A method for automatically determining tooth feature points

Abstract

The application relates to the technical field of digital oral cavity, and relates to an automatic determination method of tooth feature points, which comprises a data preprocessing stage, in the XOY plane of a global coordinate system, a projection point of a target tooth mass center coordinate, a projection point of a left adjacent tooth mass center coordinate and a projection point of a right adjacent tooth mass center coordinate form a triangle, a center and a radius of a circumscribed circle of the triangle are obtained, a local coordinate system is established, feature points of the target tooth are determined, the tooth is divided into canines, incisors and molars, and the molars are divided into premolars and molars; and a protrusion point of a mesial and distal surface of the target tooth is determined. The application can be realized through a computer program, and then the feature points of each tooth can be automatically obtained after the tooth model is imported into the computer.

Description

Technical Field

[0001] This invention relates to the field of digital oral technology, and more specifically to a method for automatically determining tooth feature points. Background Technology

[0002] In recent years, with the application of computer-aided design and computer graphics technology in the field of oral medicine, digital prosthetic restoration technology has also developed rapidly. During the dental restoration stage, technicians must first determine the characteristics of the tooth to be restored and its contact relationship with adjacent and opposing teeth, accurately identifying the characteristic points of the tooth and its occlusal relationship with the opposing teeth. Currently, the determination of tooth characteristic points mainly relies on manual selection by technicians, which is labor-intensive and places high demands on technicians. Furthermore, the results determined by different technicians are highly subjective. Summary of the Invention

[0003] The technical problem to be solved by the present invention is: how to accurately locate tooth feature points using a computer.

[0004] The technical solution adopted in this invention is: an automatic method for determining tooth feature points, comprising the following steps:

[0005] Step 1: Data Preprocessing Stage. Establish a global coordinate system. Import the entire row of teeth model into the computer. Read the point cloud data of the 3D tooth model in the global coordinate system. Set the distal direction as left and the mesial direction as right. The leftmost adjacent tooth of the target tooth O is designated as the left neighbor tooth L, and the rightmost adjacent tooth of the target tooth O is designated as the right neighbor tooth R. If the target tooth O is the rearmost molar and has no distal neighbor tooth, then the mesial nearest tooth is designated as the left neighbor tooth L, and the next closest tooth as the right neighbor tooth R. Establish a translation coordinate system, using the centroid coordinates O of the target tooth O in the global coordinate system. s (x, y, z) is the origin of the coordinate system, and the coordinate system is translated. The axis is parallel to the x-axis of the global coordinate system, and the coordinate system is translated. The axis is parallel to the y-axis of the global coordinate system, and the coordinate system is translated. The axis is parallel to the z-axis of the global coordinate system; the point cloud set of the target tooth in the global coordinate system. The point cloud set in the translation coordinate system is Point cloud set of left neighboring tooth L in global coordinates The point cloud set in the translation coordinate system is Point cloud set of the right neighbor tooth in global coordinates The point cloud set in the translation coordinate system is in, Let O be the first point cloud coordinate of the target tooth o in global coordinates. The coordinates of the second point cloud of the target tooth O in global coordinates. Let L be the l-th point cloud coordinate of the target tooth O in global coordinates. Let O be the coordinates of the first point cloud of the target tooth O in the translation coordinate system. The coordinates of the second point cloud of the target tooth O in the translation coordinate system are: The coordinates of the l-th point cloud of the target tooth O in the translation coordinate system. The point cloud coordinates of the first neighboring tooth L in global coordinates. The second point cloud coordinate of the left neighbor tooth L in global coordinates. The point cloud coordinates of the nth point of the left neighbor tooth L in global coordinates. The coordinates of the first point cloud of the left adjacent tooth L in the translation coordinate system. The coordinates of the second point cloud of the left adjacent tooth L in the translation coordinate system. The coordinates of the nth point cloud of the left adjacent tooth L in the translation coordinate system. The coordinates of the first point cloud of the right neighboring tooth R in global coordinates. The coordinates of the second point cloud of the right neighboring tooth R in global coordinates. Let R be the nth point cloud coordinate of the right neighboring tooth R in global coordinates. Let R be the coordinates of the first point cloud of the right neighboring tooth in the translation coordinate system. The coordinates of the second point cloud of the right adjacent tooth R in the translation coordinate system. Given the nth point cloud coordinates of the right adjacent tooth R in the translation coordinate system, and the centroid coordinates of the target tooth O in the translation coordinate system... left adjacent tooth centroid coordinates Right adjacent tooth centroid coordinates Projected onto the global coordinate XOY plane, the centroid coordinates of the target tooth on the XOY plane of the global coordinate system are... The projection point and the coordinates of the centroid of the left adjacent tooth The projection point and the coordinates of the centroid of the right adjacent tooth The projection points form a triangle with the center of the circumcircle of the triangle being c and the radius being r.

[0006] Step 2: Establish a local coordinate system. Under the translation coordinate system, determine the centroid coordinates of the target tooth O. The origin of the local coordinate system is used, with the centroid coordinates of the target tooth O as the reference point. and the coordinates of the centroid of the left adjacent tooth connection Let x′ be the x-axis of the local coordinate system, and draw a circle through the center c. A perpendicular line is drawn from the center of the circle, with the foot of the perpendicular at point p. The line connecting the center of the circle c and the foot of the perpendicular at point p is... Centroid coordinates of the target tooth O Make parallel to Draw a straight line h through the center c of the circle, parallel to the x′ axis, intersecting line h at point c′. The coordinates of the centroid of the target tooth O are used. Connect point c' to point c' Let y′ be the local coordinate system, and use the right-hand rule to determine the z′ axis, and stipulate that the positive direction of the z′ axis is from the root to the apex of the tooth;

[0007] Step 3: Determine the feature points of the target tooth O. Teeth are divided into canines, incisors, and molars, among which molars are further divided into premolars and molars.

[0008] If the target tooth O is a canine, translate the point cloud set of the coordinate system of the target tooth O. Projected onto the z′ axis of the local coordinate system, the maximum projection value is the feature point of the canine;

[0009] If the target tooth O is an incisor, in the local coordinate system, along y′O T ′ s The z′ plane will be the point cloud set of the target tooth O. Divided into two halves, forming two subsets, namely the first subset. Second subset Let g be the coordinates of the g-th point cloud of the target tooth O in the translation coordinate system. Let g+1 be the point cloud coordinates of the target tooth O in the translation coordinate system. Let g+2 be the point cloud coordinates of the target tooth O in the translation coordinate system, and let g be the first subset. There are a total of g point cloud coordinates;

[0010] First Subset Each point is projected onto the x′O of the local coordinate system. T ′ s The z′ plane yields the set sum. L {sum L1 ,sum L2 ,…,sum Lg}, sum L1 The coordinates of the first point cloud of the target tooth O in the translation coordinate system. The sum of the coordinates of the projection point on the x′ axis and the coordinates of the projection point on the z′ axis of the local coordinate system, sum L2 The coordinates of the second point cloud of the target tooth O in the translation coordinate system. The sum of the coordinates of the projection point on the x′ axis and the coordinates of the projection point on the z′ axis of the local coordinate system, sum Lg Let g be the coordinates of the g-th point cloud of the target tooth O in the translation coordinate system. The set sum of the coordinates of the projection points on the x′ axis and the z′ axis of the local coordinate system is called sum. L {sum L1 ,sum L2 ,…,sumLg Any element sum in} Li Satisfy the formula α1 and α2 are vectors The angle between the x′ axis and the z′ axis, Let i be the coordinates of the i-th point cloud of the target tooth O in the translation coordinate system. The centroid coordinates of the target tooth O in the translation coordinate system and the coordinates of the i-th point cloud The connection of lines, the set sum L {sum L1 ,sum L2 ,…,sum Lg The first subset corresponding to the maximum value of the elements in} The point in the middle is the first feature point of the incisor;

[0011] For the second subset Perform the same operation to obtain the second subset. The second feature point in;

[0012] If the target tooth O is a molar, in the local coordinate system, move the target tooth O along x′O T ′ s The tooth is cut in the y′ plane, retaining only the point cloud data of the half of the tooth closest to the cusp. This retained half of the tooth's point cloud data is then projected onto the y′ axis, resulting in the set y′ of the projected point cloud of the retained half of the tooth. U {y′ U1 ,y′ U2 ,…,y′ Uσ},y′ U1 To preserve the first point cloud coordinate of the tooth, y′ U2 To preserve the second point cloud coordinate of the tooth, y′ Uσ Let σ be the coordinates of the σ-th point cloud, with the subscript U indicating that it belongs to the preserved tooth, where σ is the number of point clouds containing preserved teeth; calculate the coordinates y′ of any two point clouds containing preserved teeth. Ui y′ Uj Chebyshev distance d y If i ≠ j, the calculation formula is:

[0013]

[0014] Find the Chebyshev distance d based on the Chebyshev distance. y The two largest projection points correspond to two coordinate points in the preserved teeth, with the point closer to the lingual side being the minimum point p1 and the point closer to the buccal side being the maximum point p2, where y′ Ui y′ Uj Any two points on the y′ axis projection of the preserved tooth point cloud data;

[0015] Construct a plane S with the y′ axis as the normal vector. The equation of the plane is Ax + By + Cz + D = 0, where A, B, and C are the y′ axis vectors, and D is the intercept coefficient of the plane equation. The plane S is translated along the normal vector y′ axis through the minimum point p1, with a translation step size of 0.2 mm. Each translation retains the set of projection points y′ of half a tooth. U {y′ U1 ,y′ U2 ,…,y′ Uσ All points whose Euclidean distance to the normal vector of plane S is less than or equal to 0.1 mm are projected onto plane S, and the corresponding tooth point cloud coordinates obtained from each translation are saved; the initial plane S passes through the minimum point p1, and the coordinates of the minimum point p1 are (x... p1 y p1 , z p1 If the coefficient D of plane S satisfies:

[0016] -Ax p1 -By p1 -Cz p1 =D

[0017] Plane S is translated along the y′ axis with a step size of 0.2 mm. The angles between the local coordinate y′ axis and the global coordinate X, Y, Z axes in three-dimensional space are θ1, θ2, and θ3, respectively. The translation process of plane S satisfies the following formula:

[0018] A(x p1 -0.2cosθ1)+B(y p1 -0.2cosθ2)+C(z p1 -0.2cosθ3)+D=0

[0019] The y′ is determined by each translation of plane S. U The projection points are sorted in ascending order on the local coordinate x′ axis to fit a curve, and the maximum points of the curve are determined. Each translation of the S-plane on the posterior molar yields two maximum points, and each translation of the S-plane on the anterior molar yields one maximum point. The obtained maximum points are stored and formed into a set M{M1, M2, ..., M...}. f-1 M f If the target tooth is a posterior molar, M1 and M2 are the maximum points determined by the initial position of plane S, and f is twice the number of translations of plane S. If the target tooth is a premolar, M1 is the maximum point determined by the initial position of plane S, and f is equal to the number of translations of S, which gives the number of maximum points.

[0020] If the target tooth is a molar, then all the maximum points M{M1,M2,…,M…} are considered. f-1 M f In the local coordinate system Projecting onto a plane, the plane is divided into four quadrants according to the two-dimensional plane coordinate system. The coordinates of the points in each quadrant in the target tooth set are found. All points in each quadrant are projected onto the local coordinate system z′ axis. The maximum value on the z′ axis in that quadrant is found, which gives the four cusp feature points of the posterior molar. The four cusp points are connected to form a quadrilateral, and the points in the quadrilateral region are projected onto the z′ axis. The point corresponding to the minimum projection value is the socket feature point of the posterior molar.

[0021] If the target tooth is a premolar, the projection values ​​of all the maximum points M on the y′ axis are divided into two parts: the first part is the part with positive projection values ​​on the y′ axis, and the second part is the part with negative projection values ​​on the y′ axis. Find the coordinates of the target tooth corresponding to the maximum projection values ​​of the two parts on the z′ axis, which are the two cusp feature points of the premolar.

[0022] Step 4: Determine the ridges on the mesial and distal surfaces of the target tooth, with the center point c and... The line segment corresponding to the line is τ, and passes through... Draw the perpendicular line K to τ, that is, the circle lies on... The tangent at the point will translate the point cloud set of the target tooth O into the coordinate system. Projecting onto the perpendicular line K yields the set of projection points K{k1,k2,…,k...} l}, where k1 is the projection point of the first point cloud of the target tooth O translation coordinate system onto the perpendicular line K, k2 is the projection point of the second point cloud of the target tooth O translation coordinate system onto the perpendicular line K, and k l For the l-th point cloud of the target tooth O translation coordinate system projected onto the vertical line K, calculate the distance d between any two projected points. k The formula is:

[0023]

[0024] Where, k i k j Let d be any two projection points of the target tooth onto the perpendicular line K. k The two points corresponding to the maximum value are the mesial and distal ridges of the target tooth, respectively.

[0025] Identify the buccal and lingual ridges of the target tooth, and then transfer the point cloud of the target tooth to the O-coordinate system. Projecting onto the line τ, we obtain the set of projection points τ{τ1,τ2,…,τ}. l}, where τ1 is the target tooth set. The value projected onto the vertical line τ, where τ lLet τ1 be the projection point of the first point cloud in the translation coordinate system of the target tooth O onto the straight line τ2, and let τ2 be the projection point of the second point cloud in the translation coordinate system of the target tooth O onto the straight line τ3. l For the l-th point cloud of the target tooth O translation coordinate system projected onto the straight line τ, calculate the distance d between any two projected points. τ

[0026]

[0027] Where, τ i , τ j Let d be two arbitrary projection points of the target tooth onto the straight line τ. τ The two points at their maximum correspond to the buccal and lingual ridges of the teeth.

[0028] The centroid coordinates O of the target tooth O in the global coordinate system s The method to obtain (x, y, z) is the point cloud set under the global coordinates of the target tooth O. The point cloud coordinate set of the target tooth O is calculated as follows: The average value of all point cloud coordinates is used as the centroid coordinate O of the target tooth O. s (x,y,z), the calculation formula is:

[0029]

[0030] Among them, (x j ,y j ,z j Let be the coordinates of the j-th point in the point cloud set of the target tooth O in global coordinates, where 1 ≤ j ≤ l. Let be the centroid coordinates of the target tooth O in the translation coordinate system. left adjacent tooth centroid coordinates Right adjacent tooth centroid coordinates The method obtained is the centroid coordinate O of the target tooth O in the global coordinate system. s (x,y,z) is obtained in the same way.

[0031] In the global coordinate system, the midpoint of the line segment connecting the last left molar and the last right molar is taken as the origin of the global coordinate system, and the connecting line segment is taken as the X-axis of the global coordinate system with the vector (1,0,0). A line segment perpendicular to the X-axis and pointing in the direction of the central incisors is drawn through the origin as the Y-axis of the global coordinate system with the vector (0,1,0). A line segment perpendicular to both the X-axis and Y-axis and pointing from the cusp to the root is drawn through the origin as the Z-axis of the global coordinate system with the vector (0,0,1).

[0032] The beneficial effects of this invention are: starting from a tooth model, this invention can directly calculate the characteristic points (occlusal characteristic points) of each tooth, thus providing a basis for determining tooth occlusion. This invention can be implemented through a computer program, and after importing the tooth model into the computer, the characteristic points of each tooth are automatically obtained. Attached Figure Description

[0033] Figure 1 This is a schematic diagram illustrating the implementation logic of the present invention;

[0034] Figure 2 To determine the axis diagram by establishing a circle through the centroid of the three teeth;

[0035] Figure 3 To create a schematic diagram of the local coordinate axes;

[0036] Figure 4 This is a schematic diagram of the point cloud coordinates of teeth cut by a cross-section;

[0037] Figure 5 A schematic diagram for establishing a tangent to locate the bulge point. Detailed Implementation

[0038] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0039] Tooth occlusal feature points (hereinafter referred to as tooth feature points) include the occlusal point, buccal and lingual surfaces, and mesiodistal ridges. An automatic method for determining tooth feature points includes the following steps:

[0040] Step 1: Data preprocessing stage, establish a global coordinate system.

[0041] In the global coordinate system, the midpoint of the line segment connecting the last left molar and the last right molar is taken as the origin of the global coordinate system, and the connecting line segment is taken as the X-axis of the global coordinate system with the vector (1,0,0). A line segment perpendicular to the X-axis and pointing in the direction of the central incisors is drawn through the origin as the Y-axis of the global coordinate system with the vector (0,1,0). A line segment perpendicular to both the X-axis and Y-axis and pointing from the cusp to the root is drawn through the origin as the Z-axis of the global coordinate system with the vector (0,0,1).

[0042] Import the entire row of teeth model, read the point cloud data of the 3D tooth model in global coordinates, set the distal direction as left and the mesial direction as right, the leftmost adjacent tooth of the target tooth O is the left neighbor tooth L, and the rightmost adjacent tooth of the target tooth O is the right neighbor tooth R. If the target tooth O is the last molar and has no distal adjacent tooth, then the mesial adjacent tooth is taken as the left neighbor tooth L and the second nearest tooth as the right neighbor tooth R. Establish a translation coordinate system, with the centroid coordinates O of the target tooth O in the global coordinate system as the reference coordinates. s(x, y, z) is the origin of the coordinate system. The centroid coordinates O of the target tooth O in the global coordinate system are... s The method to obtain (x, y, z) is the point cloud set under the global coordinates of the target tooth O. The point cloud coordinate set of the target tooth O is calculated as follows: The average value of all point cloud coordinates is used as the centroid coordinate O of the target tooth O. s (x,y,z), the calculation formula is:

[0043]

[0044] Among them, (x j ,y j ,z j Let be the coordinates of the j-th point in the point cloud set of the target tooth O in global coordinates, where 1 ≤ j ≤ l. Let be the centroid coordinates of the target tooth O in the translation coordinate system. left adjacent tooth centroid coordinates Right adjacent tooth centroid coordinates The method obtained is the centroid coordinate O of the target tooth O in the global coordinate system. s (x,y,z) is obtained in the same way.

[0045] Translation coordinate system The axis is parallel to the x-axis of the global coordinate system, and the coordinate system is translated. The axis is parallel to the y-axis of the global coordinate system, and the coordinate system is translated. The point cloud set of the target tooth O in global coordinates, with the axis parallel to the z-axis of the global coordinate system. The point cloud set in the translation coordinate system is Point cloud set of left neighboring tooth L in global coordinates The point cloud set in the translation coordinate system is Point cloud set of the right neighbor tooth in global coordinates The point cloud set in the translation coordinate system is in, Let O be the first point cloud coordinate of the target tooth in global coordinates. The coordinates of the second point cloud of the target tooth O in global coordinates. Let L be the l-th point cloud coordinate of the target tooth O in global coordinates. Let O be the coordinates of the first point cloud of the target tooth O in the translation coordinate system. The coordinates of the second point cloud of the target tooth O in the translation coordinate system are: The coordinates of the l-th point cloud of the target tooth O in the translation coordinate system. The point cloud coordinates of the first neighboring tooth L in global coordinates. The second point cloud coordinate of the left neighbor tooth L in global coordinates. The point cloud coordinates of the nth point of the left neighbor tooth L in global coordinates. The coordinates of the first point cloud of the left adjacent tooth L in the translation coordinate system. The coordinates of the second point cloud of the left adjacent tooth L in the translation coordinate system. The coordinates of the nth point cloud of the left adjacent tooth L in the translation coordinate system. The coordinates of the first point cloud of the right neighboring tooth R in global coordinates. The coordinates of the second point cloud of the right neighboring tooth R in global coordinates. Let R be the nth point cloud coordinate of the right neighboring tooth R in global coordinates. Let R be the coordinates of the first point cloud of the right neighboring tooth in the translation coordinate system. The coordinates of the second point cloud of the right adjacent tooth R in the translation coordinate system. Given the nth point cloud coordinates of the right adjacent tooth R in the translation coordinate system, and the centroid coordinates of the target tooth O in the translation coordinate system... left adjacent tooth centroid coordinates Right adjacent tooth centroid coordinates Projected onto the global coordinate XOY plane.

[0046] In the translation coordinate system, the centroid coordinates of the target tooth O left adjacent tooth centroid coordinates Right adjacent tooth centroid coordinates The method obtained is the centroid coordinate O of the target tooth O in the global coordinate system. s (x,y,z) is obtained in the same way.

[0047] Target tooth centroid coordinates The calculation formula is expressed as follows:

[0048]

[0049] Where (x′, y′, z′) are the centroid coordinates of the target tooth in global coordinates after translation. Translation does not change the number of point clouds of the tooth. j ,y′ j ,z′ j Let be the coordinates of the j-th point cloud after translation, where 1 ≤ j ≤ l.

[0050] like Figure 2 As shown, on the XOY plane of the global coordinate system, the centroid coordinates of the target tooth O are... The projection point and the coordinates of the centroid of the left adjacent tooth The projection point and the coordinates of the centroid of the right adjacent tooth The projection points form a triangle with the center of the circumcircle of the triangle being c and the radius being r;

[0051] Step 2: Establish a local coordinate system, such as Figure 3As shown, in the translation coordinate system, the centroid coordinates of the target tooth O are... The origin of the local coordinate system is used, with the centroid coordinates of the target tooth O as the reference point. and the coordinates of the centroid of the left adjacent tooth connection Let x′ be the x-axis of the local coordinate system, and draw a circle through the center c. A perpendicular line is drawn from the center of the circle, with the foot of the perpendicular at point p. The line connecting the center of the circle c and the foot of the perpendicular at point p is... Centroid coordinates of the target tooth O Make parallel to Draw a straight line h through the center c of the circle, parallel to the x′ axis, intersecting line h at point c′. The coordinates of the centroid of the target tooth O are used. Connect point c' to point c' Let y′ be the local coordinate system, and use the right-hand rule to determine the z′ axis, and stipulate that the positive direction of the z′ axis is from the root to the apex of the tooth.

[0052] Step 3: Determine the feature points of the target tooth O. Teeth are divided into canines, incisors, and molars, among which molars are further divided into premolars and molars.

[0053] If the target tooth O is a canine, translate the point cloud set of the coordinate system of the target tooth O. Projected onto the z′ axis of the local coordinate system, the maximum projection value is the feature point of the canine;

[0054] If the target tooth O is an incisor, in the local coordinate system, along y′O T ′ s The z′ plane will be the point cloud set of the target tooth O. Divided into two halves, forming two subsets, namely the first subset. Second subset Let g be the coordinates of the g-th point cloud of the target tooth O in the translation coordinate system. Let g+1 be the point cloud coordinates of the target tooth O in the translation coordinate system. Let g+2 be the point cloud coordinates of the target tooth O in the translation coordinate system, and let g be the first subset. There are a total of g point cloud coordinates;

[0055] First Subset Each point is projected onto the x′O of the local coordinate system. T ′ s The z′ plane yields the set sum. L {sum L1 ,sum L2 ,…,sum Lg}, sum L1 The coordinates of the first point cloud of the target tooth O in the translation coordinate system. The sum of the coordinates of the projection point on the x′ axis and the coordinates of the projection point on the z′ axis of the local coordinate system, sum L2 The coordinates of the second point cloud of the target tooth O in the translation coordinate system. The sum of the coordinates of the projection point on the x′ axis and the coordinates of the projection point on the z′ axis of the local coordinate system, sum Lg Let g be the coordinates of the g-th point cloud of the target tooth O in the translation coordinate system. The set sum of the coordinates of the projection points on the x′ axis and the z′ axis of the local coordinate system is called sum. L {sum L1 ,sum L2 ,…,sum Lg Any element sum in} Li Satisfy the formula 1≤i≤g, α1 and α2 are vectors The angle between the x′ axis and the z′ axis, Let i be the coordinates of the i-th point cloud of the target tooth O in the translation coordinate system. The centroid coordinates of the target tooth O in the translation coordinate system and the coordinates of the i-th point cloud The connection of lines, the set sum L {sum L1 ,sum L2 ,…,sum Lg The first subset corresponding to the maximum value of the elements in} The point in the middle is the first feature point of the incisor;

[0056] For the second subset Perform the same operation to obtain the second subset. The second feature point in;

[0057] If the target tooth O is a molar, such as Figure 4 As shown, in the local coordinate system, the target tooth O is moved along x′O T ′ s The tooth is cut in the y′ plane, retaining only the point cloud data of the half of the tooth closest to the cusp. This retained half of the tooth's point cloud data is then projected onto the y′ axis, resulting in the set of projected point clouds of the retained half of the tooth, y′. U {y′ U1 ,y′ U2 ,…,y′ Uσ},y′ U1 To preserve the first point cloud coordinate of the tooth, y′ U2 To preserve the second point cloud coordinate of the tooth, y′ UσLet be the coordinates of the σ-th point cloud, with the subscript U indicating that it belongs to the preserved tooth, where σ is the number of point clouds containing preserved teeth; calculate the coordinates y′ of any two point clouds containing preserved teeth. Ui y′ Uj Chebyshev distance d y If i ≠ j, the calculation formula is:

[0058]

[0059] Find the Chebyshev distance d based on the Chebyshev distance. y The two largest projection points correspond to two coordinate points in the preserved teeth, with the point closer to the lingual side being the minimum point p1 and the point closer to the buccal side being the maximum point p2, where y′ Ui y′ Uj Any two points on the y′ axis projection of the preserved tooth point cloud data;

[0060] Construct a plane S with the y′ axis as the normal vector. The equation of the plane is Ax + By + Cz + D = 0, where A, B, and C are the y′ axis vectors, and D is the intercept coefficient of the plane equation. The plane S is translated along the normal vector y′ axis through the minimum point p1, with a translation step size of 0.2 mm. Each translation retains the set of projection points y′ of half a tooth. U {y′ U1 ,y′ U2 ,…,y′ Uσ All points whose Euclidean distance to the normal vector of plane S is less than or equal to 0.1 mm are projected onto plane S, and the corresponding tooth point cloud coordinates obtained from each translation are saved; the initial plane S passes through the minimum point p1, and the coordinates of the minimum point p1 are (x... p1 y p1 , z p1 If the coefficient D of plane S satisfies:

[0061] -Ax p1 -By p1 -Cz p1 =D

[0062] Plane S is translated along the y′ axis with a step size of 0.2 mm. The local coordinates of the y′ axis and the translation coordinates in three-dimensional space are... If the included angles of the axes are θ1, θ2, and θ3, then the translation process of plane S satisfies the formula:

[0063] A(x p1 -0.2cosθ1)+B(y p1 -0.2cosθ2)+C(z p1 -0.2cosθ3)+D=0

[0064] The y′ is determined by each translation of plane S. UThe projection points are sorted in ascending order on the local coordinate x′ axis to fit a curve, and the maximum points of the curve are determined. Each translation of the S-plane on the posterior molar yields two maximum points, and each translation of the S-plane on the anterior molar yields one maximum point. The obtained maximum points are stored and formed into a set M{M1, M2, ..., M...}. f-1 M f If the target tooth is a posterior molar, M1 and M2 are the maximum points determined by the initial position of plane S, and f is twice the number of translations of plane S. If the target tooth is a premolar, M1 is the maximum point determined by the initial position of plane S, and f is equal to the number of translations of S, which gives the number of maximum points.

[0065] If the target tooth is a molar, then all the maximum points M{M1,M2,…,M…} are considered. f-1 M f In the local coordinate system Projecting onto a plane, the plane is divided into four quadrants according to the two-dimensional plane coordinate system. The coordinates of the points in each quadrant in the target tooth set are found. All points in each quadrant are projected onto the local coordinate system z′ axis. The maximum value on the z′ axis in that quadrant is found, which gives the four cusp feature points of the posterior molar. The four cusp points are connected to form a quadrilateral, and the points in the quadrilateral region are projected onto the z′ axis. The point corresponding to the minimum projection value is the socket feature point of the posterior molar.

[0066] If the target tooth is a premolar, the projection values ​​of all the maximum points M on the y′ axis are divided into two parts: the first part is the part with positive projection values ​​on the y′ axis, and the second part is the part with negative projection values ​​on the y′ axis. Find the coordinates of the target tooth corresponding to the maximum projection values ​​of the two parts on the z′ axis, which are the two cusp feature points of the premolar.

[0067] Step 4: Determine the ridges on the mesial and distal surfaces of the target tooth, such as... Figure 5 As shown, the center c and The line segment corresponding to the line is τ, and passes through... Draw the perpendicular line K to τ, that is, the circle lies on... The tangent at the point will translate the point cloud set of the target tooth O into the coordinate system. Projecting onto the perpendicular line K yields the set of projection points K{k1,k2,…,k...} l}, where k1 is the projection point of the first point cloud of the target tooth O translation coordinate system onto the perpendicular line K, k2 is the projection point of the second point cloud of the target tooth O translation coordinate system onto the perpendicular line K, and k l For the l-th point cloud of the target tooth O translation coordinate system projected onto the vertical line K, calculate the distance d between any two projected points. k The formula is:

[0068]

[0069] Where, k i k j Let d be any two projection points of the target tooth onto the perpendicular line K. k The two points corresponding to the maximum value are the mesial and distal ridges of the target tooth, respectively.

[0070] Identify the buccal and lingual ridges of the target tooth, and then transfer the point cloud of the target tooth to the O-coordinate system. Projecting onto the line τ yields the set of projection points.

[0071] τ{τ1,τ2,…,τ l}, where τ1 is the target tooth set. The value projected onto the vertical line τ, where τ l Let τ1 be the projection point of the first point cloud in the translation coordinate system of the target tooth O onto the straight line τ2, and let τ2 be the projection point of the second point cloud in the translation coordinate system of the target tooth O onto the straight line τ3. l For the l-th point cloud of the target tooth O translation coordinate system projected onto the straight line τ, calculate the distance d between any two projected points. τ

[0072]

[0073] Where, τ i , τ j Let d be two arbitrary projection points of the target tooth onto the straight line τ. τ The two points at their maximum correspond to the buccal and lingual ridges of the teeth.

Claims

1. A method for automatically determining tooth feature points, characterized in that: Includes the following steps: Step 1: Data Preprocessing Stage. Establish a global coordinate system, import the entire row of teeth model, and read the point cloud data of the 3D tooth model in the global coordinate system. Set the distal direction as left and the mesial direction as right. The leftmost adjacent tooth of the target tooth O is designated as the left neighbor tooth L, and the rightmost adjacent tooth of the target tooth O is designated as the right neighbor tooth R. If the target tooth O is the last molar and has no distal adjacent tooth, then the mesial adjacent tooth is designated as the left neighbor tooth L, and the next closest tooth is designated as the right neighbor tooth R. Establish a translation coordinate system, using the centroid coordinates O of the target tooth O in the global coordinate system. s (x, y, z) is the origin of the coordinate system. The x-axis of the translation coordinate system is parallel to the x-axis of the global coordinate system, the y-axis of the translation coordinate system is parallel to the y-axis of the global coordinate system, and the z-axis of the translation coordinate system is parallel to the z-axis of the global coordinate system. This is the point cloud set of the target tooth O in the global coordinate system. The point cloud set in the translation coordinate system is Point cloud set of left neighboring tooth L in global coordinates The point cloud set in the translation coordinate system is Point cloud set of the right neighbor tooth in global coordinates The point cloud set in the translation coordinate system is in, Let O be the first point cloud coordinate of the target tooth in global coordinates. The coordinates of the second point cloud of the target tooth O in global coordinates. Let L be the l-th point cloud coordinate of the target tooth O in global coordinates. Let O be the coordinates of the first point cloud of the target tooth O in the translation coordinate system. The coordinates of the second point cloud of the target tooth O in the translation coordinate system are: The coordinates of the l-th point cloud of the target tooth O in the translation coordinate system. The point cloud coordinates of the first neighboring tooth L in global coordinates. The second point cloud coordinate of the left neighbor tooth L in global coordinates. The point cloud coordinates of the nth point of the left neighbor tooth L in global coordinates. The coordinates of the first point cloud of the left adjacent tooth L in the translation coordinate system. The coordinates of the second point cloud of the left adjacent tooth L in the translation coordinate system. The coordinates of the nth point cloud of the left adjacent tooth L in the translation coordinate system. The coordinates of the first point cloud of the right neighboring tooth R in global coordinates. The coordinates of the second point cloud of the right neighboring tooth R in global coordinates. Let R be the nth point cloud coordinate of the right neighboring tooth R in global coordinates. Let R be the coordinates of the first point cloud of the right neighboring tooth in the translation coordinate system. The coordinates of the second point cloud of the right adjacent tooth R in the translation coordinate system are: Given the nth point cloud coordinates of the right adjacent tooth R in the translation coordinate system, and the centroid coordinates of the target tooth O in the translation coordinate system... left adjacent tooth centroid coordinates Right adjacent tooth centroid coordinates Projected onto the global coordinate XOY plane, the centroid coordinates of the target tooth on the XOY plane of the global coordinate system are... The projection point and the coordinates of the centroid of the left adjacent tooth The projection point and the coordinates of the centroid of the right adjacent tooth The projection points form a triangle with the center of the circumcircle of the triangle being c and the radius being r; Step 2: Establish a local coordinate system. Under the translation coordinate system, determine the centroid coordinates of the target tooth O. The origin of the local coordinate system is used, with the centroid coordinates of the target tooth O as the reference point. and the coordinates of the centroid of the left adjacent tooth connection Let x′ be the x-axis of the local coordinate system, and draw a circle through the center c. A perpendicular line is drawn from the center of the circle, with the foot of the perpendicular at point p. The line connecting the center of the circle c and the foot of the perpendicular at point p is... Centroid coordinates of the target tooth O Make parallel to Draw a straight line h through the center c of the circle, parallel to the x′ axis, intersecting line h at point c′. The coordinates of the centroid of the target tooth O are used. Connect point c' to point c' Let y′ be the local coordinate system, and use the right-hand rule to determine the z′ axis, and stipulate that the positive direction of the z′ axis is from the root to the apex of the tooth; Step 3: Determine the feature points of the target tooth O. Teeth are divided into canines, incisors, and molars, among which molars are further divided into premolars and molars. If the target tooth O is a canine, translate the point cloud set of the coordinate system of the target tooth O. Projected onto the z′ axis of the local coordinate system, the maximum projection value is the feature point of the canine; If the target tooth O is an incisor, in the local coordinate system, along y′O T ′ s The z′ plane will be the point cloud set of the target tooth O. Divided into two halves, forming two subsets, namely the first subset. Second subset Let g be the coordinates of the g-th point cloud of the target tooth O in the translation coordinate system. Let g+1 be the point cloud coordinates of the target tooth O in the translation coordinate system. Let g+2 be the point cloud coordinates of the target tooth O in the translation coordinate system, and let g be the first subset. There are a total of g point cloud coordinates; First Subset Each point is projected onto the x′O of the local coordinate system. T ′ s The z′ plane yields the set sum. L {sum L1 ,sum L2 ,…,sum Lg }, sum L1 The coordinates of the first point cloud of the target tooth O in the translation coordinate system. The sum of the coordinates of the projection point on the x′ axis and the coordinates of the projection point on the z′ axis of the local coordinate system, sum L2 The coordinates of the second point cloud of the target tooth O in the translation coordinate system. The sum of the coordinates of the projection point on the x′ axis and the coordinates of the projection point on the z′ axis of the local coordinate system, sum Lg Let g be the coordinates of the g-th point cloud of the target tooth O in the translation coordinate system. The set sum of the coordinates of the projection points on the x′ axis and the z′ axis of the local coordinate system is called sum. L {sum L1 ,sum L2 ,…,sum Lg Any element sum in} Li Satisfy the formula 1≤i≤g, α1 and α2 are vectors The angle between the x′ axis and the z′ axis, Let i be the coordinates of the i-th point cloud of the target tooth O in the translation coordinate system. The centroid coordinates of the target tooth O in the translation coordinate system and the coordinates of the i-th point cloud The connection, the set The first subset corresponding to the maximum value of the elements in the set. The point in the middle is the first feature point of the incisor; For the second subset Perform the same operation to obtain the second subset. The second feature point in; If the target tooth O is a molar, in the local coordinate system, move the target tooth O along x′O T ′ s The tooth is cut in the y′ plane, retaining only the point cloud data of the half closest to the cusp. This retained half of the tooth's point cloud data is then projected onto the y′ axis to obtain the set of projected point clouds of the retained half of the tooth. To preserve the first point cloud coordinates of the tooth, To preserve the second point cloud coordinates of the tooth, Let be the coordinates of the σ-th point cloud, with the subscript U indicating that it belongs to the preserved tooth, where σ is the number of point clouds containing preserved teeth; calculate the coordinates y′ of any two point clouds containing preserved teeth. Ui y′ Uj Chebyshev distance d y If i ≠ j, the calculation formula is: Find the Chebyshev distance d based on the Chebyshev distance. y The two largest projection points correspond to two coordinate points in the preserved teeth, with the point closer to the lingual side being the minimum point p1 and the point closer to the buccal side being the maximum point p2, where y′ Ui y′ Uj Any two points on the y′ axis projection of the preserved tooth point cloud data; Construct a plane S with the y′ axis as the normal vector. The equation of the plane is Ax + By + Cz + D = 0, where A, B, and C are the y′ axis vectors, and D is the intercept coefficient of the plane equation. The plane S is translated along the normal vector y′ axis through the minimum point p1, with a translation step size of 0.2 mm. Each translation retains the set of projection points y′ of half a tooth. U {y′ U1 ,y′ U2 ,…,y′ Uσ All points whose Euclidean distance to the normal vector of plane S is less than or equal to 0.1 mm are projected onto plane S, and the corresponding tooth point cloud coordinates obtained from each translation are saved; the initial plane S passes through the minimum point p1, and the coordinates of the minimum point p1 are (x p1 y p1 , z p1 If the coefficient D of plane S satisfies: -Ax p1 -By p1 -Cz p1 =D Plane S is translated along the y′ axis with a step size of 0.2 mm. The angles between the local coordinate y′ axis and the global coordinate X, Y, Z axes in three-dimensional space are θ1, θ2, and θ3, respectively. The translation process of plane S satisfies the formula: A(x p1 -0.2cosθ1)+B(y p1 -0.2cosθ2)+C(z p1 -0.2cosθ3)+D=0 The y′ is determined by each translation of plane S. U The projection points are sorted in ascending order on the local coordinate x′ axis to fit a curve, and the maximum points of the curve are determined. Each translation of the S-plane on the posterior molar yields two maximum points, and each translation of the S-plane on the anterior molar yields one maximum point. The obtained maximum points are stored and formed into a set M{M1, M2, ..., M...}. f-1 M f If the target tooth is a posterior molar, M1 and M2 are the maximum points determined by the initial position of plane S, and f is twice the number of translations of plane S. If the target tooth is a premolar, M1 is the maximum point determined by the initial position of plane S, and f is equal to the number of translations of S, which gives the number of maximum points. If the target tooth is a molar, then all the maximum points M{M1,M2,…,M…} are considered. f-1 M f In the local coordinate system Projecting onto a plane, the plane is divided into four quadrants according to a two-dimensional coordinate system. The coordinates of each point in the target tooth set are found. All points in each quadrant are projected onto the local coordinate system z′ axis. The maximum value of the projected points on the z′ axis is found, which gives the four cusp feature points of the posterior molar. Connecting the four cusp points forms a quadrilateral, and the points within the quadrilateral region are projected onto the z′ axis. The point corresponding to the minimum projection value is the socket feature point of the posterior molar. If the target tooth is a premolar, the projection values ​​of all the maximum points M on the y′ axis are divided into two parts: the first part has positive projection values ​​on the y′ axis, and the second part has negative projection values ​​on the y′ axis. The coordinates of the target tooth corresponding to the maximum projection values ​​of the two parts on the z′ axis are found, which are the two cusp feature points of the premolar. Step 4: Determine the ridge points on the mesial and distal surfaces of the target tooth, with the center point c and... The line segment corresponding to the line is τ, and passes through... Draw the perpendicular line K to τ, that is, the circle lies on... The tangent at the point will translate the point cloud set of the target tooth O into the coordinate system. Projecting onto the perpendicular line K yields the set of projection points K{k1,k2,…,k...} l }, where k1 is the projection point of the first point cloud of the target tooth O translation coordinate system onto the perpendicular line K, k2 is the projection point of the second point cloud of the target tooth O translation coordinate system onto the perpendicular line K, and k l For the l-th point cloud of the target tooth O translation coordinate system projected onto the vertical line K, calculate the distance d between any two projected points. k The formula is: Where, k i k j Let d be any two projection points of the target tooth onto the perpendicular line K. k The two points corresponding to the maximum value are the ridge points on the mesial and distal surfaces of the target tooth, respectively. Identify the buccal and lingual ridges of the target tooth, and then transfer the point cloud of the target tooth to the O-coordinate system. Projecting onto the line τ, we obtain the set of projection points τ{τ1,τ2,…,τ}. l }, where τ1 is the target tooth set. The value projected onto the vertical line τ, where τ l Let τ1 be the projection point of the first point cloud in the translation coordinate system of the target tooth O onto the straight line τ2, and let τ2 be the projection point of the second point cloud in the translation coordinate system of the target tooth O onto the straight line τ3. l For the l-th point cloud of the target tooth O translation coordinate system projected onto the straight line τ, calculate the distance d between any two projected points. τ Where, τ i , τ j Let d be two arbitrary projection points of the target tooth onto the straight line τ. τ The two points at their maximum correspond to the buccal and lingual ridges of the teeth.

2. The method for automatically determining tooth feature points according to claim 1, characterized in that: In the global coordinate system, the midpoint of the line segment connecting the last left molar and the last right molar is taken as the origin of the global coordinate system, and the connecting line segment is taken as the X-axis of the global coordinate system with the vector (1,0,0). A line segment perpendicular to the X-axis and pointing in the direction of the central incisors is drawn through the origin as the Y-axis of the global coordinate system with the vector (0,1,0). A line segment perpendicular to both the X-axis and Y-axis and pointing from the cusp to the root is drawn through the origin as the Z-axis of the global coordinate system with the vector (0,0,1).

3. The method for automatically determining tooth feature points according to claim 1, characterized in that: The centroid coordinates O of the target tooth O in the global coordinate system s The method to obtain (x, y, z) is the point cloud set under the global coordinates of the target tooth O. The point cloud coordinate set of the target tooth O is calculated as follows: The average value of all point cloud coordinates is used as the centroid coordinate O of the target tooth O. s (x,y,z), the calculation formula is: Among them, (x j ,y j ,z j Let be the j-th point cloud coordinate of the point cloud set of the target tooth O in global coordinates, where 1≤j≤l.

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