# US 2022/0036653 A1 · Automated trimming of a surface mesh

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- Number: US 2022/0036653 A1
- Document ID: US20220036653A1
- Status: Published application
- Kind: A1
- Application number: 17/309,693
- Filed: 2019-12-19
- Published: 2022-02-03
- Earliest claimed: 2018-12-20
- Assignees: Medicim N.V.
- Applicants: Medicim NV
- Inventors: Mathias DE SOMERE; Dirk ABBELOOS; Pieter VAN LEEMPUT; Wouter MOLLEMANS
- Web page: https://patentgrep.com/patent/US20220036653A1

## CPC

- G06T 17/20: Finite element generation, e.g. wire-frame surface description, {tesselation}
- G06T 19/20: Editing of three-dimensional [3D] images, e.g. changing shapes or colours, aligning objects or positioning parts
- G06T 2210/36: Level of detail
- G06T: IMAGE DATA PROCESSING OR GENERATION, IN GENERAL

## Abstract

The present invention provides a method for automating the trimming of the boundary region of a three dimensional (3D) open surface mesh model comprising an inner mesh region delineated by boundary vertices and edges. In a particular embodiment, the present invention relates to a method for automating the trimming of an open surface mesh representing an intraoral region.

## Claims

### Claim 1

A method of trimming an open surface mesh, which comprises an inner mesh region delineated by an outer boundary, said method comprising:
receiving an open surface mesh;
determining a cut-off line for trimming said open surface mesh wherein said determining comprises
computing function values for a plurality of positions on said open surface by solving a diffusion function describing the evolution in time of the spatial distribution of a quantity over said surface mesh, said diffusion function being characterized by an equation of the type
∂
f
⁡
(
ν
,
t
)
∂
t
=
∇
·
A
⁢
∇
f
⁡
(
v
,
t
)
and applying boundary conditions specifying the function values of a solution of said equation along said outer boundary, wherein v is a spatial position, t is time, ∇· is a divergence operator, A is a positive definite matrix, ∇ is a gradient operator and ƒ is a function defined on said open surface mesh;
calculating one or more isolines from said function values, each such isoline joining surface mesh positions with the same function value,
selecting from said one or more isolines an isoline enclosing a region of interest of said open surface mesh; and
using the selected isoline as a cut-off line enclosing the surface mesh region to be maintained after trimming or using the selected isoline as a reference in post-processing for defining a cut-off line wherein the trajectory of said cut-off line is situated between said selected isoline and the outer boundary of said mesh; and
trimming said open surface mesh by removing the surface mesh regions between said cut-off line and the outer boundary of said open surface mesh.

### Claim 2 (depends on 1)

The method according to claim 1, wherein said diffusion function comprises an independent variable that is a measure of a local surface mesh property selected from a measure for the distance between a mesh position and the outer boundary, a measure indicative of the surface curvature at a mesh position or a measure indicative of the color at a mesh position.

### Claim 3 (depends on 1)

The method according to claim 1, wherein computing said function values comprises calculating a steady state solution for said diffusion function.

### Claim 4 (depends on 1)

The method according to claim 1, wherein computing said function values comprises calculating a non-uniform intermediary solution of said function.

### Claim 5 (depends on 1)

The method according to claim 1, wherein said diffusion function is a heat diffusion function with an equation of the type
∂
u
⁡
(
ν
,
t
)
∂
t
=
α
⁢
∇
2
⁢
u
⁡
(
ν
,
t
)
,
wherein α∇2u(v, t) specifies a thermal diffusion term with α being a heat diffusion coefficient (with units
m
2
s
describing a virtual rate or neat transfer over said mesh and ∇2u denoting the Laplace-Beltrami operator applied to the function and wherein u(v, t) returns a virtual temperature.

### Claim 6 (depends on 5)

The method according to claim 5, wherein said heat equation further comprises a heat dissipation term −λ u(v, t) providing an equation
∂
u
⁡
(
ν
,
t
)
∂
t
=
α
⁢
∇
2
⁢
u
⁡
(
ν
,
t
)
-
λ
⁢
u
⁡
(
ν
,
t
)
,
with λ denoting a heat dissipation coefficient (s−1), wherein λ≥0.

### Claim 7 (depends on 6)

The method according to claim 6, wherein the heat diffusion coefficient (α) and/or the heat dissipation coefficient (λ) are dependent on a measure indicative of the surface curvature at a mesh position, a measure indicative of the color at a mesh position or a measure for the distance between a mesh position and the outer boundary.

### Claim 8 (depends on 7)

The method according to claim 7, wherein the heat diffusion coefficient (α) and/or the heat dissipation coefficient (λ) are dependent on the mean surface curvature or on a smoothed mean surface curvature as determined for a vertex position.

### Claim 9 (depends on 5)

The method according to claim 5, comprising the calculation of a plurality of uniformly-spaced isolines by dividing the range between the calculated lowest (umin) and highest (umax) virtual temperature into S equidistant intervals thus defining an ordered set of S+1 isolines wherein the difference between isoline values of two neighbouring isolines is
1
s
⁢
(
u
max
-
u
min
)
.

### Claim 10 (depends on 9)

The method according to claim 9, wherein identifying an open surface mesh region of interest comprises selecting one of said uniformly-spaced isolines as the isoline enclosing a region of interest based on following criteria (i) minimal average distance between the selected isoline and its neighboring isolines, (ii) maximal total surface area within the selected isoline and (iii) maximal total mean or smoothed mean curvature within the selected isoline.

### Claim 11 (depends on 1)

The method according to claim 1, wherein the selected isoline enclosing a surface mesh region of interest is identified as the cut-off line.

### Claim 12 (depends on 1)

The method according to claim 1, wherein the cut-off line is identified in post-processing using the selected isoline as a reference for identifying said cut-off line, wherein relative to the selected isoline said cut-off line is moved towards the outer boundary at positions where the shortest distance between the selected isoline and the outer boundary is below a threshold value and wherein said cut-off line is substantially maintained at the level of the selected isoline at positions where the minimal distance between the selected isoline and the outer boundary exceeds said threshold value.

### Claim 13 (depends on 12)

The method according to claim 12, wherein said post-processing comprises:
recomputing function values for a plurality of positions on said open surface mesh by applying on said mesh a diffusion function using adapted boundary conditions;
calculating one or more new isolines from said recomputed function values;
from said new isolines selecting an isoline enclosing a region of interest of said open surface mesh; and
defining a cut-off line enclosing the surface mesh region to be maintained after trimming using the newly selected isoline;
wherein said adapted boundary conditions favor a solution wherein as compared to the initial isolines the positions of the new isolines (i) shift towards the outer boundary where the smallest distance between the said initially selected isoline and the outer boundary is below a threshold distance, and (ii) are substantially maintained where this smallest distance exceeds said threshold distance.

### Claim 14 (depends on 12)

The method according to claim 12, wherein said post-processing comprises the detection of boundary vertices of outer boundary segments that either bend into said open surface mesh and delineate cracks or that delineate protruding flap regions of said surface mesh,
wherein said detection comprises determining for each outer boundary vertex the distances along the outer boundary and the Euclidean distances between a said outer boundary vertex and neighboring outer boundary vertices within a region surrounding said boundary vertex,
wherein said boundary vertex is detected as a boundary vertex of an in-bending or protruding outer boundary segment when the ratio of said geodesic distance over said Euclidean distance between said first boundary vertex and any one of said neighboring boundary vertices exceeds a threshold value.

### Claim 15 (depends on 14)

The method according to claim 14, wherein pairs of entrance vertices defining start and end points of in-bending or protruding boundary segments are identified using a method comprising:
identifying for each outer boundary vertex detected to be in an in-bending or protruding outer boundary segment the neighboring boundary vertex with the highest said ratio of boundary geodesic distance over Euclidean distance as the corresponding boundary vertex;
retaining the detected vertices that have each other as corresponding boundary vertices as candidate pairs of entrance vertices;
comparing said retained pairs of candidate entrance vertices wherein a pair of candidate entrance vertices is discarded when the outer boundary vertices between said candidate entrance vertices are a subset of the outer boundary vertices between another pair of candidate entrance vertices; and
labelling the remaining pairs of candidate entrance vertices as pairs of entrance vertices of in-bending or protruding boundary segments.

### Claim 16 (depends on 15)

The method according to claim 15, wherein an outer boundary segment defined by a said pair of entrance vertices is labelled as an in-bending outer boundary segment in case all shortest distances between the respective vertices of said segment, including the entrance pair vertices, and the initially selected isoline are below a threshold distance.

### Claim 17 (depends on 15)

The method according to claim 15, wherein an outer boundary segment defined by a said pair of entrance vertices is labelled as an outer boundary segment delineating a protruding flap region in case the shortest distance between at least one vertex of said segment, including the entrance pair vertices, and the initially selected isoline exceeds a threshold distance.

### Claim 18 (depends on 16)

The method according to claim 16, wherein said post-processing further comprises repositioning the selected isoline towards the in-bending boundary segments.

### Claim 19 (depends on 18)

The method according to claim 18, wherein said post-processing comprises (i) computing new function values by re-applying a diffusion function over said open surface mesh using adapted boundary conditions along said in-bending or protruding outer boundary segments, (ii) re-calculating isolines from said new function values, (iii) selecting one of said re-calculated isolines selected as the isoline enclosing the region of interest and (iv) determining the cut-off line for trimming said open surface mesh using said selected re-calculated isoline.

### Claim 20

A method of trimming an open surface mesh, which comprises an inner mesh region delineated by an outer boundary, said method comprising:
receiving an open surface mesh;
determining a region of said open surface mesh to be maintained after trimming wherein said determining comprises:
computing function values for a plurality of positions on said open surface by solving a diffusion function describing the evolution in time of the spatial distribution of a quantity over said surface mesh, said diffusion function being characterized by an equation of the type
∂
f
⁡
(
ν
,
t
)
∂
t
=
∇
·
A
⁢
∇
f
⁡
(
v
,
t
)
and applying boundary conditions specifying the function values of a solution of said equation along said outer boundary, wherein v is a spatial position, t is time, ∇⋅ is a divergence operator, A is a positive definite matrix, ∇ is a gradient operator and ƒ is a function defined on said open surface mesh, and
identifying an open surface mesh region to be maintained after trimming wherein said region groups mesh positions with function values within a selected range; and
trimming said open surface mesh by removing the open surface mesh regions outside the region identified to be maintained after trimming.

### Claim 21 (depends on 20)

The method according to claim 20, wherein said diffusion function comprises a measure indicative of a local surface mesh property that is a measure for the distance between a mesh position and the outer boundary, a measure indicative of the surface curvature at a mesh position or a measure indicative of the color at a mesh position.

### Claim 22 (depends on 20)

The method according to claim 20, wherein said diffusion function is a heat diffusion function.

### Claim 23 (depends on 1)

The method according to claim 1, wherein said open surface mesh is an intraoral surface mesh representing a part of the intraoral region.

### Claim 24 (depends on 23)

The method according to claim 23, wherein said intraoral surface mesh comprises a convex dental arch and one or more concave mesh regions.

### Claim 25 (depends on 23)

Use of a method according to claim 23 in a procedure of planning an intraoral surgical intervention or of designing a dental prosthesis.

### Claim 26

A system of trimming an open surface mesh, which comprises an inner mesh region delineated by an outer boundary, said system comprising a processing unit configured to perform the method comprising:
receiving an open surface mesh;
determining a cut-off line for trimming said open surface mesh wherein said determining comprises:
computing function values for a plurality of positions on said open surface by solving a diffusion function describing the evolution in time of the spatial distribution of a quantity over said surface mesh, said diffusion function being characterized by an equation of the type
∂
f
⁡
(
ν
,
t
)
∂
t
=
∇
·
A
⁢
∇
f
⁡
(
v
,
t
)
and applying boundary conditions specifying the function values of a solution of said equation along said outer boundary, wherein v is a spatial position, t is time, ∇⋅ is a divergence operator, A is a positive definite matrix, ∇ is a gradient operator and ƒ is a function defined on said open surface mesh;
calculating one or more isolines from said function values, such isoline joining surface mesh positions with the same function value,
selecting from said one or more isolines an isoline enclosing a region of interest of said open surface mesh; and
using the selected isoline as a cut-off line enclosing the surface mesh region to be maintained after trimming or using the selected isoline as a reference in post-processing for defining a cut-off line wherein the trajectory of said cut-off line is situated between said selected isoline and the outer boundary of said mesh; and
trimming said open surface mesh by removing the surface mesh regions between said cut-off line and the outer boundary of said open surface mesh.