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 non-transitory computer-implemented method for forming an orthodontic appliance, the method comprising:
using one or more three-dimensional (3D) descriptors to estimate a 3D shape in a 3D space for an at least partially un-erupted tooth of a patient's teeth based on data representing a plurality of teeth corresponding to a tooth type of the at least partially un-erupted tooth;
using the 3D shape to determine cavity attributes of a cavity to accommodate the at least partially un-erupted tooth as the at least partially un-erupted tooth erupts; and
providing instructions to form the orthodontic appliance including the cavity for the at least partially un-erupted tooth, wherein the instructions specify the cavity attributes of the cavity.
2. The method of claim 1 , further comprising determining a scaling factor for the 3D shape of the at least partially un-erupted tooth.
3. The method of claim 2 , wherein determining the scaling factor comprises matching an anticipated size of the at least partially un-erupted tooth.
4. The method of claim 1 , wherein the cavity attributes include a position and size of the cavity.
5. The method of claim 1 , wherein estimating the 3D shape comprises evaluating data from a plurality of samples of teeth according to determine a most average tooth shape.
6. The method of claim 1 , wherein estimating the 3D shape comprises using 2D Elliptic Fourier Descriptors (EFDs).
7. The method of claim 6 , wherein using EFDs comprises:
generating two-dimensional top, front, and side views from the data representing the plurality of teeth;
generating a characteristic, convex bounding shape for each two-dimensional top, front, and side views;
representing a convex bounding shape for each two-dimensional top, front, and side view using elliptic Fourier descriptors; and
normalizing the elliptic Fourier descriptors to provide rotation and size invariance.
8. The method of claim 1 , wherein determining the cavity attributes of the cavity comprises computing a principal component analysis to determine an optimal 3D shape for the cavity from the data representing the plurality of teeth.
9. The method of claim 1 , wherein estimating the 3D shape comprises determining a spherical harmonic signature of the at least partially un-erupted tooth.
10. The method of claim 9 , wherein determining the cavity attributes of the cavity comprises computing a Euclidean distance between the spherical harmonic signature of the at least partially un-erupted tooth and other of the patient's teeth.
11. The method of claim 1 , further comprising gathering an anatomical tooth identifier of the at least partially un-erupted tooth and identifying the tooth type using the anatomical tooth identifier.
12. The method of claim 1 , wherein estimating the 3D shape for the at least partially un-erupted tooth comprises identifying a representative 3D descriptor for the tooth type from the data representing the plurality of teeth.
13. The method of claim 12 , wherein the representative 3D descriptor has a minimum distance to other 3D descriptors of a plurality of 3D descriptors in a 3D descriptor space formed of the plurality of 3D descriptors.
14. The method of claim 1 , wherein the one or more 3D descriptors is associated with a 3D virtual representation of a plurality of teeth gathered from a plurality of subjects.
15. 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:
using one or more three-dimensional (3D) descriptors to estimate a 3D shape in a 3D space for an at least partially un-erupted tooth of a patient's teeth based on data representing a plurality of teeth corresponding to a tooth type of the at least partially un-erupted tooth;
using the 3D shape to determine cavity attributes of a cavity to accommodate the at least partially un-erupted tooth as the at least partially un-erupted tooth erupts; and
providing instructions to form an orthodontic appliance including the cavity for the at least partially un-erupted tooth, wherein the instructions specify the cavity attributes of the cavity.
16. The system of claim 15 , wherein the computer-implemented method further comprises determining a scaling factor for the 3D shape of the at least partially un-erupted tooth.
17. The system of claim 15 , wherein the computer-implemented method further comprises estimating 3D shapes of multiple at least partially un-erupted teeth of the patient's teeth, and providing instructions to form the orthodontic appliance including multiple cavities for the multiple at least partially un-erupted teeth.
18. The system of claim 17 , wherein the 3D space includes a plurality of 3D descriptors parametrically representing virtual surface contours corresponding to the tooth type.
19. The system of claim 15 , wherein estimating the 3D shape comprises using 2D Elliptic Fourier Descriptors (EFDs).
20. The system of claim 15 , wherein estimating the 3D shape comprises determining a spherical harmonic signature of the at least partially un-erupted tooth.
21. A non-transitory computer-implemented method comprising:
estimating a 3D shape for an at least partially un-erupted tooth of a patient's teeth by associating 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;
determining a position and size of a cavity to accommodate the at least partially un-erupted tooth as the at least partially un-erupted tooth erupts; and
providing instructions to form an orthodontic appliance including the cavity for the at least partially un-erupted tooth.