CN103700103A - Method for automatically extracting gingiva curves of three-dimensional digital dentition model - Google Patents

Method for automatically extracting gingiva curves of three-dimensional digital dentition model Download PDF

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CN103700103A
CN103700103A CN201310707219.0A CN201310707219A CN103700103A CN 103700103 A CN103700103 A CN 103700103A CN 201310707219 A CN201310707219 A CN 201310707219A CN 103700103 A CN103700103 A CN 103700103A
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gum
curve
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characteristic curve
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吴婷
张礼兵
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Jiaxing University
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Abstract

The invention discloses a method for automatically extracting gingiva curves on a three-dimensional digital dentition model. The method comprises the steps of model positioning, gingival feature line search, gingival feature line partitioning and inter-tooth space gingival line interference analysis. The method is high in automatic degree, enclosed gingival curves around each tooth on the dentition model can be constructed rapidly and accurately, the problems of low efficiency, poor accuracy and the like existing in the conventional manual design are solved effectively, and the efficiency and attractiveness of oral rehabilitation are improved.

Description

Three-dimensional digital dental arch model gum curve extraction method
Technical field
The invention belongs to Design of digital field, relate to the technical fields such as computer graphics and biomedical engineering.
Background technology
Gum tracing pattern how to obtain exactly every tooth on patient's dental arch model is that the important prerequisite being successfully achieved is repaired in oral cavity.Traditional restorative procedure need to be according to aesthetic requirement and expertise, hand engraving wax pattern or tooth plaster cast are to simulate the gum curve harmonious with adjacent teeth, yet there is the problem of efficiency and precision aspect in this method, especially when patient lacks in the situation of many teeth, this problem is particularly outstanding.
Along with developing rapidly of computing machine, emerged in large numbers large quantities of oral cavities abroad and repaired CAD/CAM system equipment.Yet, impact due to factors such as limited measuring accuracy and mesh reconstructions, on the three-dimensional digital dental arch model surface obtaining by optical measuring technique, interdental gap often merges, so the extracting method of gum curve mainly adopts manual Interactive Segmentation.(the Kondo T such as Kondo, Ong SH, Foong KW.Tooth Segmentation of Dental Study Models Using Range Images.IEEE Transactions on Medical Imaging, 2004, 23 (3): 350-362) propose the gum line drawing method based on depth image, first the method utilizes the dental features point matching arch wire detecting in the plane depth image of triangle grid model, and launch arch wire and calculate panoramic range image, then in planimetric map and panorama sketch, survey respectively gum line position, the result of last comprehensive two width images is determined the partitioning boundary of every tooth, but because depth image can not accurately reflect the three-dimensional information of tooth, so may there is the larger deviation of cutting apart in the model that the method is interfered for severe deformities and between cog.(the YuanT such as the Yuan Tianran of Nanjing Aero-Space University, LiaoW, Dal N, Cheng X, Yu Q.Single-toothmodeling for 3D dental model.Journal ofBiomedical Imaging, 2010) utilize the technology such as morphology and hole repair to extract gum skeleton line, and recover every tooth and there is the continuous anatomic form of single order; But the interactive operation that this process need is a large amount of.
Summary of the invention
For overcoming above-mentioned the deficiencies in the prior art, the present invention is from whole dental arch model anatomic form characteristic, a kind of method of utilizing the technology such as Discrete geometry, graph theory, small echo and B-spline curves to carry out the extraction of gum curve is proposed, farthest to reduce manual intervention, improve efficiency and precision that gum curve extracts.
The technical solution adopted in the present invention is:
Step 1, model orientation: first on three-dimensional digital dental arch model, choose in two first molars of cheek point and left and right far away of two frist premolars in left and right cheek sharp, utilize these four reference point to fit to biteplane, then biteplane is snapped to XY plane, YZ plane is stitched through in two central incisors, two middle cheek points far away are positioned in X-axis, thereby triangle gridding dental arch model are navigated to the direction of a standard.
Step 2, gum characteristic curve search: distribute because tooth and gingival soft tissue interphase are " concavity ", therefore these regions can be extracted by the principal curvature information of model, and the gum characteristic curve that will survey is actually an optimal path of reflection gum characteristic area.Therefore, the present invention difference interactive fetch strategy in the past, adopts the technology combining based on curvature analysis and route searching to carry out the detection of gum characteristic curve.First utilize Voronoi method to carry out discrete curvature estimation to dental arch model, then the characteristic area extracting based on curvature is mapped as to the undirected connected graph of cum rights, and the curvature value of combination model utilizes Floyd optimal path algorithm search gum characteristic curve with dissection morphological feature.Because Floyd optimal path algorithm can be converted into objective contour detection problem in region, find minimal cut set problem, so can effectively avoid teeth space to interfere branch, obtain globally optimal solution truly.
Step 3, gum characteristic curve are cut apart: gum line characteristic curve is cut apart and is intended to that characteristic curve is carried out to single tooth tooth region and divides.Owing to take teeth space between tooth as separatrix, and teeth space position is roughly seated in the place of extracted gum characteristic curve degree of crook maximum, and therefore cutting apart of task is just summed up as finds the larger position of curvature on gum characteristic curve.But because gum characteristic curve is to come from the grid vertex of shaking continuously in triangle gridding, therefore for effectively detecting the teeth space position on characteristic curve, first adopt B spline wavelets technology to carry out automatic fairing to the gum characteristic curve detecting, to repair its high dither composition, then in conjunction with the single order of characteristic curve and second-order differential characteristic and gum characteristic curve at the different direction character of cheek-tongue side, survey teeth space position to be partitioned into the gum feature data point of every tooth.
Step 4, interdental gum line interference analysis: for repairing gum side disappearance form and avoiding gum line generation between cog profile to interfere, adopt the curve-fitting method based on mapping plane and the tangent constraint of between cog to carry out gum Curve Reconstruction.First utilize gum feature data point to simulate gum B-spline curves and the dental arch B-spline curves of every tooth, and project on the biteplane of dental arch model self, intersection point by dental arch curve and gum curve after calculating projection is determined the tangent obligatory point between adjacent teeth between two, and mapping is back in the middle of three dimensions, finally utilize curve-fitting method reconstruct between cog based on feature constraint without the sealing gum curve of interfering.
Compared with prior art, the inventive method does not rely on the information of corona, avoided mathematical computations complicated between corona and teeth space triangle gridding, can effectively reject the interference branch at teeth space place, therefore the method is not only effective to the dental arch model of marshalling, and to misaligned or have the model of missing tooth also can bring forth good fruit, thereby repair and lay a good foundation recording the variation of patient's gum tracing pattern and follow-up oral cavity.
Accompanying drawing explanation
Fig. 1 is general technical route map of the present invention
Fig. 2 is dental arch model oriented graph
Fig. 3 is gum characteristic curve search graph;
Fig. 4 is that gum characteristic curve is cut apart figure
Fig. 5 is that interdental gum curve interference analysis and tangent obligatory point calculate schematic diagram
Fig. 6 is that gum curve finally extracts result figure
Embodiment
Below in conjunction with accompanying drawing, technical scheme of the present invention is described in further detail.
With reference to Fig. 1, specific implementation step of the present invention is as follows:
Step 1, model orientation: first on dental arch model, choose in two first molars of cheek point and left and right far away of two frist premolars in left and right cheek sharp, utilize these four reference point to fit to biteplane, then biteplane is snapped to XY plane, YZ plane is stitched through in two central incisors, two middle cheek points far away are positioned in X-axis, thereby triangle gridding dental arch model is navigated to the direction of a standard, as shown in Figure 2.
Step 2, the search of gum characteristic curve:
(1) the discrete curvature analysis of dental arch model
Because three-dimensional dental arch model is a kind of burst linear surface, thus adopt that the people such as Meyer propose based on Voronoi method, dental arch model is carried out to discrete curvature analysis, the method is optimum to the various curvature effects of estimation triangle mesh curved surface.Voronoi method is regarded smooth surface as the limit or the linear proximity of gang's grid, and the metric property on each summit of triangle gridding is regarded as to this space lattice is in the average tolerance of a small neighbourhood of this point.Character and the Gauss-Bonnet theorem of utilizing Laplace-Beltrami operator, can obtain grid vertex p imean curvature k hwith Gaussian curvature k gdiscrete expression be respectively:
Figure BSA0000099252170000031
k G ( p i ) = 1 A mix ( 2 π - Σ j ∈ N ( i ) θ j )
α wherein ij, β ijbe respectively connect Vertex p iwith summit p jthe diagonal angle on limit, θ jfor summit p i1 ring neighborhood N (i) summit and p ithe angle on connected limit, n is summit p inormal vector; Work as p i1 ring neighborhood triangle while being all acute angle, A mixp ithe area sum in the Voronoi region at place; Work as p i1 ring while having triangle to be obtuse triangle in neighborhood, do some to following the example of of obtuse triangle area and revise, the mid point on the mid point of obtuse angle corresponding sides and another two limits is connected and obtains area.After Gaussian curvature and mean curvature are tried to achieve, can release summit p ithe minimum and maximum principal curvatures at place is respectively:
k max ( p i ) = k H ( p i ) + k H 2 ( p i ) - k G ( p i )
k min ( p i ) = k H ( p i ) - k H 2 ( p i ) - k G ( p i )
When k H 2 ( p i ) - k G ( p i ) < 0 Time, order k H 2 ( p i ) - k G ( p i ) = 0 . Fig. 3 a is the curvature cloud atlas that utilizes the three-dimensional dental arch model of maximum principal curvatures drafting.Can find out, " concavity " region that the size of maximum principal curvatures can be measured dental arch model, a given suitable curvature threshold just can extract the characteristic area at gum line position place, these regions often comprise the interference features such as dental groove tooth nest, because they are generally high than gingival position, therefore can filter by calculating occlusal distance.Like this, remaining is exactly some residual pieces and noise, and these provincial characteristicss are that neighborhood of a point number is fewer, when neighborhood of a point number is less than certain value, just can automatically they be deleted, and the characteristic area finally obtaining as shown in Figure 3 b.
(2) search of the gum characteristic curve based on Floyd optimal path
The grid chart that optimal path is is cum rights by data-mapping, with that minimum paths of weights sum in finding in figure from source node to destination node.Because gum characteristic curve is enclosed construction, even if the longest shortest path can not connect whole closed region.Therefore, the present invention, according to source point and the terminal of the automatic calculating path of gum characteristic curve arrangement regulation, then first surveys the gum characteristic curve of tongue side, then surveys the characteristic curve of cheek side.Source node s and the destination node in path define in the following way: from Cartesian coordinates, convert gum characteristic number strong point to cylindrical coordinates, using two summits of polar angle difference maximum respectively as source point s and destination node t.For making path be close to the gum unique point of curvature maximum, weights are defined according to following mode:
w ( v i , v j ) = | | v i - v j | | k ( v i ) k ( v j )
Wherein, k (v i) and k (v j) represent respectively vertex v iand v jmaximum principal curvatures value, || v i-v j|| represent the Euclidean distance between these 2.Therefore, distance between two abutment points is nearer, curvature value is maximum, and the weights on their limits are just less.Adopt the optimal path between Floyd Algorithm for Solving source node s and destination node t, this path can effectively detect the gum characteristic curve of tongue side, and rejects the take-off point at teeth space place.Then near unique point tongue side gum profile is deleted, repeat Shortest Path Searching one time, the shortest path tried to achieve is the gum characteristic curve of cheek side.The result that complete gum characteristic curve shows in occlusal surface view as shown in Figure 3 c.
Step 3, gum characteristic curve are cut apart:
(1) gum characteristic curve B spline wavelets fairing
The fairing of B spline wavelets mainly utilizes the multi-resolution characteristics of Wavelet representation for transient to carry out filtering to curve, to remove high frequency details composition, retains low-frequency component, thereby guarantees better the original overall form of curve.For obtaining better fairing effect, the cheek side first previous step being detected and tongue side gum characteristic curve fit to respectively non-uniform B-spline curve f 3 times lingualand f buccal.To every curve, take following strategy to carry out fairing: by curve separating, to be yardstick part and detail section, and detail section is decomposed into wavelet scale part and wavelet details part again; When the mould of wavelet details matrix of coefficients is greater than setting threshold, wavelet details is partly repaired, and obtained new control vertex by wavelet reconstruction; Finally new control vertex is carried out to iterative computation, until iteration error is greater than the limits of error or reaches certain iterations.
(2) teeth space position sensing
Derivative characteristic to the gum curve after fairing is analyzed known: at tongue side gum curve f linbualteeth space position, vector
Figure BSA0000099252170000042
and vector
Figure BSA0000099252170000043
roughly in contrary direction, as shown in Fig. 4 a; For buccal curve f buccalteeth space position, vector
Figure BSA0000099252170000044
with
Figure BSA0000099252170000045
roughly in identical direction, as shown in Figure 4 b.Therefore with the dot product of curvature and vector, judge the angle between them, utilize following constraint condition to determine teeth space position corresponding on curve:
Figure BSA0000099252170000051
Wherein, ρ tfor the curvature value of this point on curve, T is given threshold value.After teeth space parameter value on gum curve finds, the data point of their correspondences is deleted, remaining tongue side and cheek side data point combine the gum feature data point that can form every tooth in order, and by sequence counterclockwise, the result of finally dividing is as shown in Fig. 4 c.
Step 4, interdental gum line interference analysis: first calculate the center of mass point of every tooth profile, the B-spline curves that these center of mass point are fitted to a fairing are as dental arch curve arch; Then the gum characteristic data point of every tooth is all fitted to the B-spline curves of sealing, and they are all mapped on biteplane.Make the gum curve of two adjacent teeth be respectively f iand f i+1, be respectively f after projecting on biteplane i pand f i+1 p, as shown in Figure 5.Utilize bounding box to cut apart and ask friendship method to obtain arch wire arch and gum curve f i ptwo intersection points, the parameter value of these two intersection point correspondences on arch wire arch is t i, 1, t i, 2, corresponding to f i pon parameter value be u 1, u 2; Equally, arch wire arch and gum curve f i+1 ptwo intersection points, corresponding parameter value is respectively t i+1,1, t i+1,2and v 1, v 2.Work as t i, 2> t i+1,1, can judge these two adjacent gum curve intersections, using their correspondences at the mean value of three-dimensional gum intersections of complex curve as f iand f i+1between tangent obligatory point T i, i+1=(f i(u 2)+f i+1(v 1))/2.Therefore, for guaranteeing that two-phase adjacent teeth gingival curvature does not overlap, and should make gum curve f iin parameters u 2, and gum curve f i+1at parameter v 1position all should pass through obligatory point T i, i+1.Finally utilize curve-fitting method reconstruct between cog based on feature constraint without the sealing gum curve of interfering.Last gum curve-fitting results as shown in Figure 6.
The foregoing is only preferred embodiments of the present invention, not in order to limit the present invention, all any modifications of doing within the spirit and principles in the present invention, be equal to and replace and improvement etc., within all should being included in protection scope of the present invention.

Claims (3)

1. a three-dimensional digital dental arch model gum curve extraction method, is characterized in that:
(1) model orientation: choose in two first molars of cheek point and left and right far away of two frist premolars in left and right cheek sharp on three-dimensional digital dental arch model, utilize these four reference point to fit to biteplane, then biteplane is snapped to XY plane, YZ plane is stitched through in two central incisors, two middle cheek points far away are positioned in X-axis, thereby dental arch model are navigated to the direction of a standard.
(2) gum characteristic curve is surveyed: adopt the technology combining based on curvature analysis and route searching to carry out the detection of gum characteristic curve, first utilize Voronoi method to carry out discrete curvature estimation to dental arch model, then the characteristic area extracting based on curvature is mapped as to the undirected connected graph of cum rights, and the curvature value of combination model utilizes Floyd optimal path algorithm search gum characteristic curve with dissection morphological feature.
(3) gum characteristic curve is cut apart: adopt B spline wavelets technology to carry out automatic fairing to the gum characteristic curve detecting, to repair its high dither composition, then in conjunction with the single order of characteristic curve and second-order differential characteristic and gum characteristic curve at the different directivity characteristics of cheek-tongue side, survey teeth space position to be partitioned into the gum feature data point of every tooth.
(4) interdental gum line interference analysis: for repairing gum side disappearance form and avoiding gum line generation between cog profile to interfere, the curve-fitting method of employing based on mapping plane and the tangent constraint of between cog carries out gum Curve Reconstruction, first utilize gum feature data point to simulate gum B-spline curves and the dental arch B-spline curves of every tooth, and project on the biteplane of dental arch model self, intersection point by dental arch curve and gum curve after calculating projection is determined the tangent obligatory point between adjacent teeth between two, and mapping is back in the middle of three dimensions, finally utilize curve-fitting method reconstruct between cog based on feature constraint without the sealing gum curve of interfering.
2. the Floyd optimal path algorithm search gum characteristic curve that utilizes according to claim 1, it is characterized in that: source node s and the destination node in path define in the following way: from Cartesian coordinates, convert gum characteristic number strong point to cylindrical coordinates, using two summits of polar angle difference maximum respectively as source point s and destination node t.For making path be close to the gum unique point of curvature maximum, weights are defined according to following mode:
w ( v i , v j ) = | | v i - v j | | k ( v i ) k ( v j )
Wherein, k (v i) and k (v j) represent respectively vertex v iand v jmaximum principal curvatures value, || v i-v j|| represent the Euclidean distance between these 2; Then adopt the optimal path between Floyd Algorithm for Solving source node s and destination node t, this path can effectively detect the gum characteristic curve of tongue side, and reject the take-off point at teeth space place, finally near unique point tongue side gum profile is deleted, repeat Shortest Path Searching one time, the shortest path tried to achieve is the gum characteristic curve of cheek side again.
3. teeth space location detection methods according to claim 1, is characterized in that: at tongue side gum curve f lingualteeth space position, vector
Figure FSA0000099252160000012
and vector
Figure FSA0000099252160000013
roughly in contrary direction; For buccal curve f buccalteeth space position, vector
Figure FSA0000099252160000021
with
Figure FSA0000099252160000022
roughly, in identical direction, utilize the dot product of curvature and vector to judge the angle between them, utilize following constraint condition to determine teeth space position corresponding on curve:
Figure FSA0000099252160000023
Wherein, ρ tfor the curvature value of this point on curve, T is given threshold value; After teeth space parameter value on gum curve finds, the data point of their correspondences is deleted, remaining tongue side and cheek side data point combine the gum feature data point that can form every tooth in order.
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