical distance, and derived the mandibular positional relationship with appropriate vertical distance. However, this study did not investigate the horizontal relationship. Han et al. used an optical scanner to obtain three-dimensional data of patients' old dentures, attached tracking targets to the old dentures to record mandibular movement trajectory data, and determined the jaw positional relationship with appropriate restoration space based on the obtained opening and closing motion trajectories. Based on the reconstructed jaw positional relationship, they designed and manufactured complete dentures. However, this study could only be conducted on patients with old dentures. For patients without old dentures, the relevant methods need further research.

[0005] In summary, existing conventional methods are time-consuming, labor-intensive, and rely heavily on the doctor's experience; however, related digital methods still require intraoral assistance. Occlusal records, bite data, or old dentures are used to record jaw relationships. Currently, there is no technology that uses mandibular motion trajectory analysis to directly and digitally determine jaw relationships in patients with severe wear or edentulous jaws.

[0006] Therefore, a method for direct digital measurement of jaw relationships in patients with severe wear or edentulous jaws is proposed, without the need for intraoral application. Using dentures, occlusal recording materials, or old dentures, achieving direct digital measurement of jaw position relationships is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0007] In view of this, the present invention provides a digital method and system for determining jaw position relationship. It utilizes intraoral 3D scanning or model 3D scanning, facial 3D scanning, and a mandibular motion trajectory recording device to construct a 3D virtual patient. Based on the physiological characteristics of individual mandibular motion trajectories, it automatically reconstructs the jaw position relationship of severely worn patients or edentulous patients in 3D, simplifying the clinical operation process and reducing reliance on physician experience. To achieve the above objectives, the present invention adopts the following technical solution:

[0008] A novel method for direct digital determination of jaw relationships in patients with severe wear or edentulous jaws, without the need for intraoral application. Using occlusal recording materials or old dentures, a three-dimensional virtual patient is constructed by applying three-dimensional data acquisition, three-dimensional data registration and fusion technology. Then, the physiological characteristics of the individual mandibular movement trajectory of the virtual patient are analyzed, and the position with the highest repeatability of mandibular movement is directly reconstructed in three dimensions, realizing the direct digital measurement of jaw position relationship.

[0009] A digital method for determining jaw position relationship includes:

[0010] Acquire the patient's three-dimensional data and the three-dimensional motion trajectory of the mandible;

[0011] A reference coordinate system is constructed based on the three-dimensional data and the three-dimensional motion trajectory of the mandible.

[0012] A simulated three-dimensional motion trajectory is constructed based on the three-dimensional motion trajectory of the mandible, and a simulated plane is constructed based on the three-dimensional data and the reference coordinate system.

[0013] Calculate the intersection point of the simulated three-dimensional motion trajectory and the simulated plane;

[0014] The optimal point is determined based on the density distribution of the intersection points, and the position of the mandible is obtained by three-dimensional reconstruction based on the optimal point.

[0015] Optionally, the specific steps for acquiring the patient's three-dimensional data are as follows:

[0016] Three-dimensional data of the patient's upper and lower dentitions or the alveolar ridges of the upper and lower jaws of edentulous patients are obtained using an intraoral 3D scanner or a model 3D scanner; three-dimensional facial images of the patient in a resting jaw position and three-dimensional facial images exposing the anterior mandibular dentition or alveolar ridge are obtained using a facial 3D scanner.

[0017] Optionally, the specific steps for obtaining the three-dimensional motion trajectory of the mandible are as follows:

[0018] The tracking target was attached to the mucosa of the upper and lower dentition or alveolar ridges. The positional relationship between the tracking target and the upper and lower dentition or mucosa was recorded before the patient exercised. The three-dimensional movement trajectory of the mandible during the patient's small-range opening and closing movements and left and right lateral movements was then recorded.

[0019] Optionally, the specific steps for constructing the reference coordinate system are as follows:

[0020] (1) Register the patient's three-dimensional data and the mandibular three-dimensional motion trajectory to the same coordinate system to construct a virtual patient;

[0021] (2) Determine the midsagittal plane based on the soft tissue nasal root point, nasal tip point, nasal infranasal point, upper lip protrusion point, left corner of mouth point, right corner of mouth point, left nasal ala point, right nasal ala point, left tragus point, right tragus point, left lateral canthus point and right lateral canthus point in the three-dimensional data of the virtual patient;

[0022] (3) Construct a reference point for the anterior mandible based on the intersection of the midsagittal plane and the incisal edge of the mandibular anterior teeth or the crest of the mandibular alveolar ridge in the three-dimensional data of the virtual patient;

[0023] (4) The horizontal line is defined as the line connecting the pupils on both sides or the line connecting the outer canthi on both sides, and the mandibular reference plane is the plane that passes through the anterior reference point of the mandible and is parallel to the nasal ala-tragus line and the horizontal line.

[0024] (5) Establish a coordinate system with the intersection of the midsagittal plane and the incisal edge of the upper anterior teeth or the crest of the maxillary alveolar ridge as the origin. The Z-axis is parallel to the horizontal line, and the XOZ plane is parallel to the mandibular reference plane. The coordinate system is determined based on the origin, Z-axis and XOZ plane, with forward, right and upward as positive directions.

[0025] Optionally, the specific steps for constructing the simulated three-dimensional motion trajectory are as follows:

[0026] Based on the three-dimensional motion trajectory of the mandible, the three-dimensional motion trajectory of the reference point at the front of the mandible is calculated as the simulated three-dimensional motion trajectory.

[0027] Optionally, the specific steps for constructing the simulated plane are as follows:

[0028] Construct a plane parallel to the XOZ plane and located 2mm or 3mm above the reference point at the front of the mandible. This plane is a simulated plane, and the Y-axis position of this plane is the position of the vertical distance. The simulated plane is the plane where the vertical distance is located.

[0029] Optionally, the specific steps for determining the optimal point based on the density distribution of the intersection points and performing three-dimensional reconstruction based on the optimal point to obtain the mandibular position are as follows:

[0030] Construct the intersection points of the simulated 3D motion trajectory and the simulated plane, and calculate the density distribution of all intersection points;

[0031] Among all intersection points, the position with the highest density represents the position with the highest repetitive mandibular movement. This position represents the horizontal positional relationship. Based on the coordinates of the mandibular tracking target corresponding to this point, the position of the mandible is reconstructed in three dimensions to obtain the jaw position relationship.

[0032] Optionally, a digital measurement system for jaw position relationships includes:

[0033] Acquisition module: Acquires the patient's 3D data and the 3D motion trajectory of the mandible;

[0034] Construction Module: Construct a reference coordinate system based on 3D data and the 3D motion trajectory of the mandible; construct a simulated 3D motion trajectory based on the 3D motion trajectory of the mandible; and construct a simulated plane based on the 3D data and the reference coordinate system.

[0035] Processing module: Calculates the intersection points of the simulated 3D motion trajectory and the simulated plane;

[0036] Reconstruction module: Determine the optimal point based on the density distribution of the intersection points, and perform three-dimensional reconstruction based on the optimal point to obtain the position of the mandible.

[0037] As can be seen from the above technical solution, compared with the prior art, the present invention discloses a digital measurement method and system for jaw position relationship, which has the following beneficial effects:

[0038] The method of the present invention involves directly attaching the adhesive target to the upper and lower teeth or gums, eliminating the need for any physical objects inside the mouth.

[0039] A digital method for creating a three-dimensional virtual patient was constructed by applying three-dimensional data acquisition, registration, and fusion techniques. This method then eliminates the need for an intraoral physical patient. With the aid of braces, occlusal recording materials, or old dentures, the positional relationship between the upper and lower jaws of edentulous patients can be reconstructed in three dimensions by analyzing the three-dimensional motion trajectory characteristics of the individual mandible, thus realizing the direct digital measurement of the jaw position relationship of edentulous patients. Attached Figure Description

[0040] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0041] Figure 1 This is a model diagram of the maxilla.

[0042] Figure 2 This is a model diagram of the mandible.

[0043] Figure 3 This is a three-dimensional facial image of the jaw in a resting position.

[0044] Figure 4 Three-dimensional facial scans to expose the lower anterior teeth or alveolar ridge.

[0045] Figure 5 This is a diagram showing the movement trajectories of the upper and lower jaws.

[0046] Figure 6 This is a diagram of a virtual patient.

[0047] Figure 7 This is a schematic diagram of the horizontal line and the nasal ala-tragus line.

[0048] Figure 8 A schematic diagram of the constructed coordinate system.

[0049] Figure 9 This is a schematic diagram for determining the vertical distance.

[0050] Figure 10 This is a schematic diagram of the density distribution at the intersection points.

[0051] Figure 11 This is a schematic diagram of jaw positional relationships determined directly from the point with the highest density.

[0052] Figure 12 This is a schematic diagram of a digital method for determining jaw position relationships. Detailed Implementation

[0053] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0054] This invention discloses a digital method for determining jaw position relationship, comprising:

[0055] Acquire the patient's three-dimensional data and the three-dimensional motion trajectory of the mandible;

[0056] A reference coordinate system is constructed based on the three-dimensional data and the three-dimensional motion trajectory of the mandible.

[0057] A simulated three-dimensional motion trajectory is constructed based on the three-dimensional motion trajectory of the mandible, and a simulated plane is constructed based on the three-dimensional data and the reference coordinate system.

[0058] Calculate the intersection point of the simulated three-dimensional motion trajectory and the simulated plane;

[0059] The optimal point is determined based on the density distribution of the intersection points, and the position of the mandible is obtained by three-dimensional reconstruction based on the optimal point.

[0060] In a specific implementation,

[0061] S1: As Figure 1 - Figure 2 As shown, a 3D model scanner was used to obtain maxillary and mandibular model data of edentulous patients.

[0062] S2: As Figure 3 As shown, a 3D facial scanner was used to obtain a 3D facial image of the patient in a resting jaw position.

[0063] S3: As Figure 4 As shown, when the patient is in a resting jaw position, gently pull or roll the lower lip to expose the lower anterior teeth or alveolar ridge, and then perform a three-dimensional facial scan again.

[0064] S4: As Figure 5 As shown, the target point is attached to the mucosa of the upper and lower dentition or alveolar ridges. The upper lip is pulled upward and the lower lip is pulled downward. The upward and downward pulling does not affect the opening and closing movements. The positional relationship between the target point and the upper and lower dentition or mucosa is recorded before the patient moves. Then, the patient is instructed to perform small-range opening and closing movements and left and right lateral movements. The three-dimensional movement trajectory of the mandible is recorded.

[0065] S5: As Figure 6As shown, based on the facial and dental data obtained in S3, the data obtained in S1, S2 and S4 are registered to the same coordinate system to construct a three-dimensional virtual patient that integrates intraoral dental or alveolar ridge three-dimensional data, facial three-dimensional data and mandibular three-dimensional motion trajectory data.

[0066] S6: Based on the data from the virtual patient obtained in S2, construct the midsagittal plane. The midsagittal plane is determined based on 12 reference points: the soft tissue nasal root point, nasal tip point, subnasal point, upper lip protrusion point, left corner of mouth point, right corner of mouth point, left nasal alar point, right nasal alar point, left tragus point, right tragus point, left lateral canthus point, and right lateral canthus point.

[0067] S7: As Figure 7 As shown, a reference point and a reference plane for the anterior mandible are constructed. The reference point for the anterior mandible is the intersection of the midsagittal plane determined in S6 and the incisal edge of the mandibular anterior teeth or the crest line of the mandibular alveolar ridge in the data obtained in S1. The reference plane for the mandible is a plane that passes through the reference point for the anterior mandible and is parallel to the nasal ala-tragus line and the horizontal line. The horizontal line is the line connecting the two outer canthi points.

[0068] S8, such as Figure 8 As shown, establish a coordinate system: the origin is the intersection of the midsagittal plane and the incisal edge of the upper anterior teeth or the crest of the maxillary alveolar ridge, the Z-axis is parallel to the horizontal line, and the XOZ plane is parallel to the mandibular reference plane. The coordinate system is determined based on the aforementioned origin, X-axis and XOZ plane, with forward, right and upward being the positive directions.

[0069] S9: As Figure 9 - Figure 10 As shown, the three-dimensional motion trajectory of the mandibular anterior reference point is calculated based on the individual's mandibular three-dimensional motion trajectory. A plane parallel to the XOZ plane and located 2mm or 3mm above the mandibular anterior reference point is constructed; the Y-axis position of this plane is the location of the vertical distance. The intersection points of the mandibular anterior reference point's three-dimensional motion trajectory and the plane containing the vertical distance are constructed, and the density distribution of all intersection points is calculated.

[0070] like Figure 11 As shown, the position with the highest intersection density represents the position with the highest repetitive mandibular movement. This position represents the horizontal positional relationship. Based on the coordinates of the mandibular tracking target point corresponding to this point, the position of the mandible is reconstructed in three dimensions, realizing the direct digital measurement of the jaw position relationship.

[0071] Furthermore, a digital measurement system for jaw position relationships includes:

[0072] Acquisition module: Acquires the patient's 3D data and the 3D motion trajectory of the mandible;

[0073] Construction Module: Construct a reference coordinate system based on 3D data and the 3D motion trajectory of the mandible; construct a simulated 3D motion trajectory based on the 3D motion trajectory of the mandible; and construct a simulated plane based on the 3D data and the reference coordinate system.

[0074] Processing module: Calculates the intersection points of the simulated 3D motion trajectory and the simulated plane;

[0075] Reconstruction module: Determine the optimal point based on the density distribution of the intersection points, and perform three-dimensional reconstruction based on the optimal point to obtain the position of the mandible.

[0076] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0077] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A digital method for determining jaw position relationship, characterized in that, include: Acquire the patient's three-dimensional data and the three-dimensional motion trajectory of the mandible; A reference coordinate system is constructed based on the three-dimensional data and the three-dimensional motion trajectory of the mandible. The specific steps for constructing the reference coordinate system are as follows: (1) Register the patient's three-dimensional data and the mandibular three-dimensional motion trajectory to the same coordinate system to construct a virtual patient; (2) Determine the midsagittal plane based on the soft tissue nasal root point, nasal tip point, nasal infranasal point, upper lip protrusion point, left corner of mouth point, right corner of mouth point, left nasal alar point, right nasal alar point, left tragus point, right tragus point, left lateral canthus point and right lateral canthus point in the three-dimensional data of the virtual patient; (3) Construct a reference point for the anterior part of the mandible based on the intersection of the midsagittal plane and the incisal edge of the mandibular anterior teeth or the crest of the mandibular alveolar ridge in the three-dimensional data of the virtual patient; (4) The horizontal line is defined as the line connecting the pupils on both sides or the line connecting the outer canthi on both sides, and the mandibular reference plane is the plane that passes through the anterior reference point of the mandible and is parallel to the nasal ala-tragus line and the horizontal line. (5) Establish a coordinate system with the intersection of the midsagittal plane and the incisal edge of the upper anterior teeth or the crest of the maxillary alveolar ridge as the origin. The Z-axis is parallel to the horizontal line, and the XOZ plane is parallel to the mandibular reference plane. The coordinate system is determined based on the origin, Z-axis and XOZ plane, with forward, right and upward as positive directions. A simulated three-dimensional motion trajectory is constructed based on the three-dimensional motion trajectory of the mandible, and a simulated plane is constructed based on the three-dimensional data and the reference coordinate system. The specific steps for constructing the simulated three-dimensional motion trajectory are as follows: Based on the three-dimensional motion trajectory of the mandible, the three-dimensional motion trajectory of the reference point at the front of the mandible is calculated as the simulated three-dimensional motion trajectory. The specific steps for constructing the simulated plane are as follows: Construct a plane parallel to the XOZ plane and located 2mm or 3mm above the reference point at the front of the mandible. This plane is a simulated plane, and the Y-axis position of this plane is the position of the vertical distance. The simulated plane is the plane where the vertical distance is located. Calculate the intersection point of the simulated three-dimensional motion trajectory and the simulated plane; The optimal point is determined based on the density distribution of the intersection points, and the mandibular position is obtained by three-dimensional reconstruction based on the optimal point. The specific steps for determining the optimal point based on the density distribution of the intersection points, and then performing three-dimensional reconstruction based on the optimal point to obtain the mandibular position are as follows: Construct the intersection points of the simulated 3D motion trajectory and the simulated plane, and calculate the density distribution of all intersection points; Among all intersection points, the position with the highest density represents the position with the highest repetitive mandibular movement. This position represents the horizontal positional relationship. Based on the coordinates of the mandibular tracking target corresponding to this position, the position of the mandible is reconstructed in three dimensions to obtain the jaw position relationship.

2. The method for digitally determining jaw position relationship according to claim 1, characterized in that, The specific steps for obtaining the patient's three-dimensional data are as follows: Three-dimensional data of the patient's upper and lower dentitions or the alveolar ridges of the upper and lower jaws of edentulous patients are obtained using an intraoral 3D scanner or a model 3D scanner; three-dimensional facial images of the patient in a resting jaw position and three-dimensional facial images exposing the anterior mandibular dentition or alveolar ridge are obtained using a facial 3D scanner.

3. The method for digitally determining jaw position relationship according to claim 1, characterized in that, The specific steps for obtaining the three-dimensional motion trajectory of the mandible are as follows: The tracking target was attached to the mucosa of the upper and lower dentition or alveolar ridges. The positional relationship between the tracking target and the upper and lower dentition or mucosa was recorded before the patient exercised. The three-dimensional movement trajectory of the mandible during the patient's small-range opening and closing movements and left and right lateral movements was then recorded.

4. A digital measurement system for jaw position relationship, characterized in that, include: Acquisition module: Acquires the patient's 3D data and the 3D motion trajectory of the mandible; Construction module: Constructs a reference coordinate system based on 3D data and the 3D motion trajectory of the mandible; A simulated three-dimensional motion trajectory is constructed based on the three-dimensional motion trajectory of the mandible, and a simulated plane is constructed based on the three-dimensional data and the reference coordinate system. The specific steps for constructing the reference coordinate system are as follows: (1) Register the patient's three-dimensional data and the mandibular three-dimensional motion trajectory to the same coordinate system to construct a virtual patient; (2) Determine the midsagittal plane based on the soft tissue nasal root point, nasal tip point, nasal infranasal point, upper lip protrusion point, left corner of mouth point, right corner of mouth point, left nasal alar point, right nasal alar point, left tragus point, right tragus point, left lateral canthus point and right lateral canthus point in the three-dimensional data of the virtual patient; (3) Construct a reference point for the anterior part of the mandible based on the intersection of the midsagittal plane and the incisal edge of the mandibular anterior teeth or the crest of the mandibular alveolar ridge in the three-dimensional data of the virtual patient; (4) The horizontal line is defined as the line connecting the pupils on both sides or the line connecting the outer canthi on both sides, and the mandibular reference plane is the plane that passes through the anterior reference point of the mandible and is parallel to the nasal ala-tragus line and the horizontal line. (5) Establish a coordinate system with the intersection of the midsagittal plane and the incisal edge of the upper anterior teeth or the crest of the maxillary alveolar ridge as the origin. The Z-axis is parallel to the horizontal line, and the XOZ plane is parallel to the mandibular reference plane. The coordinate system is determined based on the origin, Z-axis and XOZ plane, with forward, right and upward as positive directions. The specific steps for constructing the simulated three-dimensional motion trajectory are as follows: Based on the three-dimensional motion trajectory of the mandible, the three-dimensional motion trajectory of the reference point at the front of the mandible is calculated as the simulated three-dimensional motion trajectory. The specific steps for constructing the simulated plane are as follows: Construct a plane parallel to the XOZ plane and located 2mm or 3mm above the reference point at the front of the mandible. This plane is a simulated plane, and the Y-axis position of this plane is the position of the vertical distance. The simulated plane is the plane where the vertical distance is located. Processing module: Calculates the intersection points of the simulated 3D motion trajectory and the simulated plane; Reconstruction module: Determines the optimal point based on the density distribution of the intersection points, and performs three-dimensional reconstruction based on the optimal point to obtain the mandibular position; The specific steps for determining the optimal point based on the density distribution of the intersection points, and then performing three-dimensional reconstruction based on the optimal point to obtain the mandibular position are as follows: Construct the intersection points of the simulated 3D motion trajectory and the simulated plane, and calculate the density distribution of all intersection points; Among all intersection points, the position with the highest density represents the position with the highest repetitive mandibular movement. This position represents the horizontal positional relationship. Based on the coordinates of the mandibular tracking target corresponding to this position, the position of the mandible is reconstructed in three dimensions to obtain the jaw position relationship.

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