A method for positioning a maxillary anterior tooth opening hole based on multi-section feature point fitting

Abstract

The patent discloses a kind of maxillary anterior tooth opening marrow hole positioning method based on multi-section feature point fitting, belong to root canal treatment technical field, the present application proposes a kind of maxillary anterior tooth opening marrow hole positioning method based on multi-section feature point fitting, to solve the lack of current root canal treatment technique about the estimation method of pulp cavity entering position and hole shape;Technical points are as follows: establish maxillary anterior tooth bounding box coordinate system, carry out section division to bounding box, and judge whether it meets the requirement, and carry out curve fitting on the outer contour of root canal and the outer contour of dental crown on each section, determine feature point, then carry out path fitting to these feature points;This method can effectively solve the difficulty of maxillary anterior tooth opening marrow hole shape and position determination in root canal treatment process, improve the accuracy and success rate of root canal treatment.

Description

Technical Field

[0001] This invention patent relates to a method for locating the access cavity of maxillary anterior teeth based on fitting of multi-faceted feature points, belonging to the field of root canal treatment technology. Background Technology

[0002] Pulp access is the first step in root canal treatment, and a well-designed access cavity is the technical foundation for successful root canal treatment. Currently, when designing the access cavity for maxillary anterior teeth, dentists determine the shape of the access cavity by observing the projection of the pulp cavity onto the coronal plane and the projection positions of the pulp horns or the orifices of each root canal. The cavity is then drilled perpendicularly to the lingual surface, from the center of the lingual fossa near the lingual protuberance, and expanded parallel to the long axis of the tooth. This undoubtedly places high demands on the dentist's clinical experience and tactile sensitivity. If the access cavity is too small or its location is inappropriate, it will prevent the complete exposure of all root canal orifices and the establishment of a straight pathway for instruments to reach the orifices. If the access cavity is too large, it will cause excessive damage to tooth structure, thereby reducing the tooth's resistance. Therefore, determining the location and shape of the access cavity for maxillary anterior teeth is crucial.

[0003] For maxillary anterior teeth, dentists usually locate and determine the position of the coronal entrance before surgery by projecting the anatomical structure of the pulp chamber onto the surface to be accessed. The surgeon must carefully observe and evaluate the morphology of the pulp chamber and the location of the root canal orifices on the X-ray. However, in clinical practice, the surgeon's operation is sometimes difficult and is often affected by the following factors: if the opening is too small, the pulp horn will not be sufficiently exposed, leaving pulp behind; if the opening is too large, the sidewall of the pulp chamber will be hollowed out into a "beer barrel" shape, causing excessive loss of tooth tissue, thereby reducing the tooth's resistance and causing the treatment to fail to achieve the expected results. Summary of the Invention

[0004] To address the aforementioned issues, this invention proposes a method for locating the pulp chamber opening in maxillary anterior teeth based on fitting multi-faceted feature points, thus solving the current lack of estimation methods for the entry point location and cavity shape in the field of root canal treatment.

[0005] A method for locating the access cavity of maxillary anterior teeth based on fitting of multi-section feature points, the specific implementation process of the method is as follows:

[0006] Step 1: Establishing the coordinate system of the maxillary anterior teeth surrounding box:

[0007] First, a 3D reconstruction model is obtained based on the CT data of the maxillary anterior teeth. The 3D reconstruction model is then imported into reverse engineering software to generate a world coordinate system. The point cloud data of the maxillary anterior tooth outer contour and pulp chamber were obtained; these data were then imported into the slicing tool software, and the data were processed in the world coordinate system of the slicing tool software. In the middle, establish the maxillary anterior teeth Type of enclosure ,noodle Coordinate plane of the world coordinate system in slicing software parallel, plane With coordinate plane parallel, plane With coordinate plane Parallel; in the world coordinate system of the slicing tool Above, establish the coordinate system of the maxillary anterior teeth bounding box. ,point The origin of the coordinate system for the maxillary anterior bounding box is [the point where the coordinate system is defined]. The edges of the maxillary anterior bounding box [are defined]. Defined as a bounding box coordinate system Axis, edge Defined as a bounding box coordinate system Axis, edge Defined as a bounding box coordinate system axis;

[0008] Step 2: Divide the maxillary anterior teeth surround box into sections:

[0009] The access cavity shapes for the maxillary anterior teeth are either rounded triangles (incisors) or elliptical (canines). Based on the shape of the cavity, the surrounding box of the maxillary anterior teeth is segmented; in the world coordinate system of the slicing tool... In the middle, the coordinates are Define the bounding box coordinate plane The bounding box coordinate system is defined using the reference plane for segmenting the bounding box section of the maxillary anterior teeth. The positive axis is the direction in which the bounding box is segmented, represented by a direction vector. ;Based on the reference plane Towards The plane is divided by translation in the direction, and the division distance is denoted as . ,in The range of values ​​is The newly segmented bounding box coordinate plane is denoted as The number of plane segments is ,in , ; The value is determined by the segmentation distance. Determined by the size of the medullary cavity;

[0010] Step 3: Determine if the cross-section of the maxillary anterior teeth surround box meets the requirements:

[0011] Set and adjust The value;

[0012] Specifically:

[0013] By observing the morphology of the pulp chamber and root canals of the maxillary anterior teeth, we can determine... The initial value;

[0014] Determine whether the first section of the maxillary anterior tooth surround box meets the requirements;

[0015] Determine the coordinate plane of the first maxillary anterior tooth bounding box. Check if the outer contour of the root canal is displayed. If it meets the requirements, proceed to step four.

[0016] If the coordinate plane of the first maxillary anterior teeth surround box If the outer contour of the root canal is not shown, proceed to step three. ;

[0017] Step 4: Perform curve fitting on the outer contours of the root canals and crowns in the first coordinate plane of the maxillary anterior tooth surround box:

[0018] when At that time, in the coordinate plane of the maxillary anterior teeth surrounding box In the process, fitting points are selected for the outer contour of the root canal. The scatter plot of the fitting points has two lines, approximating two curves; the distance from the curve is defined as... The curves that are close to the axis are The other one is The polynomials of the two curves are solved as follows:

[0019] Regarding the first point curve:

[0020] The coordinates of the fitting point are ;definition The polynomial of degree is , , for The fitting coefficients of the polynomial of degree 1; to make the fitted curve more accurate, the sum of squared deviations is defined as... Sum of squared deviations The minimum curve fit is the most accurate. The expression is:

[0021] (1)

[0022] Find the minimum sum of squared deviations :make ,have:

[0023] (2)

[0024] Solving , The polynomial of the curve is , ;

[0025] Similarly, the second curve is obtained. The fitting coefficient is , The polynomial of the curve is , ;

[0026] when At that time, in the coordinate plane of the maxillary anterior teeth surrounding box In the process, fitting points are selected for the outer contour of the tooth crown. The scatter plot of the fitting points has one line, and the curve is defined as follows. Solve for the polynomial of the curve, the solution method and the curve , The solution is the same;

[0027] Solving for the curve The fitting coefficient is , The polynomial of the curve is , ;

[0028] In the coordinate plane of the maxillary anterior teeth surrounding box middle, , and The polynomials of the curves are as follows:

[0029] , ;

[0030] , ;

[0031] , ;

[0032] Step 5: Determine the feature points in the first coordinate plane of the maxillary anterior teeth enclosure box:

[0033] when At that time, in the first coordinate plane of the section segmentation In the middle, two curves fitted by the outer contour of the root canal , Curve fitted to the outer contour of the crown Find two feature points:

[0034] In the coordinate plane of the maxillary anterior teeth surrounding box middle , and The polynomials of the curves are as follows:

[0035] , ;

[0036] , ;

[0037] , ;

[0038] curve and curve Determine the coordinate plane The first characteristic point is determined by the nonlinear equation system (3):

[0039] (3)

[0040] Solve for characteristic points, defined by the curve and curve The solved feature points are Similarly:

[0041] curve and curve Determine the coordinate plane The second characteristic point is determined by the nonlinear equation system (4):

[0042] (4)

[0043] Solve for characteristic points, defined by the curve and curve The solved feature points are ;

[0044] Step 6: In the bounding box coordinate plane Curve fitting and feature point determination are performed in the following ways:

[0045] In the maxillary anterior teeth surround box Curve fitting is performed on the outer contours of the root canal and the outer contours of the crown in a coordinate plane:

[0046] In the coordinate plane of the maxillary anterior teeth surrounding box In this process, curve fitting is performed on the outer contours of the root canal and the outer contours of the crown, and then compared with the coordinate plane. The method for finding the coordinate plane of the maxillary anterior teeth enclosure is the same. middle , and The polynomials of the curves are as follows:

[0047] , ;

[0048] , ;

[0049] , ;

[0050] In the coordinate plane of the maxillary anterior teeth surrounding box Determine feature points in the middle:

[0051] In the coordinate plane of the maxillary anterior teeth surrounding box middle , and The polynomials of the curves are as follows:

[0052] , ;

[0053] , ;

[0054] , ;

[0055] curve and curve Determine the coordinate plane The first characteristic point is determined by the nonlinear equation system (5):

[0056] (5)

[0057] Solve for characteristic points, defined by the curve and curve The solved feature points are Similarly:

[0058] curve and curve Determine the coordinate plane The second characteristic point is determined by the nonlinear equation system (6):

[0059] (6)

[0060] Solve for characteristic points, defined by the curve and curve The solved feature points are ;

[0061] Determine the first segment of the segment. The coordinate plane, at the coordinate plane, Has the curve fitting and feature point determination of the root canal outer contour and crown outer contour on the coordinate plane been completed? If the condition is met, proceed to step seven; otherwise, return to step four.

[0062] Step 7: For the segmented... Path fitting is performed on feature points on the bounding box coordinate plane:

[0063] In the coronal preparation of the pulp chamber, the outline of the entrance cavity is the projection of the pulp chamber shape onto the coronal surface. The projection positions of each root canal orifice on the crown surface to be entered are determined, and the smooth line connecting these orifices forms the shape of the entrance cavity. Path fitting is performed on the feature points on the multiple segmented surfaces, as follows:

[0064] Transform feature points in multiple segmented coordinate planes into feature points in a spatial coordinate system:

[0065] In the first coordinate plane and coordinate plane The feature points in the data are as follows:

[0066] , ;

[0067] In the world coordinate system The reference plane for dividing the maxillary anterior teeth surrounding box section. On Axis coordinates are The first segmentation plane superior The axis coordinates are , No. A segmented section superior The axis coordinates are Transform feature points in a two-dimensional coordinate plane into a spatial coordinate system. Feature points in In the middle, the first segmentation plane , No. A segmented section The coordinates of the feature points are as follows:

[0068] , ;

[0069] In the world coordinate system Path fitting is performed on feature points:

[0070] In the world coordinate system In this process, path fitting is performed on feature points in different cross-sections, using the world coordinate system. The feature points in the data are:

[0071] , , , , ;

[0072] By performing path fitting on the above feature points, the fitted path is obtained, and the location of the pulp chamber foramen of the maxillary anterior teeth is completed.

[0073] The beneficial effects of this invention are as follows:

[0074] 1. By fitting the curves of the root canal and crown outlines onto the surrounding box section, the location of the entrance cavity was determined. This method effectively reduces the number of times the dentist needs to trim the entrance cavity edges and improves work efficiency. Precisely locating the access cavity allows the dentist to perform subsequent treatments more accurately.

[0075] 2. Solve the fitted curve in the coordinate plane of the section segment to determine the feature points. By fitting the path of the feature points, provide a suitable entrance cavity shape to prevent excessive loss of tooth tissue due to an excessively large entrance cavity shape, which is not conducive to restoration and aesthetics; and to prevent insufficient exposure of the pulp horn due to an excessively small entrance cavity shape, which would leave pulp behind.

[0076] 3. By fitting the curve of the outer contour of the root canal, the approach route of the lateral dentition was determined, forming a smooth path into the root canal. This allows all root canal orifices to be directly exposed in the direct view of the entrance, preventing the removal of too much healthy tooth tissue during the formation of the lateral dentition. This takes into account the resistance strength of the remaining tooth tissue and minimizes the amount of tooth tissue lost. Attached Figure Description

[0077] For ease of explanation, the present invention will be described in detail below with reference to specific embodiments and accompanying drawings.

[0078] Figure 1 This is a flowchart of a method for locating the access cavity of maxillary anterior teeth based on fitting multi-faceted feature points.

[0079] Figure 2 A schematic diagram illustrating the establishment of the coordinate system for the maxillary anterior teeth bounding box;

[0080] Figure 3 This is a schematic diagram showing the cross-sectional segmentation of the maxillary anterior teeth surround box;

[0081] Figure 4 A schematic diagram of a two-dimensional scatter plot in the coordinate system of the sectional plane of the maxillary anterior teeth surround box;

[0082] Figure 5 This is a schematic diagram of the fitting path for feature points in different cross-sections; Detailed Implementation

[0083] To make the objectives, technical solutions, and advantages of this invention patent clearer, the invention patent is described below with reference to specific embodiments shown in the accompanying drawings. However, it should be understood that these descriptions are merely exemplary and not intended to limit the scope of this invention patent. Furthermore, in the following description, descriptions of well-known structures and technologies are omitted to avoid unnecessarily obscuring the concepts of this invention patent.

[0084] Example 1: As Figure 1 , Figure 2 , Figure 3 , Figure 4 As shown, this specific embodiment adopts the following technical solution: a method for locating the maxillary anterior tooth access foramen based on multi-plane feature point fitting, the specific implementation process of the method is as follows:

[0085] Step 1: Establishing the coordinate system of the maxillary anterior teeth surrounding box:

[0086] First, a 3D reconstruction model is obtained based on the CT data of the maxillary anterior teeth. The 3D reconstruction model is then imported into reverse engineering software to generate a world coordinate system. The point cloud data of the maxillary anterior tooth outer contour and pulp chamber were obtained; these data were then imported into the slicing tool software, and the data were processed in the world coordinate system of the slicing tool software. In the middle, establish the maxillary anterior teeth Type of enclosure ,noodle Coordinate plane of the world coordinate system in slicing software parallel, plane With coordinate plane parallel, plane With coordinate plane Parallel; in the world coordinate system of the slicing tool Above, establish the coordinate system of the maxillary anterior teeth bounding box. ,point The origin of the coordinate system for the maxillary anterior bounding box is [the point where the coordinate system is defined]. The edges of the maxillary anterior bounding box [are defined]. Defined as a bounding box coordinate system Axis, edge Defined as a bounding box coordinate system Axis, edge Defined as a bounding box coordinate system axis;

[0087] Step 2: Divide the maxillary anterior teeth surround box into sections:

[0088] The access cavity shapes for the maxillary anterior teeth are either rounded triangles (incisors) or elliptical (canines). Based on the shape of the cavity, the surrounding box of the maxillary anterior teeth is segmented; in the world coordinate system of the slicing tool... In the middle, the coordinates are Define the bounding box coordinate plane The bounding box coordinate system is defined using the reference plane for segmenting the bounding box section of the maxillary anterior teeth. The positive axis is the direction in which the bounding box is segmented, represented by a direction vector. ;Based on the reference plane Towards The plane is divided by translation in the direction, and the division distance is denoted as . ,in The range of values ​​is The newly segmented bounding box coordinate plane is denoted as The number of plane segments is ,in , ; The value is determined by the segmentation distance. Determined by the size of the medullary cavity;

[0089] Step 3: Determine if the cross-section of the maxillary anterior teeth surround box meets the requirements:

[0090] Set and adjust The value;

[0091] Specifically:

[0092] By observing the morphology of the pulp chamber and root canals of the maxillary anterior teeth, we can determine... The initial value;

[0093] Determine whether the first section of the maxillary anterior tooth surround box meets the requirements;

[0094] Determine the coordinate plane of the first maxillary anterior tooth bounding box. Check if the outer contour of the root canal is displayed. If it meets the requirements, proceed to step four.

[0095] If the coordinate plane of the first maxillary anterior teeth surround box If the outer contour of the root canal is not shown, proceed to step three. ;

[0096] Step 4: Perform curve fitting on the outer contours of the root canals and crowns in the first coordinate plane of the maxillary anterior tooth surround box:

[0097] when At that time, in the coordinate plane of the maxillary anterior teeth surrounding box In the process, fitting points are selected for the outer contour of the root canal. The scatter plot of the fitting points has two lines, approximating two curves; the distance from the curve is defined as... The curves that are close to the axis are The other one is The polynomials of the two curves are solved as follows:

[0098] Regarding the first point curve:

[0099] The coordinates of the fitting point are ;definition The polynomial of degree is , , for The fitting coefficients of the polynomial of degree 1; to make the fitted curve more accurate, the sum of squared deviations is defined as... Sum of squared deviations The minimum curve fit is the most accurate. The expression is:

[0100] (1)

[0101] Find the minimum sum of squared deviations :make ,have:

[0102] (2)

[0103] Solving , The polynomial of the curve is , ;

[0104] Similarly, the second curve is obtained. The fitting coefficient is , The polynomial of the curve is , ;

[0105] when At that time, in the coordinate plane of the maxillary anterior teeth surrounding box In the process, fitting points are selected for the outer contour of the tooth crown. The scatter plot of the fitting points has one line, and the curve is defined as follows. Solve for the polynomial of the curve, the solution method and the curve , The solution is the same;

[0106] Solving for the curve The fitting coefficient is , The polynomial of the curve is , ;

[0107] In the coordinate plane of the maxillary anterior teeth surrounding box middle, , and The polynomials of the curves are as follows:

[0108] , ;

[0109] , ;

[0110] , ;

[0111] Step 5: Determine the feature points in the first coordinate plane of the maxillary anterior teeth enclosure box:

[0112] when At that time, in the first coordinate plane of the section segmentation In the middle, two curves fitted by the outer contour of the root canal , Curve fitted to the outer contour of the crown Find two feature points:

[0113] In the coordinate plane of the maxillary anterior teeth surrounding box middle , and The polynomials of the curves are as follows:

[0114] , ;

[0115] , ;

[0116] , ;

[0117] curve and curve Determine the coordinate plane The first characteristic point is determined by the nonlinear equation system (3):

[0118] (3)

[0119] Solve for characteristic points, defined by the curve and curve The solved feature points are Similarly:

[0120] curve and curve Determine the coordinate plane The second characteristic point is determined by the nonlinear equation system (4):

[0121] (4)

[0122] Solve for characteristic points, defined by the curve and curve The solved feature points are ;

[0123] Step 6: In the bounding box coordinate plane Curve fitting and feature point determination are performed in the following ways:

[0124] In the maxillary anterior teeth surround box Curve fitting is performed on the outer contours of the root canal and the outer contours of the crown in a coordinate plane:

[0125] In the coordinate plane of the maxillary anterior teeth surrounding box In this process, curve fitting is performed on the outer contours of the root canal and the outer contours of the crown, and then compared with the coordinate plane. The method for finding the coordinate plane of the maxillary anterior teeth enclosure is the same. middle , and The polynomials of the curves are as follows:

[0126] , ;

[0127] , ;

[0128] , ;

[0129] In the coordinate plane of the maxillary anterior teeth surrounding box Determine feature points in the middle:

[0130] In the coordinate plane of the maxillary anterior teeth surrounding box middle , and The polynomials of the curves are as follows:

[0131] , ;

[0132] , ;

[0133] , ;

[0134] curve and curve Determine the coordinate plane The first characteristic point is determined by the nonlinear equation system (5):

[0135] (5)

[0136] Solve for characteristic points, defined by the curve and curve The solved feature points are Similarly:

[0137] curve and curve Determine the coordinate plane The second characteristic point is determined by the nonlinear equation system (6):

[0138] (6)

[0139] Solve for characteristic points, defined by the curve and curve The solved feature points are ;

[0140] Determine the first segment of the segment. The coordinate plane, at the coordinate plane, Has the curve fitting and feature point determination of the root canal outer contour and crown outer contour on the coordinate plane been completed? If the condition is met, proceed to step seven; otherwise, return to step four.

[0141] Step 7: For the segmented... Path fitting is performed on feature points on the bounding box coordinate plane:

[0142] In the coronal preparation of the pulp chamber, the outline of the entrance cavity is the projection of the pulp chamber shape onto the coronal surface. The projection positions of each root canal orifice on the crown surface to be entered are determined, and the smooth line connecting these orifices forms the shape of the entrance cavity. Path fitting is performed on the feature points on the multiple segmented surfaces, as follows:

[0143] Transform feature points in multiple segmented coordinate planes into feature points in a spatial coordinate system:

[0144] In the first coordinate plane and coordinate plane The feature points in the data are as follows:

[0145] , ;

[0146] In the world coordinate system The reference plane for dividing the maxillary anterior teeth surrounding box section. On The axis coordinates are The first segmentation plane superior The axis coordinates are , No. A segmented section superior The axis coordinates are Transform feature points in a two-dimensional coordinate plane into a spatial coordinate system. Feature points in In the middle, the first segmentation plane , No. A segmented section The coordinates of the feature points are as follows:

[0147] , ;

[0148] In the world coordinate system Path fitting is performed on feature points:

[0149] In the world coordinate system In this process, path fitting is performed on feature points in different cross-sections, using the world coordinate system. The feature points in the data are:

[0150] , , , , ;

[0151] By performing path fitting on the above feature points, the fitted path is obtained, and the location of the pulp chamber foramen of the maxillary anterior teeth is completed.

[0152] Example 2: As Figure 5 As shown, a three-dimensional reconstruction model was obtained based on CT data of the maxillary anterior teeth. The three-dimensional reconstruction model was then imported into reverse engineering software to generate a world coordinate system. The point cloud data of the maxillary anterior tooth outer contour and pulp chamber were obtained; these data were then imported into the slicing tool software, and the data were processed in the world coordinate system of the slicing tool software. In the middle, establish the maxillary anterior teeth Type of enclosure ,noodle Coordinate plane of the world coordinate system in slicing software parallel, plane With coordinate plane parallel, plane With coordinate plane Parallel; in the world coordinate system of the slicing tool Above, establish the coordinate system of the maxillary anterior teeth bounding box. ,point The origin of the coordinate system for the maxillary anterior bounding box is [the point where the coordinate system is defined]. The edges of the maxillary anterior bounding box [are defined]. Defined as a bounding box coordinate system Axis, edge Defined as a bounding box coordinate system Axis, edge Defined as a bounding box coordinate system Axis; in the world coordinate system of the slicing tool In the middle, the coordinate point is Define the bounding box coordinate plane The bounding box coordinate system is defined using the reference plane for segmenting the bounding box section of the maxillary anterior teeth. The positive axis is the direction in which the bounding box is segmented, represented by a direction vector. ;Based on the reference plane Towards The plane is translated and divided in the direction, with a division distance of . By observing the morphology of the pulp chamber and root canals of the maxillary anterior teeth, four new planes were identified. The coordinate plane of the first maxillary anterior tooth enclosure box was then determined. Does the upper part show the outer contour of the root canal? If so, then in the coordinate plane of the maxillary anterior tooth surround box. In the process, fitting points are selected for the outer contour of the root canal, and the distance from the fitting points is defined. The curves that are close to the axis are The other one is Solve for the polynomials of the two curves, select fitting points for the outer contour of the tooth crown, and generate a scatter plot of the fitting points. Define the curve as follows. In the first coordinate plane of the section segmentation In the middle, two curves fitted by the outer contour of the root canal , Curve fitted to the outer contour of the crown Find two feature points, and then use the curve. and curve The solved feature points are , by curve and curve The solved feature points are In the bounding box coordinate plane Curve fitting and feature point determination are performed to determine the segmentation of the first segment. The coordinate plane, at the coordinate plane, Has the curve fitting and feature point determination of the root canal outer contour and crown outer contour on the coordinate plane been completed? If the condition is met, proceed to step seven; otherwise, return to step four. Assuming the condition is met, perform path fitting on the feature points in the four bounding box coordinate planes, transforming the feature points in the four coordinate planes into feature points in the spatial coordinate system, specifically in the world coordinate system. The path is fitted to 8 feature points to obtain the fitted path, as shown below. Figure 5 As shown, the location of the pulp chamber foramen of the maxillary anterior teeth has been completed.

Claims

1. A method for locating the access foramen of maxillary anterior teeth based on fitting multi-faceted feature points, characterized in that: The specific implementation process of the method is as follows: Step 1: Establishing the coordinate system of the maxillary anterior teeth surrounding box: First, a 3D reconstruction model is obtained based on the CT data of the maxillary anterior teeth. The 3D reconstruction model is then imported into reverse engineering software to generate a world coordinate system. The point cloud data of the maxillary anterior tooth outer contour and pulp chamber were obtained; these data were then imported into the slicing tool software, and the data were processed in the world coordinate system of the slicing tool software. In the middle, establish the maxillary anterior teeth Type of enclosure ,noodle Coordinate plane of the world coordinate system in slicing software parallel, plane With coordinate plane parallel, plane With coordinate plane Parallel; in the world coordinate system of the slicing tool Above, establish the coordinate system of the maxillary anterior teeth bounding box. ,point The origin of the coordinate system for the maxillary anterior bounding box is [the point where the coordinate system is defined]. The edges of the maxillary anterior bounding box [are defined]. Defined as a bounding box coordinate system Axis, edge Defined as a bounding box coordinate system Axis, edge Defined as a bounding box coordinate system axis; Step 2: Divide the maxillary anterior teeth surround box into sections: The access cavity shapes for the maxillary anterior teeth are either rounded triangles (incisors) or elliptical (canines). Based on the shape of the cavity, the surrounding box of the maxillary anterior teeth is segmented; in the world coordinate system of the slicing tool... In the middle, the coordinates are Define the bounding box coordinate plane The bounding box coordinate system is defined using the reference plane for segmenting the bounding box section of the maxillary anterior teeth. The positive axis is the direction in which the bounding box is segmented, represented by a direction vector. ;Based on the reference plane Towards The plane is divided by translation in the direction, and the division distance is denoted as . ,in The range of values ​​is The newly segmented bounding box coordinate plane is denoted as The number of plane segments is ,in , ; The value is determined by the segmentation distance. Determined by the size of the medullary cavity; Step 3: Determine if the cross-section of the maxillary anterior teeth surround box meets the requirements: Set and adjust The value; Specifically: By observing the morphology of the pulp chamber and root canals of the maxillary anterior teeth, we can determine... The initial value; Determine whether the first section of the maxillary anterior tooth surround box meets the requirements; Determine the coordinate plane of the first maxillary anterior tooth bounding box. Check if the outer contour of the root canal is displayed. If it meets the requirements, proceed to step four. If the coordinate plane of the first maxillary anterior teeth surround box If the outer contour of the root canal is not shown, proceed to step three. ; Step 4: Perform curve fitting on the outer contours of the root canals and crowns in the first coordinate plane of the maxillary anterior tooth surround box: when At that time, in the coordinate plane of the maxillary anterior teeth surrounding box In the process, fitting points are selected for the outer contour of the root canal. The scatter plot of the fitting points has two lines, approximating two curves; the distance from the curve is defined as... The curves that are close to the axis are The other one is The polynomials of the two curves are solved as follows: Regarding the first point curve: The coordinates of the fitting point are ;definition The polynomial of degree is , , for The fitting coefficients of the polynomial of degree 1; to make the fitted curve more accurate, the sum of squared deviations is defined as... Sum of squared deviations The minimum curve fit is the most accurate. The expression is: （1） Find the minimum sum of squared deviations :make ,have: （2） Solving , The polynomial of the curve is , ; Similarly, the second curve is obtained. The fitting coefficient is , The polynomial of the curve is , ; when At that time, in the coordinate plane of the maxillary anterior teeth surrounding box In the process, fitting points are selected for the outer contour of the tooth crown. The scatter plot of the fitting points has one line, and the curve is defined as follows. Solve for the polynomial of the curve, the solution method and the curve , The solution is the same; Solving for the curve The fitting coefficient is , The polynomial of the curve is , ; In the coordinate plane of the maxillary anterior teeth surrounding box middle, , and The polynomials of the curves are as follows: ， ； ， ； ， ； Step 5: Determine the feature points in the first coordinate plane of the maxillary anterior teeth enclosure box: when At that time, in the first coordinate plane of the section segmentation In the middle, two curves fitted by the outer contour of the root canal , Curve fitted to the outer contour of the crown Find two feature points: In the coordinate plane of the maxillary anterior teeth surrounding box middle , and The polynomials of the curves are as follows: ， ； ， ； ， ； curve and curve Determine the coordinate plane The first characteristic point is determined by the nonlinear equation system (3): （3） Solve for characteristic points, defined by the curve and curve The solved feature points are Similarly: curve and curve Determine the coordinate plane The second characteristic point is determined by the nonlinear equation system (4): （4） Solve for characteristic points, defined by the curve and curve The solved feature points are ; Step 6: In the bounding box coordinate plane Curve fitting and feature point determination are performed in the following ways: In the maxillary anterior teeth surround box Curve fitting is performed on the outer contours of the root canal and the outer contours of the crown in a coordinate plane: In the coordinate plane of the maxillary anterior teeth surrounding box In this process, curve fitting is performed on the outer contours of the root canal and the outer contours of the crown, and then compared with the coordinate plane. The method for finding the coordinate plane of the maxillary anterior teeth enclosure is the same. middle , and The polynomials of the curves are as follows: ， ； ， ； ， ； In the coordinate plane of the maxillary anterior teeth surrounding box Determine feature points in the middle: In the coordinate plane of the maxillary anterior teeth surrounding box middle , and The polynomials of the curves are as follows: ， ； ， ； ， ； curve and curve Determine the coordinate plane The first characteristic point is determined by the nonlinear equation system (5): （5） Solve for characteristic points, defined by the curve and curve The solved feature points are Similarly: curve and curve Determine the coordinate plane The second characteristic point is determined by the nonlinear equation system (6): （6） Solve for characteristic points, defined by the curve and curve The solved feature points are ; Determine the first segment of the segment. The coordinate plane, at the coordinate plane, Has the curve fitting and feature point determination of the root canal outer contour and crown outer contour on the coordinate plane been completed? If the condition is met, proceed to step seven; otherwise, return to step four. Step 7: For the segmented... Path fitting is performed on feature points on the bounding box coordinate plane: In the coronal preparation of the pulp chamber, the outline of the entrance cavity is the projection of the pulp chamber shape onto the coronal surface. The projection positions of each root canal orifice on the crown surface to be entered are determined, and the smooth line connecting these orifices forms the shape of the entrance cavity. Path fitting is performed on the feature points on the multiple segmented surfaces, as follows: Transform feature points in multiple segmented coordinate planes into feature points in a spatial coordinate system: In the first coordinate plane and coordinate plane The feature points in the data are as follows: ， ； In the world coordinate system The reference plane for dividing the maxillary anterior teeth surrounding box section. On The axis coordinates are The first segmentation plane superior The axis coordinates are , No. A segmented section superior The axis coordinates are Transform feature points in a two-dimensional coordinate plane into a spatial coordinate system. Feature points in In the middle, the first segmentation plane , No. A segmented section The coordinates of the feature points are as follows: ， ； In the world coordinate system Path fitting is performed on feature points: In the world coordinate system In this process, path fitting is performed on feature points in different cross-sections, using the world coordinate system. The feature points in the data are: ， ， ， ， ； By performing path fitting on the above feature points, the fitted path is obtained, and the location of the pulp chamber foramen of the maxillary anterior teeth is completed.

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