Method and system for dental boundary determination

1. A method of determining a boundary between a plurality of teeth and gingiva of an archform, the method executable by an electronic device, the method comprising:

receiving a three-dimensional (3D) digital model of the archform comprising a representation of the gingiva and the plurality of teeth of the archform;

defining, for each tooth of the plurality of teeth of the archform, a plurality of curves, wherein each curve of the plurality of curves crosses the boundary between the plurality of teeth and the gingiva;

determining, for each point of a plurality of points of each of the plurality of curves, an indication of curvature of the respective curve at each point;

determining, based on the plurality of curves, average curvature properties corresponding to the plurality of teeth;

determining, based on the plurality of curves, average curvature properties corresponding to the gingiva;

inputting the average curvature properties corresponding to the plurality of teeth and the average curvature properties corresponding to the gingiva as training features to a machine learning algorithm (MLA) to generate a function that predicts a likelihood that each point of the plurality of points corresponds to the boundary between the plurality of teeth and the gingiva;

determining, for each point of the plurality of points, based on the indication of curvature corresponding to the respective point, and using the function, a predicted likelihood parameter indicating whether each point corresponds to the boundary between the plurality of teeth and the gingiva; and

selecting, for each curve of the plurality of curves, using a smoothing function and the predicted likelihood parameter, a single point, of the plurality of points, on the respective curve as a boundary point corresponding to the boundary between the plurality of teeth and the gingiva of the archform.

2. The method of claim 1 , wherein the plurality of curves comprise a plurality of 3D curves, and wherein the method further comprises converting the plurality of curves to two dimensional (2D) curves.

3. The method of claim 2 , wherein the determining the indication of curvature comprises determining the indication of curvature based on the 2D curves.

4. The method of claim 1 , wherein the method further comprises:

determining that a curve of the plurality of curves comprises a loop; and

omitting the curve comprising the loop from further analysis.

5. The method of claim 1 , wherein the method further comprises:

determining that a curve of the plurality of curves corresponds to two or more teeth; and

omitting the curve corresponding to two or more teeth from further analysis.

6. The method claim 1 , wherein the method further comprises removing, from each curve of the plurality of curves, a portion of each curve corresponding to a tooth head.

7. An apparatus comprising:

at least one processor; and

a memory device comprising executable instructions, which, when executed by the at least one processor, cause the apparatus to:

receive a three-dimensional (3D) digital model of an archform comprising a representation of gingiva and a plurality of teeth of the archform;

define, for each tooth of the plurality of teeth of the archform, a plurality of curves, wherein each curve of the plurality of curves crosses a boundary between the plurality of teeth and the gingiva;

determine, for each point of a plurality of points of each of the plurality of curves, an indication of curvature of the respective curve at each point;

determine, based on the plurality of curves, average curvature properties corresponding to the plurality of teeth;

determine, based on the plurality of curves, average curvature properties corresponding to the gingiva;

input the average curvature properties corresponding to the plurality of teeth and the average curvature properties corresponding to the gingiva as training features to a machine learning algorithm (MLA) to generate a function that predicts a likelihood that each point of the plurality of points corresponds to the boundary between the plurality of teeth and the gingiva;

determine, for each point of the plurality of points, based on the indication of curvature corresponding to the respective point, and using the function, a predicted likelihood parameter indicating whether each point corresponds to the boundary between the plurality of teeth and the gingiva; and

select, for each curve of the plurality of curves, using a smoothing function and the predicted likelihood parameter, a single point, of the plurality of points, on the respective curve as a boundary point corresponding to the boundary between the plurality of teeth and the gingiva of the archform.

8. The apparatus of claim 7 , wherein the executable instructions further cause the apparatus to execute the MLA to determine the predicted likelihood parameter.

9. The apparatus of claim 7 , wherein a first curve of the plurality of curves corresponds to an inner side of a tooth of the plurality of teeth, and wherein a second curve of the plurality of curves corresponds to an outer side of the tooth.

10. The apparatus of claim 7 , wherein the executable instructions that cause the apparatus to determine the indication of curvature comprise executable instructions that further cause the apparatus to determine a derivative of each curve of the plurality of curves.

11. The apparatus of claim 7 , wherein the executable instructions that cause the apparatus to select the boundary points comprise executable instructions that cause the apparatus to:

maximize a sum of the predicted likelihood parameters; and

minimize a curvature of a curve connecting the boundary points.

12. The apparatus of claim 7 , wherein the executable instructions further cause the apparatus to:

determine a curve connecting the boundary points; and

output, for display, the 3D digital model of the archform and the curve connecting the boundary points.

13. The apparatus of claim 12 , wherein the executable instructions further cause the apparatus to apply a shortest path algorithm to determine the curve connecting the boundary points.

14. The apparatus of claim 12 , wherein the executable instructions further cause the apparatus to analyze the curve connecting the boundary points to interpolate corrective points to a boundary region that has missing determined boundary points.

15. The apparatus of claim 12 , wherein the executable instructions further cause the apparatus to:

determine a portion of the curve connecting the boundary points, the portion corresponding to a given tooth of the plurality of teeth; and

merge the portion of the curve connecting the boundary points between missing determined boundary points to define the curve connecting the boundary points.

16. The apparatus of claim 15 , wherein the executable instructions further cause the apparatus to:

identify closest segments between neighboring portions of the curve; and

apply a shortest path algorithm to the closest segments to smoothen a transition between them to form the curve.

17. One or more non-transitory computer-readable media storing executable instructions that, when executed, cause an apparatus to:

receive a three-dimensional (3D) digital model of an archform comprising a representation of gingiva and a plurality of teeth of the archform;

define, for each tooth of the plurality of teeth of the archform, a plurality of curves, wherein each curve of the plurality of curves crosses a boundary between the plurality of teeth and the gingiva;

determine, for each point of a plurality of points of each of the plurality of curves, an indication of curvature of the respective curve at each point;

determine, based on the plurality of curves, average curvature properties corresponding to the plurality of teeth;

determine, based on the plurality of curves, average curvature properties corresponding to the gingiva;

input the average curvature properties corresponding to the plurality of teeth and the average curvature properties corresponding to the gingiva as training features to a machine learning algorithm (MLA) to generate a function that predicts a likelihood that each point of the plurality of points corresponds to the boundary between the plurality of teeth and the gingiva;

determine, for each point of the plurality of points, based on the indication of curvature corresponding to the respective point, and using the function, a predicted likelihood parameter indicating whether each point corresponds to the boundary between the plurality of teeth and the gingiva; and

select, for each curve of the plurality of curves, using a smoothing function and the predicted likelihood parameter, a single point, of the plurality of points, on the respective curve as a boundary point corresponding to the boundary between the plurality of teeth and the gingiva of the archform.

18. The one or more non-transitory computer-readable media of claim 17 , wherein the instructions, when executed, further cause the apparatus to:

determine that a curve of the plurality of curves comprises a loop; and

omit the curve comprising the loop from further analysis.

19. The one or more non-transitory computer-readable media of claim 17 , wherein the instructions, when executed, further cause the apparatus to maximize a sum of the predicted likelihood parameters.

20. The one or more non-transitory computer-readable media of claim 17 , wherein the instructions, when executed, further cause the apparatus to minimize a curvature of a curve connecting the boundary points.