Reconstruction of non-visible part of tooth

Claim 2

A computer-implemented method for modeling a complete tooth of a patient to facilitate dental and/or orthodontic treatment comprising: generating a first set of digital data representing a clinical crown; generating a second set of digital data representing a plurality of digital tooth models of a particular tooth type each having a first parameterization; processing the second set of digital data to obtain a third set of digital data representing an average tooth model of the particular tooth type having a second parameterization which is less than the first parameterization; establishing a boundary value for a number of parameters of the second parameterization to prevent an area of each face of a mesh from decreasing beyond a particular fraction of an initial area of each face while being affected by any change in the number of parameters, thereby avoiding self-intersection of the mesh, where the number of parameters represent changes to the average tooth model, where the mesh represents surfaces of the average tooth model, and where establishing boundary values includes minimizing a quadratic function including a vector with a direction of a normal to a particular face of the average tooth model and a magnitude equal to an area of the particular face for the number of parameters; fitting the third set of digital data to the first set of digital data to create a set of digital data representing an interim tooth model; and morphing the set of digital data representing the interim tooth model to substantially mimic the anatomical shape of the clinical crown of the first set of digital data.

Claim 3

The computer-implemented method of claim 1 , wherein generating a first set of digital data representing a clinical crown comprises: scanning a patient's tooth to generate three-dimensional clinical crown data.

Claim 4

The computer-implemented method of claim 1 , wherein generating a second set of digital data representing a plurality of digital tooth models of a particular tooth type comprises: collecting a set of reconstructed teeth samples of a particular type representing a variety of features.

Claim 5

The computer-implemented method of claim 1 , wherein processing the second set of digital data to obtain a third set of digital data representing an average tooth model of the particular tooth type comprises: representing surfaces of the digital tooth models with a triangular mesh, wherein each surface of the digital tooth models includes the same number of vertices, and wherein each vertex is located in a substantially similar position on each corresponding surface.

Claim 6

The computer-implemented method of claim 1 , wherein establishing the boundary value includes minimizing the quadratic function: S ⁡ ( f ) T ⁢ S ⁡ ( f , 1 , 0 , … ⁢ , a i , … ⁢ , 0 ) ) S 2 ⁡ ( f ) ≥ c , where c is the fraction of the initial area of each face and where 0<c<1; where S(f,α) is the vector; where f is the particular face; and where α i is one of the number of parameters.

Claim 7

The computer-implemented method of claim 1 , wherein processing the second set of digital data to obtain a third set of digital data comprises: applying a numerical analysis technique to the second set of digital data to create the average tooth model and the second parameterization of the average tooth model.

Claim 8

The computer-implemented method of claim 6 , wherein the numerical analysis technique comprises a Principal Components Analysis (PCA) technique.

Claim 9

The computer-implemented method of claim 1 , wherein fitting the third set of digital data to the first set of digital data comprises: selecting a linear combination of the average tooth model data and second parameterization which minimizes the differences between the third set of digital data and the first set of digital data.

Claim 10

The computer-implemented method of claim 1 , wherein fitting the third set of digital data to the first set of digital data comprises: a) sampling points on a surface represented in one of the digital data sets; b) forming point pairs using corresponding points on the surface represented in the other digital data set; c) transforming the point pairs to cause the points to converge; and repeating steps a), b), and c) until the point pairs are substantially the same on each surface.

Claim 11

The computer-implemented method of claim 9 , further comprising assigning a weighting factor to each point, wherein transforming the point pairs comprises transforming the point pairs to cause the points to converge based on their assigned weighting factor.

Claim 12

A computerized system for modeling a complete tooth crown of a patient to facilitate dental and/or orthodontic treatment, said computerized modeling system comprising: a microprocessor; and a memory device, said microprocessor configured to: generate a first set of digital data representing a clinical crown; generate a second set of digital data representing a plurality of digital tooth models of a particular tooth type each having a first parameterization; process the second set of digital data to obtain a third set of digital data representing an average tooth model of the particular tooth type having a second parameterization which is less than the first parameterization; establish a boundary value for a number of parameters of the second parameterization to prevent an area of each face of a mesh from decreasing beyond a particular fraction of an initial area of each face while being affected by any change in the number of parameters, thereby avoiding self-intersection of the mesh, where the number of parameters represent changes to the average tooth model where the mesh represents surfaces of the average tooth model, and where establishing boundary values includes minimizing a quadratic function including a vector with a direction of a normal to a particular face of the average tooth model and magnitude equal to an area of the particular face for the number of parameters; fit the third set of digital data to the first set of digital data to create a set of digital data representing an interim tooth model; and morph the set of digital data representing the interim tooth model to substantially mimic the anatomical shape of the clinical crown of the first set of digital data.

Claim 13

A computerized system for modeling a complete tooth crown of a patient to facilitate dental and/or orthodontic treatment, said computerized modeling system comprising: a microprocessor; and a memory device, said microprocessor configured to: generate a first set of digital data representing a clinical crown; generate a second set of digital data representing a plurality of digital tooth models of a particular tooth type each having a first parameterization; process the second set of digital data to obtain a third set of digital data representing an average tooth model of the particular tooth type having a second parameterization which is less than the first parameterization; establish a boundary value for a number of parameters of the second parameterization to prevent an area of each face of a mesh from decreasing beyond a particular fraction of an initial area of each face while being affected by any change in the number of parameters, thereby avoiding self-intersection of the mesh, where the number of parameters represent changes to the average tooth model where the mesh represents surfaces of the average tooth model, and where establishing boundary values includes minimizing a quadratic function including a vector with a direction of a normal to a particular face of the average tooth model and magnitude equal to an area of the particular face for the number of parameters; fit the third set of digital data to the first set of digital data to create a set of digital data representing an interim tooth model; and morph the set of digital data representing the interim tooth model to substantially mimic the anatomical shape of the clinical crown of the first set of digital data.

Claim 14

The computerized system of claim 11 , wherein to process the second set of digital data to obtain a third set of digital data representing an average tooth model of the particular tooth type, said microprocessor is configured to: represent surfaces of the digital tooth models with a triangular mesh, wherein each surface of the digital tooth models includes the same number of vertices, and wherein each vertex is located in a substantially similar position on each corresponding surface.

Claim 15

The computerized system of claim 11 , wherein to process the second set of digital data to obtain a third set of digital data, said microprocessor is configured to: apply a numerical analysis technique to the second set of digital data to create the average tooth model and the second parameterization of the average tooth model.

Claim 16

The computerized system of claim 13 , wherein the numerical analysis technique comprises a Principal Components Analysis (PCA) technique.

Claim 17

The computerized system of claim 11 , wherein to fit the third set of digital data to the first set of digital data, said microprocessor is configured to: select a linear combination of the average tooth model data and second parameterization which minimizes the differences between the third set of digital data and the first set of digital data.

Claim 18

The computerized system of claim 11 , wherein to fit the third set of digital data to the first set of digital data, said microprocessor is configured to: a) sample points on a surface represented in one of the digital data sets; b) form point pairs using corresponding points on the surface represented in the other digital data set; c) transform the point pairs to cause the points to converge; and repeat steps a), b), and c) until the point pairs are substantially the same on each surface.

Claim 19

The computerized system of claim 16 , wherein said microprocessor is further configured to: assign a weighting factor to each point, wherein transforming the point pairs comprises converging the points together based on their assigned weighting factor.

Claim 20

A computer-implemented method for modeling a complete tooth of a patient to facilitate dental and/or orthodontic treatment comprising: scanning a patient's tooth to generate a digital clinical crown model; generating a plurality of digital tooth models of a particular tooth type each having a first parameterization; processing the digital tooth models using a numerical analysis technique to generate a digital average tooth model of the particular tooth type, the digital average tooth model having a second parameterization which is less than the first parameterization; establishing a boundary value for a number of parameters of the second parameterization to prevent an area of each face of a mesh from decreasing beyond a particular fraction of an initial area of each face while being affected by any change in the number of parameters, thereby avoiding self-intersection of the mesh, where the number of parameters represent changes to the average tooth model, where the mesh represents surfaces of the average tooth model and where establishing boundary values includes minimizing a quadratic function including a vector with a direction of a normal to a particular face of the average tooth model and a magnitude equal to an area of the particular face for the number of parameters; fitting the digital clinical crown model to the digital average tooth model to form an interim tooth model, said fitting including: a) sampling points on a surface of either the digital clinical crown model or the digital average tooth model; b) forming point pairs using corresponding points on the surface not selected in a); c) transforming the point pairs to cause the points to converge; and d) repeating steps a), b), and c) until the point pairs are substantially the same on each surface represented by the digital interim tooth model; and morphing the digital interim tooth model to substantially mimic the anatomical shape of the digital clinical crown model.

Claim 21

A computer-implemented method for modeling a complete tooth of a patient to facilitate dental and/or orthodontic treatment comprising: scanning a patient's tooth to generate a digital clinical crown model; generating a plurality of digital tooth models of a particular tooth type each having a first parameterization; processing the digital tooth models using a numerical analysis technique to generate a digital average tooth model of the particular tooth type, the digital average tooth model having a second parameterization which is less than the first parameterization; establishing a boundary value for a number of parameters of the second parameterization to prevent an area of each face of a mesh from decreasing beyond a particular fraction of an initial area of each face while being affected by any change in the number of parameters, thereby avoiding self-intersection of the mesh, where the number of parameters represent changes to the average tooth model, where the mesh represents surfaces of the average tooth model and where establishing boundary values includes minimizing a quadratic function including a vector with a direction of a normal to a particular face of the average tooth model and a magnitude equal to an area of the particular face for the number of parameters; fitting the digital clinical crown model to the digital average tooth model to form an interim tooth model, said fitting including: a) sampling points on a surface of either the digital clinical crown model or the digital average tooth model; b) forming point pairs using corresponding points on the surface not selected in a); c) transforming the point pairs to cause the points to converge; and d) repeating steps a), b), and c) until the point pairs are substantially the same on each surface represented by the digital interim tooth model; and morphing the digital interim tooth model to substantially mimic the anatomical shape of the digital clinical crown model.

Claim 22

The computer-implemented method of claim 18 , wherein the numerical analysis technique comprises a Principal Components Analysis (PCA) technique.

Claim 23

The computer-implemented method of claim 18 , wherein the fitting further comprises assigning a weighting factor to each point, wherein transforming the point pairs includes converging the points together based on their assigned weighting factor.