Orthodontic appliances including at least partially un-erupted teeth and method of forming them
The example systems, methods, and/or computer-readable media described herein help with design of highly accurate models of un-erupted or partially erupted teeth and help fabricate of aligners for un-erupted or partially erupted teeth. Automated agents that use machine learning models to parametrically represent three-dimensional (3d) virtual representations of teeth as 3D descriptors in a 3D descriptor space are provided herein. In some implementations, the automated agents described herein provide instructions to fabricate aligners for at least partially un-erupted teeth using representative 3D descriptor(s) of a tooth type.
1. A computer-implemented method comprising:
gathering a first anatomical tooth identifier of an at least partially un-erupted tooth of a patient, the first anatomical tooth identifier forming a basis to identify the at least partially un-erupted tooth;
identifying a tooth type using the first anatomical tooth identifier;
gathering a representative 3D descriptor for the tooth type from a plurality of 3D descriptors for the tooth type,
each of the plurality of 3D descriptors, including the representative 3D descriptor, parametrically representing a plurality of virtual surface contours of the tooth type according to a plurality of spatial parameters,
the representative 3D descriptor having a minimum distance to other 3D descriptors of the plurality of 3D descriptors in a 3D descriptor space formed of the plurality of 3D descriptors, and
each of the plurality of 3D descriptors being associated with one of the plurality of 3D virtual representations of a plurality of teeth gathered from a plurality of subjects;
forming a virtual 3D tooth shape for the at least partially un-erupted tooth using the representative 3D descriptor; and
providing instructions to form at least a portion of a removable orthodontic appliance for the at least partially un-erupted tooth using the 3D tooth shape for the at least partially un-erupted tooth.
2. The computer-implemented method of claim 1 , wherein the plurality of 3D virtual representations of teeth each comprise a plurality of orthoscopic views of the plurality of teeth.
3. The computer-implemented method of claim 1 , wherein the plurality of 3D descriptors comprise a convex bounding 3D shape.
4. The computer-implemented method of claim 1 , wherein the plurality of 3D descriptors are represented using an Elliptic Fourier Descriptor (EFD) of the plurality of virtual surface contours.
5. The computer-implemented method of claim 4 , wherein the plurality of spatial parameters comprise one or more locational components.
6. The computer-implemented method of claim 1 , wherein the plurality of 3D descriptors comprises a plurality of spheres.
7. The computer-implemented method of claim 1 , wherein the plurality of spheres comprise a plurality of voxelized spheres.
8. The computer-implemented method of claim 1 , wherein the plurality of spatial parameters comprise a plurality of polar coordinates to virtually represent a plurality of voxelized spheres.
9. The computer-implemented of claim 1 , wherein the removable orthodontic appliances comprises a polymeric appliance.
10. The computer-implemented of claim 1 , wherein providing instructions to form at least the portion of the removable orthodontic appliance comprises providing instructions to three-dimensionally print the at least the portion of the removable orthodontic appliance.
11. The computer-implemented of claim 1 , wherein the representative 3D descriptor comprises an average 3D descriptor of the plurality of 3D descriptors.
12. The computer-implemented method of claim 1 , further comprising:
gathering a second anatomical tooth identifier of the tooth type, the second anatomical tooth identifier forming a basis to identify the tooth type;
gathering, using the second anatomical tooth identifier, the plurality of 3D virtual representations of a plurality of teeth from a plurality of subjects,
identifying the plurality of virtual surface contours for the tooth type;
identifying the plurality of 3D descriptors to parametrically represent the plurality of virtual surface contours according to the plurality of spatial parameters;
identifying a descriptor location in the 3D descriptor space of each of the plurality of 3D descriptors;
assigning a descriptor distance to each of the plurality of 3D descriptors, the descriptor distance representing a difference between the descriptor location of the each 3D descriptor and the descriptor location of a rest of the plurality of 3D descriptors; and
identifying the representative 3D descriptor for the tooth type by finding a minimum descriptor distance between two or more of the plurality of 3D descriptors.
13. The computer-implemented method of claim 12 , wherein assigning the descriptor distance comprises:
identifying a variance between each of the plurality of 3D descriptors and the rest of the plurality of 3D descriptors; and
minimizing the variance.
14. The computer-implemented method of claim 12 , further comprising normalizing rotational orientations or sizes of the plurality of 3D descriptors before identifying the representative 3D descriptor for the tooth type.
15. The computer-implemented method of claim 1 , wherein identifying the plurality of 3D descriptors comprises creating at least one spherical harmonic based signature based on a sum of spherical harmonics for the plurality of 3D descriptors.
16. The computer-implemented method of claim 15 , wherein:
the at least one spherical harmonic based signature comprises a plurality of spherical harmonic based signatures; and
finding the minimum descriptor distance comprises identifying a minimum distance between two or more of the plurality of spherical harmonic based signatures in the 3D descriptor space.
17. The computer-implemented method of claim 16 , wherein identifying the minimum distance comprises performing a least squares analysis of a Euclidean distance between the two or more of the plurality of spherical harmonic based signatures.
18. A computer-implemented method comprising:
gathering an anatomical tooth identifier of a tooth type, the anatomical tooth identifier forming a basis to identify the tooth type;
gathering, using the anatomical tooth identifier, a plurality of three-dimensional (3D) virtual representations of a plurality of teeth from a plurality of subjects, each of the plurality of teeth having the tooth type;
identifying a plurality of virtual surface contours corresponding to surfaces of each of the plurality of 3D virtual representations;
identifying a plurality of 3D descriptors to parametrically represent the plurality of virtual surface contours according to a plurality of spatial parameters, the plurality of 3D descriptors having descriptor locations in a 3D descriptor space;
assigning a descriptor distance to each of the plurality of 3D descriptors, the descriptor distance representing a difference between the descriptor location of the each 3D descriptor and the descriptor location of a rest of the plurality of 3D descriptors; and
identifying a representative 3D descriptor for the tooth type using the descriptor distances, the representative 3D descriptor having a minimum distance to the rest of the plurality of 3D descriptors.
19. A system comprising:
one or more processors;
memory coupled to the one or more processors, the memory configured to store computer-program instructions, that, when executed by the one or more processors, perform a computer-implemented method comprising:
gathering a first anatomical tooth identifier of an at least partially un-erupted tooth of a patient, the first anatomical tooth identifier forming a basis to identify the at least partially un-erupted tooth;
identifying a tooth type using the first anatomical tooth identifier;
gathering a representative 3D descriptor for the tooth type from a plurality of 3D descriptors for the tooth type,
each of the plurality of 3D descriptors, including the representative 3D descriptor, parametrically representing a plurality of virtual surface contours of the tooth type according to a plurality of spatial parameters,
the representative 3D descriptor having a minimum distance to other 3D descriptors of the plurality of 3D descriptors in a 3D descriptor space formed of the plurality of 3D descriptors, and
each of the plurality of 3D descriptors being associated with one of the plurality of 3D virtual representations of a plurality of teeth gathered from a plurality of subjects;
forming a virtual 3D tooth shape for the at least partially un-erupted tooth using the representative 3D descriptor; and
providing instructions to form at least a portion of a removable orthodontic appliance for the at least partially un-erupted tooth using the 3D tooth shape for the at least partially un-erupted tooth.
20. The system of claim 19 , wherein the computer-implemented method further comprises:
gathering a second anatomical tooth identifier of the tooth type, the second anatomical tooth identifier forming a basis to identify the tooth type;
gathering, using the second anatomical tooth identifier, the plurality of 3D virtual representations of a plurality of teeth from a plurality of subjects,
identifying the plurality of virtual surface contours for the tooth type;
identifying the plurality of 3D descriptors to parametrically represent the plurality of virtual surface contours according to the plurality of spatial parameters;
identifying a descriptor location in the 3D descriptor space of each of the plurality of 3D descriptors;
assigning a descriptor distance to each of the plurality of 3D descriptors, the descriptor distance representing a difference between the descriptor location of the each 3D descriptor and the descriptor location of a rest of the plurality of 3D descriptors; and
identifying the representative 3D descriptor for the tooth type by finding a minimum descriptor distance between two or more of the plurality of 3D descriptors.
21. A system comprising:
one or more processors;
memory coupled to the one or more processors, the memory configured to store computer-program instructions, that, when executed by the one or more processors, perform a computer-implemented method comprising:
gathering an anatomical tooth identifier of a tooth type, the anatomical tooth identifier forming a basis to identify the tooth type;
gathering, using the anatomical tooth identifier, a plurality of three-dimensional (3D) virtual representations of a plurality of teeth from a plurality of subjects, each of the plurality of teeth having the tooth type;
identifying a plurality of virtual surface contours corresponding to surfaces of each of the plurality of 3D virtual representations;
identifying a plurality of 3D descriptors to parametrically represent the plurality of virtual surface contours according to a plurality of spatial parameters, the plurality of 3D descriptors having descriptor locations in a 3D descriptor space;
assigning a descriptor distance to each of the plurality of 3D descriptors, the descriptor distance representing a difference between the descriptor location of the each 3D descriptor and the descriptor location of a rest of the plurality of 3D descriptors; and
identifying a representative 3D descriptor for the tooth type using the descriptor distance, the representative 3D descriptor having a minimum distance to the rest of the plurality of 3D descriptors.