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 for forming an orthodontic appliance, the method comprising:
associating an at least partially un-erupted tooth of a patient's teeth with a representative 3D descriptor in 3D descriptor space, the 3D descriptor space including a plurality of 3D descriptors parametrically representing virtual surface contours corresponding to a tooth type, each of the plurality of 3D descriptors being associated with one of a plurality of 3D virtual representations of a plurality of teeth of a plurality of subjects, the representative 3D descriptor having a minimum distance to other 3D descriptors in the 3D descriptor space;
forming a virtual 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 the orthodontic appliance for the at least partially un-erupted tooth using the virtual tooth shape.
2. The computer-implemented method of claim 1 , wherein the plurality of 3D descriptors comprise a convex bounding 3D shape.
3. The computer-implemented method of claim 1 , wherein the plurality of 3D descriptors are represented using an Elliptic Fourier Descriptor (EFD) of the virtual surface contours.
4. The computer-implemented method of claim 1 , wherein the virtual surface contours are according to locational coordinates identified along orthogonal systems.
5. The computer-implemented method of claim 4 , wherein the location coordinates are polar coordinates that virtually represent a plurality of voxelized spheres.
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 6 , wherein the plurality of spheres comprise a plurality of voxelized spheres.
8. The computer-implemented method of claim 1 , wherein the orthodontic appliance comprises a removable polymeric appliance.
9. The computer-implemented method of claim 1 , wherein providing instructions to form at least the portion of the orthodontic appliance comprises providing instructions to three-dimensionally print the at least the portion of the orthodontic appliance.
10. The computer-implemented method of claim 1 , wherein the representative 3D descriptor comprises an average 3D descriptor of the plurality of 3D descriptors.
11. The computer-implemented method of claim 1 , further comprising identifying the plurality of 3D descriptors to parametrically represent the virtual surface contours according to a plurality of spatial parameters.
12. The computer-implemented method of claim 11 , 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.
13. The computer-implemented method of claim 12 , wherein the at least one spherical harmonic-based signature comprises a plurality of spherical harmonic-based signatures.
14. The computer-implemented method of claim 13 , further comprising finding the minimum distance by identifying a minimum distance between two or more of the plurality of spherical harmonic-based signatures in the 3D descriptor space.
15. The computer-implemented method of claim 14 , 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.
16. 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:
associating an at least partially un-erupted tooth of a patient's teeth with a representative 3D descriptor in 3D descriptor space, the 3D descriptor space including a plurality of 3D descriptors parametrically representing virtual surface contours corresponding to a tooth type, each of the plurality of 3D descriptors being associated with one of a plurality of 3D virtual representations of a plurality of teeth of a plurality of subjects, the representative 3D descriptor having a minimum distance to other 3D descriptors in the 3D descriptor space;
forming a virtual 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 an orthodontic appliance for the at least partially un-erupted tooth using the virtual tooth shape.
17. The system of claim 16 , wherein the computer-implemented method further comprises identifying the plurality of 3D descriptors to parametrically represent the virtual surface contours according to a plurality of spatial parameters.
18. The system of claim 17 , 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.
19. The system of claim 18 , wherein the at least one spherical harmonic-based signature comprises a plurality of spherical harmonic-based signatures.
20. The system of claim 19 , wherein the computer-implemented method further comprises finding the minimum distance by identifying a minimum distance between two or more of the plurality of spherical harmonic-based signatures in the 3D descriptor space.