# US 11,439,481 B2 · Systems and methods for determining tooth center of resistance > Agents: this data is available as JSON from the patentgrep API and MCP server — see https://patentgrep.com/llms.txt - Number: US 11,439,481 B2 - Document ID: US11439481B2 - Status: Granted - Kind: B2 - Application number: 17/104,704 - Filed: 2020-11-25 - Published: 2021-11-25 - Granted: 2022-09-13 - Earliest claimed: 2020-05-19 - Assignees: ARKIMOS Ltd - Applicants: Oxilio Ltd - Inventors: Islam Khasanovich Raslambekov - Web page: https://patentgrep.com/patent/US11439481B2 ## CPC - A61C 7/002: {Orthodontic computer assisted systems} - A61C 7/12: Brackets; Arch wires; Combinations thereof; Accessories therefor - A61C 19/04: Measuring instruments specially adapted for dentistry ({A61C5/44 takes precedence; testing vitality of teeth A61B5/0534;} radiation diagnosis specially adapted for dentistry A61B6/51) - G06T 7/0012: {Biomedical image inspection} - G06T 7/60: Analysis of geometric attributes - G06T 17/20: Finite element generation, e.g. wire-frame surface description, {tesselation} - A61C 2007/004: {Automatic construction of a set of axes for a tooth or a plurality of teeth} - G06T 2207/10081: Computed x-ray tomography [CT] - G06T 2207/10116: X-ray image - G06T 2207/30036: Dental; Teeth - G06T 2210/21: Collision detection, intersection - G06T 2210/41: Medical - A61C: DENTISTRY; APPARATUS OR METHODS FOR ORAL OR DENTAL HYGIENE (non-driven toothbrushes A46B; {tongue scrapers A61B17/24;} preparations for dentistry A61K6/00; preparations for cleaning the teeth or mouth A61K8/00, A61Q11/00) - G06T: IMAGE DATA PROCESSING OR GENERATION, IN GENERAL ## Abstract A method and a system for determining a center of resistance point of a tooth for orthodontic treatment planning are provided. The method comprises: obtaining a tooth mesh from image data associated with a tooth crown of a patient; identifying a mesiodistal center of the tooth crown; determining a reference plane in the image data to extend through the mesiodistal center; determining an intersection curve based on an intersection of the reference plane and the tooth mesh, the intersection curve following a shape of the surface of the crown at the reference plane; determining a tooth axis of the tooth crown based on the intersection curve; determining a crown height of the tooth crown based on the tooth axis; and determining the center of resistance of the tooth based on the determined crown height and the determined tooth axis. ## Claims ### Claim 1 A method for determining a center of resistance point of a tooth for orthodontic treatment planning, the method being executable by a processor, the method comprising: obtaining image data associated with a tooth crown of a patient, the image data including a tooth mesh representative of a surface of the tooth crown; identifying a mesiodistal center of the tooth crown from the image data; determining a reference plane in the image data, the reference plane being at a predetermined relationship to a mesiodistal line and a mesiodistal center, the mesiodistal line comprising a line extending between a mesial side of the tooth crown and a distal side of the tooth crown; determining an intersection curve based on an intersection of the reference plane and the tooth mesh, the intersection curve following a shape of the surface of the crown at the reference plane; determining a tooth axis of the tooth crown based on the intersection curve by: bisecting the intersection curve into two intersection curve parts based on a separation point; generating an average intersection curve using the two intersection curve parts; generating, based on the average intersection curve, a guide axis using a linear regression algorithm; and determining the tooth axis based on the guide axis; determining a crown height of the tooth crown based on the tooth axis; and determining the center of resistance of the tooth based on the determined crown height and the determined tooth axis. ### Claim 2 (depends on 1) The method of claim 1, wherein the predetermined relationship of the reference plane to the mesiodistal line comprises the reference plane being perpendicular to the mesiodistal line and extending through the mesiodistal center. ### Claim 3 (depends on 1) The method of claim 1, wherein the identifying the internal reference point comprises: obtaining a mesial point on the mesial side of the tooth crown, and a distal point on the distal side of the tooth crown; generating the mesiodistal line joining the mesial point and the distal point; identifying the mesiodistal center as a midpoint on the mesiodistal line. ### Claim 4 (depends on 1) The method of claim 1, wherein if the tooth is a premolar tooth or a molar tooth, the separation point comprises: a point on the intersection curve which is closest to the internal reference point, and the tooth axis is determined as the guide axis. ### Claim 5 (depends on 1) The method of claim 1, wherein if the tooth is an incisor tooth or a canine tooth, the separation point comprises: for maxillary teeth, a minimum point of the intersection curve along a Z axis direction for maxillary teeth; and for mandibular teeth, a maximum point of the intersection curve in a Z axis direction for mandibular teeth. ### Claim 6 (depends on 5) The method of claim 5, wherein the determining the tooth axis comprises: determining a linguolabial reference plane which is parallel to the mesiodistal line; dissecting the surface of the tooth crown, by the linguolabial reference plane, into a lingual surface and a labial surface; identifying lingual naked edges on the lingual surface of the surface of the tooth crown; identifying labial naked edges on the labial surface of the surface of the tooth crown; generating a lingual edge curve based on projecting the lingual naked edges onto the linguolabial reference plane; generating a labial edge curve based on projecting the labial naked edges onto the linguolabial reference plane; generating, based on the lingual edge curve and the labial edge curve, an average linguolabial edge curve; determining a linguolabial edge point, the determining comprises: for maxillary teeth, identifying a maximum point of the linguolabial edge curve along a Z axis associated with the linguolabial reference plane; and for mandibular teeth, identifying a minimum point of the linguolabial edge curve along the Z axis associated with the linguolabial reference plane; and determining the tooth axis by rotating the guide axis around the Z axis associated with the linguolabial reference plane until it matches the linguolabial edge point on the linguolabial plane. ### Claim 7 (depends on 4) The method of claim 4, wherein the determining the crown height comprises generating a bounding box around the tooth mesh and along the determined tooth axis, and determining the crown height as a height of the tooth mesh along the tooth axis. ### Claim 8 (depends on 4) The method of claim 4, wherein the determining the crown height comprises projecting tooth mesh vertices of the tooth mesh onto the tooth axis, and determining a distance difference between a minimum point and maximum point along the tooth axis. ### Claim 9 (depends on 1) The method of claim 1, further comprising modulating the determined crown height by a predetermined distance. ### Claim 10 (depends on 1) The method of claim 1, wherein the determining the center of resistance of the tooth based on the determined crown height and the determined tooth axis comprises: retrieving, from a memory, an approximate root length based on the determined crown height; dividing the approximate root length by two to define a center of resistance distance; determining the center of resistance of the tooth as a point along the tooth axis at a distance relating to the center of resistance distance from a crown start point. ### Claim 11 (depends on 1) The method of claim 1, wherein the image data is associated with a plurality of teeth of the patient, and the method further comprises segmenting the image data to obtain a separate tooth mesh for each one of the plurality of teeth. ### Claim 12 (depends on 1) The method of claim 1, further comprising displaying the image data and one or both of the determined tooth axis and the determined center of resistance. ### Claim 13 (depends on 1) The method of claim 1, further comprising determining an orthodontic treatment using the determined center of resistance. ### Claim 14 A method for determining a center of resistance point of a tooth for orthodontic treatment planning, the method being executable by a processor, the method comprising: obtaining image data associated with a tooth crown of a patient, the image data including a tooth mesh representative of a surface of the tooth crown; identifying an internal reference point in the image data, the internal reference point being based on a predetermined internal reference point instruction for locating the internal reference point in a given tooth crown; determining a reference plane in the image data, the reference plane crossing the internal reference point and the tooth mesh and being based on a predetermined reference plane instruction for locating the reference plane relative to the internal reference point for a given tooth; determining an intersection curve based on an intersection of the reference plane and the tooth mesh, the intersection curve following a shape of the surface of the crown at the reference plane; determining a tooth axis of the tooth crown based on the intersection curve by: bisecting the intersection curve into two intersection curve parts based on a separation point; generating an average intersection curve using the two intersection curve parts; generating, based on the average intersection curve, a guide axis using a linear regression algorithm; and determining the tooth axis based on the guide axis; determining a crown height of the tooth crown based on the tooth axis; and determining the center of resistance of the tooth based on the determined crown height and the determined tooth axis. ### Claim 15 (depends on 14) The method of claim 14, wherein the internal reference point comprises a mesiodistal center of the tooth crown, the identifying the internal reference point comprising: obtaining a mesial point on a mesial side of the tooth crown, and a distal point on a distal side of the tooth crown, generating a mesiodistal line joining the mesial point and the distal point; and identifying the mesiodistal center as a midpoint on the mesiodistal line. ### Claim 16 (depends on 15) The method of claim 15, wherein the reference plane is perpendicular to the mesiodistal line and extends through the mesiodistal center. ### Claim 17 (depends on 14) The method of claim 14, wherein if the tooth is a premolar tooth or a molar tooth, the separation point comprises: a point on the intersection curve which is closest to the internal reference point, and the tooth axis is determined as the guide axis; and if the tooth is an incisor tooth or a canine tooth, the separation point comprises: for maxillary teeth, a minimum point of the intersection curve along a Z axis direction for maxillary teeth; and for mandibular teeth, a maximum point of the intersection curve in a Z axis direction for mandibular teeth. ### Claim 18 (depends on 17) The method of claim 17, wherein the determining the tooth axis comprises: determining a linguolabial reference plane which is parallel to the mesiodistal line; dissecting the surface of the tooth crown, by the linguolabial reference plane, into a lingual surface and a labial surface; identifying lingual naked edges on the lingual surface of the surface of the tooth crown; identifying labial naked edges on the labial surface of the surface of the tooth crown; generating a lingual edge curve based on projecting the lingual naked edges onto the linguolabial reference plane; generating a labial edge curve based on projecting the labial naked edges onto the linguolabial reference plane; generating, based on the lingual edge curve and the labial edge curve, an average linguolabial edge curve; determining a linguolabial edge point, the determining comprises: for maxillary teeth, identifying a maximum point of the linguolabial edge curve along a Z axis associated with the linguolabial reference plane; and for mandibular teeth, identifying a minimum point of the linguolabial edge curve along the Z axis associated with the linguolabial reference plane; determining the tooth axis by rotating the guide axis around the Z axis associated with the linguolabial reference plane until it matches the linguolabial edge point on the linguolabial plane. ### Claim 19 A system for determining a center of resistance point of a tooth for orthodontic treatment planning, the system comprising a processor arranged to execute a method, the method comprising: obtaining image data associated with a tooth crown of a patient, the image data including a tooth mesh representative of a surface of the tooth crown; identifying an internal reference point in the image data, the internal reference point being based on a predetermined internal reference point instruction for locating the internal reference point in a given tooth crown; determining a reference plane in the image data, the reference plane crossing the internal reference point and the tooth mesh and being based on a predetermined reference plane instruction for locating the reference plane relative to the internal reference point for a given tooth; determining an intersection curve based on an intersection of the reference plane and the tooth mesh, the intersection curve following a shape of the surface of the crown at the reference plane; determining a tooth axis of the tooth crown based on the intersection curve by: bisecting the intersection curve into two intersection curve parts based on a separation point; generating an average intersection curve using the two intersection curve parts; generating, based on the average intersection curve, a guide axis using a linear regression algorithm; and determining the tooth axis based on the guide axis; determining a crown height of the tooth crown based on the tooth axis; and determining the center of resistance of the tooth based on the determined crown height and the determined tooth axis.