Systems and methods for planning an orthodontic treatment

A system for reconstructing a 3D representation of a gingiva associated with an arch form of a subject, the system comprising a processor configured to execute a method, the method comprising:

• acquiring a 3D representation of an arch form associated with the subject, the 3D representation including a representation of the gingiva and a plurality of teeth of the subject;
• the 3D representation of the arch form including data of a transverse plane associated with a skull of the subject;
• the transverse plane being associated with a common median axis lying therein and a common vertical axis perpendicular thereto;
• segmenting, in the 3D representation of the arch form, associated representations of the plurality of teeth and the gingiva to generate a plurality of segmentation loops, each segmentation loop respectively associated with each tooth of the plurality of teeth and representing an interface of a given tooth with the gingiva;
• determining, between each adjacent two segmentation loops of the plurality of segmentation loops, a midpoint, thereby generating a plurality of primary midpoints for the plurality of segmentation loops;
• based on the plurality of midpoints, generating a primary central curve;
• generating, based on the primary central curve, a first inner mesh curve and a first outer mesh curve, the first inner mesh curve positioned along a first horizontal plane and the first outer mesh curve positioned along a second horizontal plane, both the first horizontal plane and the second horizontal plane being parallel to the transverse plane and being vertically offset, along the common vertical axis, from a highest vertex of the plurality of segmentation loops;
• the first inner mesh curve being offset along the common median axis posteriorly relative to the primary central curve along the first horizontal plane;
• and
• the first outer mesh curve being offset along the common median axis anteriorly relative to the primary central curve along the second horizontal plane;
• projecting the plurality of primary midpoints onto the first inner mesh curve and the first outer mesh curve, thereby generating a first plurality of inner midpoints and a first plurality of outer midpoints;
• generating a first segment of the reconstructed 3D representation of the gingiva by joining each one from the plurality of primary midpoints with respective ones from the first plurality of inner midpoints and from the first plurality of outer midpoints;
• and
• causing display of the first segment of the reconstructed 3D representation of the gingiva.