CN108836522B - Method and device for simulating gum deformation - Google Patents
Method and device for simulating gum deformation Download PDFInfo
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- CN108836522B CN108836522B CN201810230780.7A CN201810230780A CN108836522B CN 108836522 B CN108836522 B CN 108836522B CN 201810230780 A CN201810230780 A CN 201810230780A CN 108836522 B CN108836522 B CN 108836522B
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- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61C—DENTISTRY; APPARATUS OR METHODS FOR ORAL OR DENTAL HYGIENE
- A61C7/00—Orthodontics, i.e. obtaining or maintaining the desired position of teeth, e.g. by straightening, evening, regulating, separating, or by correcting malocclusions
- A61C7/002—Orthodontic computer assisted systems
Abstract
The invention discloses a gum deformation simulation method and device, relates to the technical field of oral cavities, and can solve the problems of low efficiency and unreality of the existing gum deformation simulation method. The method mainly comprises the following steps: determining a gum boundary point, a tooth corresponding to the gum boundary point and a motionless point participating in gum grid deformation, wherein the gum boundary point is a boundary point of a junction of a tooth grid and the gum grid; taking a point between a boundary line formed by the gum boundary points and a boundary line formed by the immobile points as a deformation point, and determining teeth corresponding to each deformation point; when the teeth are transferred, the positions of the gum boundary points and the deformation points corresponding to the transferred teeth are updated by using a transfer matrix and a radial basis function interpolation method of the transferred teeth so as to update the gum grid. The method is mainly suitable for a scene of automatically simulating the soft tissue deformation of the gum.
Description
Technical Field
The invention relates to the technical field of oral cavity, in particular to a method and a device for simulating gum deformation.
Background
In virtual orthodontics, a three-dimensional dental mesh model of a patient is typically obtained by intraoral scanning, the three-dimensional dental mesh model being divided into a crown region and a gum region, typically the gum region being a connected streaming mesh. When correcting a deformed tooth, as the tooth is corrected to reach a target position, the gum also moves with the transfer of the tooth and causes a change in condition.
The current methods for simulating gum deformation mainly comprise a physical method and a non-physical method. The physical method mainly considers the biomechanical characteristics of stress-strain relationship, non-uniformity, anisotropy, viscoelasticity and the like of the gum soft tissue, and simulates the deformation of the gum by utilizing the biomechanical characteristics; the non-physical method mainly constructs a constrained surface through the divided dental crown and gum boundary and adopts minimized energy to realize continuous deformation of the surface. However, the current physical method depends on the definition of force, not only the deformation of the mesh at the dental crown boundary point is excessive and the change of the mesh far away from the boundary point is not obvious, but also the deformation results are different due to different definitions of force, namely the deformation standards are not uniform; current non-physical methods can change the topology of the gingival mesh. In addition, the two methods have the problems of large calculation amount and low simulation efficiency. Therefore, how to effectively and truly simulate the deformation of the gum is urgent to be solved.
Disclosure of Invention
In view of this, the present invention provides a method and an apparatus for simulating gum deformation, which aims to solve the problems of low efficiency and unreality of the existing gum deformation simulation method.
In order to solve the above problems, the present invention mainly provides the following technical solutions:
in a first aspect, the present invention provides a method for simulating gum deformation, the method comprising:
determining a gum boundary point, a tooth corresponding to the gum boundary point and a motionless point participating in gum grid deformation, wherein the gum boundary point is a boundary point of a junction of a tooth grid and the gum grid;
taking a point between a boundary line formed by the gum boundary points and a boundary line formed by the immobile points as a deformation point, and determining teeth corresponding to each deformation point;
when the teeth are transferred, the positions of the gum boundary points and the deformation points corresponding to the transferred teeth are updated by using a transfer matrix and a radial basis function interpolation method of the transferred teeth so as to update the gum grid.
In a second aspect, the present invention provides a gingival deformation simulation device, the device comprising:
the first determining unit is used for determining a gum boundary point, a tooth corresponding to the gum boundary point and an immobile point participating in gum grid deformation, wherein the gum boundary point is a boundary point of a tooth grid and the gum grid;
a second determining unit, configured to determine a tooth corresponding to each deformed point by using a point between a boundary line formed by the gum boundary points and a boundary line formed by the fixed point as a deformed point;
and the updating unit is used for updating the positions of the gingival boundary point and the deformation point corresponding to the tooth with the transfer when the tooth is transferred by utilizing the transfer matrix and the radial basis function interpolation method of the tooth with the transfer so as to update the gingival grid.
In a third aspect, the present invention provides a storage medium comprising a stored program, wherein the program is executed to control a device on which the storage medium is located to perform the method for simulating gum deformation according to the first aspect.
In a fourth aspect, the present invention provides a gingival deformation simulation device, the device comprising a storage medium and a processor;
the processor is suitable for realizing instructions;
the storage medium adapted to store a plurality of instructions;
the instructions are adapted to be loaded by the processor and to perform a method of simulating gum deformation as described in the first aspect.
By the technical scheme, the technical scheme provided by the invention at least has the following advantages:
the gum deformation simulation method and the gum deformation simulation device provided by the invention can determine gum boundary points, teeth corresponding to the gum boundary points and immobile points participating in gum grid deformation, then take points between boundary lines formed by the gum boundary points and boundary lines formed by the immobile points as deformation points, determine teeth corresponding to each deformation point, and finally update the positions of the gum boundary points and the deformation points corresponding to the teeth which are subjected to the transfer by directly using a transfer matrix and a radial basis function interpolation method of the teeth which are subjected to the transfer when the teeth are transferred, wherein the positions of the immobile points are not changed. Therefore, the three characteristic points, namely the gingival boundary point, the fixed point and the deformation point, participating in the gum deformation are determined based on the gum deformation process, and the three characteristic points move along with the tooth transfer according to the deformation characteristics of the three characteristic points, so that excessive deformation and unobvious deformation are avoided, the topological structure of a gum grid is not changed, and the gum deformation is simulated more truly. And when the tooth is transferred again, the positions of the feature points can be updated only by performing operation according to the current positions of the three feature points and by utilizing the transfer matrix of the transferred tooth and a radial basis function interpolation method, so that the re-deformation of the gum is simulated.
The foregoing description is only an overview of the technical solutions of the present invention, and the embodiments of the present invention are described below in order to make the technical means of the present invention more clearly understood and to make the above and other objects, features, and advantages of the present invention more clearly understandable.
Drawings
Various other advantages and benefits will become apparent to those of ordinary skill in the art upon reading the following detailed description of the preferred embodiments. The drawings are only for purposes of illustrating the preferred embodiments and are not to be construed as limiting the invention. Also, like reference numerals are used to refer to like parts throughout the drawings. In the drawings:
FIG. 1 illustrates an exemplary graph of distortion of a mesh caused by radial basis function interpolation provided in the prior art;
FIG. 2 is a flowchart illustrating a method for simulating gum deformation according to an embodiment of the present invention;
FIG. 3 is a flow chart illustrating another method for simulating gum deformation according to an embodiment of the present invention;
FIG. 4 is a block diagram illustrating a simulation apparatus for gum deformation according to an embodiment of the present invention;
fig. 5 is a block diagram illustrating another simulation apparatus for gum deformation according to an embodiment of the present invention.
Detailed Description
Exemplary embodiments of the present application will be described in more detail below with reference to the accompanying drawings. While exemplary embodiments of the present application are shown in the drawings, it should be understood that the present application may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.
The radial basis function is a function whose argument is distance, which may be euclidean distance or otherwise. In the grid deformation, different application scenes can define the movement of different boundary points, the algorithm is independent of grid edges, and only the displacement condition of the points needs to be calculated, so that the topological structure of the grid is not changed at all. The radial basis function interpolation is to solve a new numerical value by using a plurality of radial basis functions. If some points in the data of one point cloud model are constrained, that is, the motion of the points is known in advance or can be predicted, the motion of the rest points or any specified points in the point cloud can be simulated by interpolating the radial basis functions of the motion of the constrained points. Fig. 1 is a schematic diagram of grid deformation caused by a radial basis function interpolation method. Since the deformation of the gum mesh is close to the algorithm of the radial basis function, the deformation of the gum mesh can be realized by using the radial basis function. The specific implementation mode is as follows:
the embodiment of the invention provides a method for simulating gum deformation, which mainly comprises the following steps of:
101. and determining a gum boundary point, teeth corresponding to the gum boundary point and an immobile point participating in gum grid deformation.
Wherein the gum boundary point is a boundary point where a tooth mesh and the gum mesh are intersected with the gum mesh. When the radial basis function is used for simulating the deformation of the gum grid, the constraint points are determined, and then the moving positions of other points (namely the constrained points) are calculated by using the radial basis function interpolation method. The gum boundary point is closest to the teeth, so the gum boundary point directly moves along with the teeth, the moving degree of the gum boundary point is the same as that of the teeth, and other points can be restrained from moving along with the gum boundary point in different degrees; as a point on the gum mesh is farther from the tooth, the point is less affected by tooth migration until a critical area is reached that is unaffected by tooth migration but is closest to the tooth and can constrain the deformation state of other points. The constraint points in the gingival grid deformation thus include gingival boundary points and motionless points involved in the gingival grid deformation.
Since there are many teeth in a set of teeth, each tooth will only affect the peripheral gingival boundary point to move, so after obtaining the gingival boundary point, it is also necessary to determine the tooth corresponding to each gingival boundary point.
It is added that the motionless points that do not participate in the deformation of the gum mesh do not participate in the subsequent operations, which can greatly reduce the computation of the mesh points.
102. And taking a point between a boundary line formed by the gum boundary points and a boundary line formed by the immobile points as a deformation point, and determining the tooth corresponding to each deformation point.
After the gum boundary point and the immobile point are determined, other non-constraint points constrained by the gum boundary point and the immobile point need to be found out, namely points between a boundary line formed by the gum boundary point and a boundary line formed by the immobile point are located, the found points are used as deformation points, and then teeth corresponding to each deformation point are determined so that each deformation point can move along with the corresponding teeth to be closer to real gum deformation.
103. When the teeth are transferred, the positions of the gum boundary points and the deformation points corresponding to the transferred teeth are updated by using a transfer matrix and a radial basis function interpolation method of the transferred teeth so as to update the gum grid.
When the teeth move, the transfer matrix of the moved teeth can be used for updating the positions of the gum boundary points corresponding to the teeth, then the updated positions of the deformed points corresponding to the teeth which move are calculated by using the updated positions of the gum boundary points and a radial basis function interpolation method, the fixed points which participate in the gum grid deformation keep the positions of the deformed points, and finally the gum grid is updated by updating the positions of the gum boundary points and the deformed points, so that the gum grid deformation is realized.
It should be noted that the embodiment of the present invention can be applied to a scene in which only a single tooth is transferred (e.g. gingival grid deformation during interactive tooth arrangement), and can also be applied to a scene in which multiple teeth are transferred (e.g. gingival grid deformation after automatic tooth arrangement). The interactive tooth arrangement is realized by manually transferring a certain tooth by using tooth arrangement software, for example, the interactive operation includes axial translation of a crown root, lateral translation of a buccolingual side, mesial translation, axial rotation around the crown root, lateral rotation around the buccolingual side, mesial rotation, and the like. When applied to interactive tooth arrangement, the gingival mesh may be deformed in real time with the transfer of teeth; when the method is applied to automatic tooth arrangement, the gum grid deformation can be realized according to the tooth and gum condition before tooth arrangement and the tooth arrangement result, so as to obtain the gum grid information corresponding to the tooth arrangement result.
In addition, the radial basis function used in the embodiment of the present invention may be a global support function MQB, and the radial basis function is taken as
The gum deformation simulation method provided by the embodiment of the invention can determine gum boundary points, teeth corresponding to the gum boundary points and immobile points participating in gum grid deformation, then take points between boundary lines formed by the gum boundary points and boundary lines formed by the immobile points as deformation points, determine teeth corresponding to each deformation point, and finally update the positions of the gum boundary points and the deformation points corresponding to the teeth which are subjected to the transfer by directly using a transfer matrix and a radial basis function interpolation method of the teeth which are subjected to the transfer when the teeth are transferred, wherein the positions of the immobile points are not changed. Therefore, the three characteristic points, namely the gingival boundary point, the fixed point and the deformation point, participating in the gum deformation are determined based on the gum deformation process, and the three characteristic points move along with the tooth transfer according to the deformation characteristics of the three characteristic points, so that excessive deformation and unobvious deformation are avoided, the topological structure of a gum grid is not changed, and the gum deformation is simulated more truly. When the tooth is transferred again, the positions of the feature points can be updated only by performing operation according to the current positions of the three feature points and by using a radial basis function interpolation method, so that the re-deformation of the gum is simulated.
Further, according to the method shown in fig. 2, another embodiment of the present invention further provides a method for simulating gum deformation, as shown in fig. 3, the method comprising:
201. and determining a gum boundary point, teeth corresponding to the gum boundary point and an immobile point participating in gum grid deformation.
In practical applications, the specific implementation methods for determining the teeth corresponding to the gingival boundary points and the immobile points participating in the deformation of the gingival grid can be various, and the following methods are respectively described by taking a preferred mode as an example:
the specific implementation manner of determining the gum boundary point and the tooth corresponding to the gum boundary point may be: firstly, acquiring a tooth boundary point of each tooth and a gum boundary point of the gum grid; then determining the centroid point of each tooth; respectively calculating the distance between each gum boundary point and each center of mass point according to each gum boundary point, and taking the teeth corresponding to the minimum distance and the next minimum distance as candidate teeth corresponding to the gum boundary points; and finally, respectively calculating the distance from each tooth boundary point of the candidate teeth to the corresponding gum boundary point, and determining the candidate teeth corresponding to the minimum distance as the teeth corresponding to the gum boundary point.
When the tooth boundary point of each tooth and the gum boundary point of the gum grid are obtained, an algorithm for extracting the characteristic edge of the grid boundary is adopted, namely, a set of the searched edges is obtained. Each edge only exists on one triangle, and the implementation adopts the vtkFeatureEdges.
(II) the specific implementation manner of determining the motionless point participating in the gingival grid deformation can be as follows: moving the upper jaw target plane for a certain distance along the upward direction of the normal of the upper jaw target plane, and moving the lower jaw target plane for a certain distance along the downward direction of the normal of the lower jaw target plane, so that two cutting lines are obtained by enabling the moved target plane to be tangent with the gum mesh; and sequencing the points on each cutting line, sampling according to the sequence of the points so that the distance between two adjacent points in the collected points is greater than a preset threshold value, and determining the points obtained by sampling as immobile points. Wherein the specific tooth comprises an incisor and a first molar; and/or the preset threshold value is 10 mm. The sampling reason can reduce the number of the constraint points in the subsequent equation system solving calculation on one hand, and relatively uniform sampling can be performed on the sequenced cutting line according to rules on the other hand, so that the correctness of the constraint points when the radial basis interpolation deformation is applied is also ensured.
The process of sorting the points on the cutting line may be as follows: starting from any node, judging whether two neighbor nodes (each point has two neighbor nodes) are added into the result, if one of the two neighbor nodes is not added, the next judged node is the node which is not added. The cutting line after the point sequencing can be obtained by the circulation.
For example, the upper jaw is fitted to an upper jaw target plane with the centroid points of the four teeth 11, 21, 16, 26, and then the target plane is translated upward by 10mm to generate a cutting line of the upper jaw, the lower jaw is fitted to a lower jaw target plane with the centroid points of the four teeth 31, 41, 36, 46, and the target plane is translated downward by 10mm to generate a cutting line of the lower jaw; then, the immobile points of the upper jaw and the lower jaw are obtained by sequencing and sampling the points on the two cutting lines. Here, the tooth marks 11, 21, 16, 26, 31, 41, 36, 46 are marked according to the FDI (F d ration dental association) dentition marking method.
202. And taking a point between a boundary line formed by the gum boundary points and a boundary line formed by the immobile points as a deformation point, and determining the tooth corresponding to each deformation point.
When determining the tooth corresponding to each deformation point, the centroid point of each tooth may be determined first, then the distance between the deformation point and each centroid point is calculated, and finally the tooth to which the centroid point closest to the deformation point belongs is directly determined as the tooth corresponding to the deformation point.
203. When the teeth are transferred, determining the position of the gum boundary point corresponding to the transferred teeth after moving according to the transfer matrix of the transferred teeth and the position of the gum boundary point corresponding to the transferred teeth before moving.
Since the gum boundary point is close to the tooth, the tooth transfer matrix can be directly used as the transfer matrix corresponding to the gum boundary point, and the position of the gum boundary point after moving can be calculated by combining the position of the gum boundary point before moving.
204. And calculating the displacement of the gum boundary point according to the position of the gum boundary point before the movement and the position after the movement.
205. And determining the displacement of each deformation point by using the radial basis function interpolation method according to the displacement of the gum boundary point and the orthogonality of the weight coefficients of all the constraint points.
Specifically, a linear equation set may be obtained by using an equation formed based on orthogonality of the weight coefficients of the respective constraint points and an equation formed by a radial basis function interpolation formula satisfied by the constraint points; then, substituting the components of the displacement of the gum boundary point in each dimension into the linear equation set respectively, calculating to obtain the components of the vector consisting of the unknown parameters in the radial basis function interpolation formula in each dimension, and determining each unknown parameter based on the calculated components; and finally, calculating the displacement of each deformation point by a radial basis function interpolation formula after each unknown parameter is determined.
Wherein the constraint points comprise gum boundary points and motionless points. The equation formed based on the orthogonality of the weight coefficients of the constraint points is
The equation formed by the radial basis function interpolation formula satisfied by the constraint points is
When ordering radial basis function
When, the system of linear equations is
The interpolation formula of the radial basis function is
Wherein, wiWeight value of i-th constraint point, ciIs the ith constraint point, cjIs the jth constraint point, vjIs the displacement of the jth constraint point, r is an arbitrary position, p0、p1、p2、p3Is a parameter with a fixed value.
That is, in the radial basis function
Can be based on the equation
Sum equation
A system of linear equations is obtained:
the left coefficient matrix is a symmetric positive semi-definiteThe linear equation system can be expressed as Ax ═ b, i.e., a represents the left matrix, x represents the middle matrix, and b represents the right matrix in the equation. Constructing a vector b by taking position values of all constraint points in the x direction as scalar values1Solving for Ax1＝b1To obtain a solution vector x1(ii) a Constructing a vector b by taking position values of all constraint points in the y direction as scalar values2Solving for Ax2＝b2To obtain a solution vector x2(ii) a Constructing a vector b by taking position values in the z direction of all the constraint points as scalar values3Solving for Ax3＝b3To obtain a solution vector x3(ii) a From x1、x2And x3Can obtain w1、w2…wn、p0、p1、p2And p3The specific values of the unknown parameters are finally determined by the radial basis function interpolation formula after each unknown parameter is determined
And calculating the displacement of each deformation point so as to determine the position after the movement according to the displacement and the position before the movement.
206. And determining the position of each deformed point after movement according to the position of each deformed point before movement and the corresponding displacement.
Since the directional line segment from the initial position to the final position is called a displacement, when the position before the movement (i.e., the initial position) and the displacement are known, the position after the movement (i.e., the final position) can be calculated.
207. And updating the gum grid based on the position of the gum boundary point after movement and the position of the deformed point after movement.
Further, according to the above method embodiment, another embodiment of the present invention provides a gingival deformation simulation device, as shown in fig. 4, the device mainly includes:
a first determining unit 31, configured to determine a gum boundary point, a tooth corresponding to the gum boundary point, and an immobile point participating in deformation of a gum mesh, where the gum boundary point is a boundary point where a tooth mesh and the gum mesh are connected;
a second determining unit 32 configured to determine a tooth corresponding to each deformed point by using a point between a boundary line formed by the gum boundary points and a boundary line formed by the fixed point as a deformed point;
and an updating unit 33, configured to update positions of the gingival boundary point and the inflection point corresponding to the tooth with the transition matrix and the radial basis function interpolation method of the tooth with the transition when the tooth has the transition, so as to update the gingival mesh.
Optionally, as shown in fig. 5, the first determining unit 31 includes:
an obtaining module 311, configured to obtain a tooth boundary point of each tooth and a gum boundary point of the gum grid;
a first determination module 312 for determining a centroid point for each tooth;
a first calculation module 313, which calculates the distance between each gum boundary point and each centroid point;
the first determining module 312 is further configured to select the tooth corresponding to the minimum distance and the next minimum distance as the candidate tooth corresponding to the gum boundary point;
the first calculating module 313 is further configured to calculate distances from each tooth boundary point of the candidate teeth to the corresponding gum boundary point, respectively;
the first determining module 31 is further configured to determine the candidate tooth corresponding to the minimum distance as the tooth corresponding to the gum boundary point.
Optionally, as shown in fig. 5, the first determining unit 31 includes:
a fitting module 314 for fitting an upper jaw target plane and a lower jaw target plane from the centroid points of specific teeth in the upper and lower jaws;
a moving module 315, configured to move the upper jaw target plane by a specific distance in an upward direction along a normal of the upper jaw target plane, and move the lower jaw target plane by a specific distance in a downward direction along a normal of the lower jaw target plane, so that two cutting lines are obtained by tangency between the moved target plane and the gum mesh;
a sorting module 316, configured to sort the points on each cutting line;
the sampling module 317 is configured to sample in the order of the points, so that a distance between two adjacent points in the taken points is greater than a preset threshold, and determine the points obtained by sampling as stationary points.
Optionally, the specific teeth comprise an incisor and a first molar; and/or the preset threshold value is 10 mm.
Optionally, as shown in fig. 5, the second determining unit 32 is configured to be used in a second determining module 321 for determining a centroid point of each tooth; and determining the tooth to which the centroid point closest to the deformation point belongs as the tooth corresponding to the deformation point.
Optionally, as shown in fig. 5, the updating unit 33 includes:
the second determining module 331 is configured to determine, when a tooth is shifted, a position after a gum boundary point corresponding to the shifted tooth is shifted according to a shift matrix of the shifted tooth and a position before the gum boundary point corresponding to the shifted tooth is shifted;
a second calculating module 332, configured to calculate a displacement of the gum boundary point according to the position of the gum boundary point before moving and the position of the gum boundary point after moving;
a third determining module 333, configured to determine, according to the displacement of the gum boundary point and orthogonality of the weight coefficients of the constraint points, the displacement of each deformed point by using the radial basis function interpolation method, where the constraint points include the gum boundary point and the immobile point;
a fourth determining module 334, configured to determine, according to the position of each deformed point before movement and the corresponding displacement, the position of each deformed point after movement;
and an updating module 335, configured to update the gingival mesh based on the moved position of the gingival boundary point and the moved position of the deformed point.
Optionally, the third determining module 333 is configured to obtain a linear equation set by using an equation formed based on orthogonality of the weight coefficients of the respective constraint points and an equation formed by a radial basis function interpolation formula satisfied by the constraint points; substituting the components of the displacement of the gum boundary point in each dimension into the linear equation set respectively, calculating to obtain the components of the vector consisting of the unknown parameters in the radial basis function interpolation formula in each dimension, and determining each unknown parameter based on the calculated components; and calculating the displacement of each deformation point by a radial basis function interpolation formula after each unknown parameter is determined.
Optionally, the equation formed based on the orthogonality of the weight coefficients of the constraint points is
The equation formed by the radial basis function interpolation formula satisfied by the constraint points is
When ordering radial basis function
When, the system of linear equations is
The interpolation formula of the radial basis function is
Wherein, wiWeight value of i-th constraint point, ciIs the ith constraint point, cjIs the jth constraint point, vjIs the displacement of the jth constraint pointR is an arbitrary position, p0、p1、p2、p3Is a parameter with a fixed value.
The gum deformation simulation device provided by the embodiment of the invention can determine gum boundary points, teeth corresponding to the gum boundary points and immobile points participating in gum grid deformation, then take points between boundary lines formed by the gum boundary points and boundary lines formed by the immobile points as deformation points, determine teeth corresponding to each deformation point, and finally update the positions of the gum boundary points and the deformation points corresponding to the teeth which are subjected to the transfer by directly using a transfer matrix and a radial basis function interpolation method of the teeth which are subjected to the transfer when the teeth are transferred, wherein the positions of the immobile points are not changed. Therefore, the three characteristic points, namely the gingival boundary point, the fixed point and the deformation point, participating in the gum deformation are determined based on the gum deformation process, and the three characteristic points move along with the tooth transfer according to the deformation characteristics of the three characteristic points, so that excessive deformation and unobvious deformation are avoided, the topological structure of a gum grid is not changed, and the gum deformation is simulated more truly. When the tooth is transferred again, the positions of the feature points can be updated only by performing operation according to the current positions of the three feature points and by using a radial basis function interpolation method, so that the re-deformation of the gum is simulated.
The embodiment of the invention provides a storage medium, which comprises a stored program, wherein when the program runs, a device on which the storage medium is arranged is controlled to execute the simulation method of gum deformation.
The storage medium may include volatile memory in a computer readable medium, Random Access Memory (RAM), nonvolatile memory such as Read Only Memory (ROM) or flash memory (flash RAM), and the like, and the memory includes at least one memory chip.
The instructions stored in the storage medium provided by the embodiment of the invention can determine the gum boundary point, the tooth corresponding to the gum boundary point and the immobile point participating in the gum grid deformation, then take the point between the boundary line formed by the gum boundary point and the boundary line formed by the immobile point as the deformation point, determine the tooth corresponding to each deformation point, and finally, when the tooth is transferred, the positions of the gum boundary point and the deformation point corresponding to the tooth which is transferred can be updated directly by using the transfer matrix and the radial basis function interpolation method of the tooth which is transferred, and the position of the immobile point is not changed. Therefore, the three characteristic points, namely the gingival boundary point, the fixed point and the deformation point, participating in the gum deformation are determined based on the gum deformation process, and the three characteristic points move along with the tooth transfer according to the deformation characteristics of the three characteristic points, so that excessive deformation and unobvious deformation are avoided, the topological structure of a gum grid is not changed, and the gum deformation is simulated more truly. When the tooth is transferred again, the positions of the feature points can be updated only by performing operation according to the current positions of the three feature points and by using a radial basis function interpolation method, so that the re-deformation of the gum is simulated.
The embodiment of the invention provides a gum deformation simulation device, which comprises a storage medium and a processor;
the processor is suitable for realizing instructions;
the storage medium adapted to store a plurality of instructions;
the instructions are adapted to be loaded by the processor and to perform a method of simulating gum deformation as described above.
The processor comprises a kernel, and the kernel calls the corresponding program unit from the storage medium. One or more than one kernel can be set, and the deformation of the gum can be effectively and truly simulated by adjusting the kernel parameters.
The gum deformation simulation device provided by the embodiment of the invention can determine gum boundary points, teeth corresponding to the gum boundary points and immobile points participating in gum grid deformation, then take points between boundary lines formed by the gum boundary points and boundary lines formed by the immobile points as deformation points, determine teeth corresponding to each deformation point, and finally update the positions of the gum boundary points and the deformation points corresponding to the teeth which are subjected to the transfer by directly using a transfer matrix and a radial basis function interpolation method of the teeth which are subjected to the transfer when the teeth are transferred, wherein the positions of the immobile points are not changed. Therefore, the three characteristic points, namely the gingival boundary point, the fixed point and the deformation point, participating in the gum deformation are determined based on the gum deformation process, and the three characteristic points move along with the tooth transfer according to the deformation characteristics of the three characteristic points, so that excessive deformation and unobvious deformation are avoided, the topological structure of a gum grid is not changed, and the gum deformation is simulated more truly. When the tooth is transferred again, the positions of the feature points can be updated only by performing operation according to the current positions of the three feature points and by using a radial basis function interpolation method, so that the re-deformation of the gum is simulated.
The present application further provides a computer program product adapted to perform program code for initializing the following method steps when executed on a simulation device of gingival deformation:
determining a gum boundary point, a tooth corresponding to the gum boundary point and a motionless point participating in gum grid deformation, wherein the gum boundary point is a boundary point of a junction of a tooth grid and the gum grid;
taking a point between a boundary line formed by the gum boundary points and a boundary line formed by the immobile points as a deformation point, and determining teeth corresponding to each deformation point;
when the teeth are transferred, the positions of the gum boundary points and the deformation points corresponding to the transferred teeth are updated by using a transfer matrix and a radial basis function interpolation method of the transferred teeth so as to update the gum grid.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
In a typical configuration, a computing device includes one or more processors (CPUs), input/output interfaces, network interfaces, and memory.
The memory may include forms of volatile memory in a computer readable medium, Random Access Memory (RAM), and non-volatile memory, such as Read Only Memory (ROM) or flash memory (flash RAM). The memory is an example of a computer-readable medium.
Computer-readable media, including both non-transitory and non-transitory, removable and non-removable media, may implement information storage by any method or technology. The information may be computer readable instructions, data structures, modules of a program, or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), Static Random Access Memory (SRAM), Dynamic Random Access Memory (DRAM), other types of Random Access Memory (RAM), Read Only Memory (ROM), Electrically Erasable Programmable Read Only Memory (EEPROM), flash memory or other memory technology, compact disc read only memory (CD-ROM), Digital Versatile Discs (DVD) or other optical storage, magnetic cassettes, magnetic tape magnetic disk storage or other magnetic storage devices, or any other non-transmission medium that can be used to store information that can be accessed by a computing device. As defined herein, a computer readable medium does not include a transitory computer readable medium such as a modulated data signal and a carrier wave.
It should also be noted that the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in the process, method, article, or apparatus that comprises the element.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The above are merely examples of the present application and are not intended to limit the present application. Various modifications and changes may occur to those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the scope of the claims of the present application.
Claims (10)
1. A method for simulating gum deformation, the method comprising:
determining a gum boundary point, a tooth corresponding to the gum boundary point and a motionless point participating in gum grid deformation, wherein the gum boundary point is a boundary point of a junction of a tooth grid and the gum grid;
taking a point between a boundary line formed by the gum boundary points and a boundary line formed by the immobile points as a deformation point, and determining teeth corresponding to each deformation point;
when the teeth are transferred, updating the positions of the gum boundary point and the deformation point corresponding to the transferred teeth by using a transfer matrix and a radial basis function interpolation method of the transferred teeth so as to update the gum grid;
wherein, the determining the gum boundary point and the tooth corresponding to the gum boundary point comprises:
acquiring a tooth boundary point of each tooth and a gum boundary point of the gum grid;
determining a centroid point for each tooth;
respectively calculating the distance between each gum boundary point and each center of mass point aiming at each gum boundary point, and taking the teeth corresponding to the minimum distance and the next minimum distance as candidate teeth corresponding to the gum boundary points;
and respectively calculating the distance from each tooth boundary point of the candidate teeth to the corresponding gum boundary point, and determining the candidate teeth corresponding to the minimum distance as the teeth corresponding to the gum boundary point.
2. The method of claim 1, wherein determining the immobile points involved in the deformation of the gingival mesh comprises:
fitting an upper jaw target plane and a lower jaw target plane by using mass center points of specific teeth in the upper jaw and the lower jaw;
moving the upper jaw target plane for a certain distance along the upward direction of the normal of the upper jaw target plane, and moving the lower jaw target plane for a certain distance along the downward direction of the normal of the lower jaw target plane, so that two cutting lines are obtained by enabling the moved target plane to be tangent with the gum mesh;
and sequencing the points on each cutting line, sampling according to the sequence of the points so that the distance between two adjacent points in the collected points is greater than a preset threshold value, and determining the points obtained by sampling as immobile points.
3. The method of claim 2, wherein the specific teeth include an incisor and a first molar; and/or the preset threshold value is 10 mm.
4. The method of claim 1, wherein determining the tooth corresponding to each deformed point comprises:
determining a centroid point for each tooth;
and determining the tooth to which the centroid point closest to the deformation point belongs as the tooth corresponding to the deformation point.
5. The method according to any one of claims 1 to 4, wherein when the tooth is shifted, updating the positions of the gingival boundary points and inflection points corresponding to the shifted tooth by using the shift matrix and the radial basis function interpolation method of the shifted tooth to update the gingival grid comprises:
when the teeth are transferred, determining the position of the gum boundary point corresponding to the transferred teeth after moving according to the transfer matrix of the transferred teeth and the position of the gum boundary point corresponding to the transferred teeth before moving;
calculating the displacement of the gum boundary point according to the position of the gum boundary point before movement and the position of the gum boundary point after movement;
determining the displacement of each deformation point by using the radial basis function interpolation method according to the displacement of the gum boundary point and the orthogonality of the weight coefficient of each constraint point, wherein the constraint points comprise gum boundary points and immobile points;
determining the position of each deformation point after movement according to the position of each deformation point before movement and the corresponding displacement;
and updating the gum grid based on the position of the gum boundary point after movement and the position of the deformed point after movement.
6. The method of claim 5, wherein determining the displacement of each deformed point by the radial basis function interpolation based on the orthogonality of the displacements of the gum boundary points and the weighting coefficients of the respective constraint points comprises:
obtaining a linear equation set by utilizing an equation formed by orthogonality of the weight coefficients based on each constraint point and an equation formed by a radial basis function interpolation formula satisfied by the constraint points;
substituting the components of the displacement of the gum boundary point in each dimension into the linear equation set respectively, calculating to obtain the components of the vector consisting of the unknown parameters in the radial basis function interpolation formula in each dimension, and determining each unknown parameter based on the calculated components;
and calculating the displacement of each deformation point by a radial basis function interpolation formula after each unknown parameter is determined.
7. The method of claim 6, wherein the constructing is based on orthogonality of weight coefficients of the respective constraint pointsHas the equation of
The equation formed by the radial basis function interpolation formula satisfied by the constraint points is
When ordering radial basis function
When, the system of linear equations is
The interpolation formula of the radial basis function is
Wherein, wiWeight value of i-th constraint point, ciIs the ith constraint point, cjIs the jth constraint point, vjIs the displacement of the jth constraint point, r is an arbitrary position, p0、p1、p2、p3Is a parameter with a fixed value.
8. A device for simulating gum deformation, the device comprising:
the first determining unit is used for determining a gum boundary point, a tooth corresponding to the gum boundary point and an immobile point participating in gum grid deformation, wherein the gum boundary point is a boundary point of a tooth grid and the gum grid;
a second determining unit, configured to determine a tooth corresponding to each deformed point by using a point between a boundary line formed by the gum boundary points and a boundary line formed by the fixed point as a deformed point;
the updating unit is used for updating the positions of the gum boundary point and the deformation point corresponding to the tooth with the transfer matrix and the radial basis function interpolation method of the tooth with the transfer to update the gum grid when the tooth with the transfer occurs;
wherein the first determination unit includes:
the acquisition module is used for acquiring the tooth boundary point of each tooth and the gum boundary point of the gum grid;
a first determining module for determining a centroid point of each tooth;
the first calculation module is used for calculating the distance between each gum boundary point and each centroid point aiming at each gum boundary point;
the first determining module is further configured to take the tooth corresponding to the minimum distance and the next minimum distance as the candidate tooth corresponding to the gum boundary point;
the first calculation module is further used for calculating the distance from each tooth boundary point of the candidate tooth to the corresponding gum boundary point;
the first determining module is further configured to determine the candidate tooth corresponding to the minimum distance as the tooth corresponding to the gum boundary point.
9. A storage medium, characterized in that the storage medium comprises a stored program, wherein the program is executed to control a device on which the storage medium is located to execute the method for simulating gum deformation according to any one of claims 1 to 7.
10. A simulation apparatus of gum deformation, the apparatus comprising a storage medium and a processor;
the processor is suitable for realizing instructions;
the storage medium adapted to store a plurality of instructions;
the instructions are adapted to be loaded by the processor and to perform a method of simulating gum deformation according to any of claims 1 to 7.
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| CN112006791B (en) * | 2020-08-31 | 2021-11-09 | 正雅齿科科技(上海)有限公司 | Method and system for acquiring tooth correction information |
| CN113034532B (en) * | 2021-03-02 | 2023-02-03 | 四川大学 | Method for predicting soft tissue deformation after plastic surgery based on mesh-free model |
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