CN108335318A - The method and device of corona and fusion of roots - Google Patents
The method and device of corona and fusion of roots Download PDFInfo
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Abstract
The present invention discloses a kind of method and device of corona and fusion of roots, is related to oral cavity technical field, can solve the problems, such as to merge corona root of the tooth poor robustness in the prior art.Method includes：Scanning corona model and CBCT tooth models are registrated；Abnormal point deletion, the processing of smooth edge are carried out to scanning corona model, to the scanning corona model and the secondary registration of CBCT tooth models progress after smoothing processing；To after secondary registration scanning corona model and CBCT tooth models in the relatively small model of density into line density increase handle so that the density contrast of two models be no more than pre-set density difference range；Using geodesic curve split plot design, the corona part on density treated CBCT tooth models is removed, CBCT root models are obtained；Using default bridging algorithm, multistage bridge joint is carried out to scanning corona model and CBCT root models；The hole obtained after being bridged to multistage is repaired, and carries out Mesh smoothing processing.The present invention is mainly suitable for the scenes of automatic fusion corona root of the tooth.
Description
Technical field
The present invention relates to oral cavity technical fields, more particularly to the method and device of a kind of corona and fusion of roots.
Background technology
With the development of digitized medical, oral cavity field also progresses into digitlization.Scanner can obtain in mouth at present
To the three-dimensional mesh data of accurately corona, medical imaging device can collect the CBCT image datas comprising corona, root of the tooth,
And three-dimensional mesh data can be obtained by mesh reconstruction, but accuracy is relatively low.In dentistry field, generally require complete
Tooth model, and it is higher to the required precision of corona.Therefore, it is carried out with root model in CBCT by the way that corona model will be scanned
It blends, obtains a tooth model that is complete and meeting the requirements and have become more popular processing mode.
There is the method that corona, fusion of roots are realized by human-computer interaction at present, also there is automation to realize corona, fusion of roots
Method.Wherein, the specific implementation of automation fusion corona and root of the tooth includes mainly：(1) first will scanning corona model with
CBCT tooth data are registrated, and are then removed the corona part in CBCT tooth data, are obtained CBCT root models, then foundation
The local normal information of corona model and the edge point of root model is scanned, part abnormal point is removed, finally by smooth behaviour
Make, obtains corona model to be spliced and root model；(2) control is generated in corona model and the fringe region of root model
Point is segmented splicing regions then according to control point；It is close according to bezier surface equation and corona model, root model
The difference of degree, is sampled on bezier surface, is finally carried out triangulation to sampled point, is generated initial bezier surface
Mosaic face；(3) it uses mean curvature flow to carry out fairing processing to Mosaic face, obtains the tooth model of relative smooth.
However, when corona root of the tooth density contrast away from it is larger when, using the above method obtain Mosaic face will appear grid lines hand over
The phenomenon that fork, mesh topology does not meet demand, and when corona edge portions are more complicated, calculated using bezier surface
Method can not construct accurate Mosaic face, to be unable to get accurate fusion results.
Invention content
In view of this, the method and device of corona provided by the invention and fusion of roots, its object is to solve existing skill
The problem of corona root of the tooth poor robustness is merged in art.
To solve the above-mentioned problems, present invention generally provides following technical solutions：
In a first aspect, the present invention provides a kind of method of corona and fusion of roots, the method includes：
Scanning corona model and CBCT tooth models are registrated；
Delete the abnormal point on the scanning corona model；
Smooth edge processing is carried out to the scanning corona model after suppressing exception point；
Secondary registration is carried out to treated at smooth edge scanning corona model and CBCT tooth models；
To after secondary registration scanning corona model and CBCT tooth models in the relatively small model of density into line density
Increase is handled, so that the density contrast of two models is no more than pre-set density difference range；
Using geodesic curve split plot design, the corona part on density treated CBCT tooth models is removed, CBCT is obtained
Root model；
Using default bridging algorithm, multistage bridge joint is carried out to the scanning corona model and the CBCT root models；
The hole obtained after being bridged to multistage is repaired, and carries out Mesh smoothing processing, obtains fusion results.
Second aspect, the present invention provides the device of a kind of corona and fusion of roots, described device includes：
Registration unit is registrated for that will scan corona model and CBCT tooth models；
Deleting unit, for deleting the abnormal point on the scanning corona model；
Smoothing processing unit, for carrying out smooth edge processing to the scanning corona model after suppressing exception point；
The registration unit is additionally operable to carry out two to treated at smooth edge scanning corona model and CBCT tooth models
Secondary registration；
Density processing unit, for after secondary registration scanning corona model and CBCT tooth models in density relatively
Small model is handled into line density increase, so that the density contrast of two models is no more than pre-set density difference range；
Removal unit, for utilizing geodesic curve split plot design, by the corona part on density treated CBCT tooth models
Removal obtains CBCT root models；
Bridge-jointing unit, for using presetting bridging algorithm, to the scanning corona model and the CBCT root models into
Row multistage bridges；
Unit is repaired, the hole for being obtained after being bridged to multistage is repaired；
Fairing unit obtains fusion results for carrying out Mesh smoothing processing.
The third aspect, the present invention provides a kind of storage medium, the storage medium includes the program of storage, wherein
Equipment executes the side of corona and fusion of roots as described in relation to the first aspect described program controls the storage medium when running where
Method.
Fourth aspect, the present invention provides the device of a kind of corona and fusion of roots, described device include storage medium and
Processor；
The processor is adapted for carrying out each instruction；
The storage medium is suitable for storing a plurality of instruction；
Described instruction is suitable for being loaded by the processor and being executed the side of corona and fusion of roots as described in relation to the first aspect
Method.
By above-mentioned technical proposal, technical solution provided by the invention at least has following advantages：
The method and device of corona and fusion of roots provided by the invention can be obtained dividing from CBCT tooth models
It before root model, is first registrated, abnormal point deletion, smooth edge, secondary registration is then carried out, to exclude abnormal point to matching
The influence of quasi- effect, then to after secondary registration scanning corona model and CBCT tooth models in the relatively small model of density into
Line density increase is handled, so that the density contrast of two models is no more than pre-set density difference range, to avoid the spelling being subsequently generated
The phenomenon that there are grid lines to intersect for junction, mesh topology does not meet demand.Geodesic curve split plot design is being utilized, from CBCT teeth
After segmentation obtains CBCT root models in model, using default bridging algorithm, to scanning corona model and CBCT root models
Multistage bridge joint is carried out, and the hole by being obtained after being bridged to multistage is repaired, then carries out Mesh smoothing processing, melted
Close result.Splice since corona edge is divided into multiple segments by multistage bridge joint, the complexity of each segment is opposite
It is relatively low, so this connecting method is not influenced by corona edge complexity, for opposite bezier surface splicing method, this
Invention can be higher in corona edge complexity, ensures the corona fusion of roots effect of high robust.
Above description is only the general introduction of technical solution of the present invention, in order to better understand the technical means of the present invention,
And can be implemented in accordance with the contents of the specification, and in order to allow above and other objects of the present invention, feature and advantage can
It is clearer and more comprehensible, below the special specific implementation mode for lifting the present invention.
Description of the drawings
By reading the detailed description of hereafter preferred embodiment, various other advantages and benefit are common for this field
Technical staff will become clear.Attached drawing only for the purpose of illustrating preferred embodiments, and is not considered as to the present invention
Limitation.And throughout the drawings, the same reference numbers will be used to refer to the same parts.In the accompanying drawings：
Fig. 1 shows the flow chart of a kind of method of corona and fusion of roots provided in an embodiment of the present invention；
Fig. 2 shows the flow charts of the method for another corona provided in an embodiment of the present invention and fusion of roots；
Fig. 3 shows a kind of composition frame chart of the device of corona and fusion of roots provided in an embodiment of the present invention；
Fig. 4 shows the composition frame chart of the device of another corona and fusion of roots provided in an embodiment of the present invention.
Specific implementation mode
The exemplary embodiment of the application is more fully described below with reference to accompanying drawings.Although showing the application in attached drawing
Exemplary embodiment, it being understood, however, that may be realized in various forms the application without should be by embodiments set forth here
It is limited.It is to be able to be best understood from the application on the contrary, providing these embodiments, and can be by scope of the present application
Completely it is communicated to those skilled in the art.
An embodiment of the present invention provides a kind of methods of corona and fusion of roots, as shown in Figure 1, the method is mainly wrapped
It includes：
101, scanning corona model and CBCT tooth models are registrated.
After obtaining scanning corona model and CBCT tooth models, in order to scan in corona model and CBCT tooth models
Root model merged, need first scan the tune that corona model and CBCT tooth models carry out position in three dimensions
It is whole, realize the registration of position.
Specifically, first can be roughly aligned scanning corona model and CBCT tooth models in three dimensions,
Then scanning corona model and CBCT teeth type are subjected to careful registration in three dimensions again.
Wherein, the realization method of gross alignment can be：The mean center coordinate a1 of scanning corona model is calculated first,
Left-half scans the mean center coordinate a2 of corona model, and right half part scans the mean center coordinate a3 of corona model.So
The mean center coordinate b1 of CBCT tooth models, the mean center coordinate b2 of left-half CBCT tooth models are calculated afterwards, it is right
The mean center coordinate b3 of half part CBCT tooth models.Finally, corresponding, a3 and b3 pairs by a1 is corresponding with b1, a2 and b2
Answer, calculate the scanning transfer matrix M1 that be aligned to CBCT tooth models of corona model, allow scan corona model according to M1 to
CBCT tooth models are shifted, to obtain a rough alignment as a result, CBCT tooth models can also be calculated to sweeping
The transfer matrix M2 for retouching the alignment of corona model allows CBCT tooth models to be shifted to scanning corona model according to M2, to
The alignment result rough to one.
In the centre coordinate of computation model, the centre coordinate of lower jaw entirety can be calculated, can also only calculate the upper jaw
Or the centre coordinate of lower jaw, the foundation using one of which centre coordinate as a model to another Model transfer.
The realization method of careful registration can be：Point of the point on corona model on CBCT tooth models will be scanned gradually
Movement is approached, it is final to realize registration.It can be realized using ICP (Iterative ClosestPoints) algorithms.Main thought
According to given source point and target point, spin matrix and translation matrix to be sought by way of iteration so that the source after transformation
Point is overlapped with target point as possible.
Specifically, assuming that P is the point set scanned on corona model, M is the point set on CBCT tooth models, then is taken in P
One point Pi, distance P is found out in MiNearest point Mi, to put to (Pi, Mi) one group of correspondence point set is just constituted, it is deposited between 2 points
In rotation relationship R and translation relation T.Each point in point set P is obtained with transformation relation if there are n points in P
Point set M defines energy function equation E：
Above-mentioned equation is calculated by least square method again, acquires the R and T when making E minimums.Finally according to R and T,
Rotation and translation is carried out to P, is overlapped with M.
102, the abnormal point on the scanning corona model is deleted.
Scanning corona model is split in the model gone out from scanner scanning, so usually will appear partitioning algorithm
It is imperfect, and cause some regions for scanning corona model edge that can clearly deviate from root of the tooth.Therefore corona root of the tooth spelling is being carried out
Before connecing operation, the subregion for deviating considerably from root of the tooth on the first borderline region to scanning corona model is needed to remove.
Wherein, specific implementation can be：If scanning vertex v on corona modeliNormal vector and its neighborhood point method
The vertex is then determined as abnormal point, and deleted by vector difference away from more than predetermined threshold value.
Abnormal index anomaly (vi) be defined as follows：
In formula, N1(vi) it is viFirst order neighbors, tjIt is the triangle in first order neighbors, ntIt is first order neighbors intermediate cam shape
Quantity, normal (tj) be triangle unit normal vector, normal (vi) it is vertex viUnit normal vector.
You need to add is that the embodiment of the present invention is not limited the execution sequence of step 101 and step 102.It can be first
Step 101 is executed, then executes step 102；Step 102 can also be first carried out, then executes step 101；Can also both hold simultaneously
Row.
103, smooth edge processing is carried out to the scanning corona model after suppressing exception point.
After it will scan the abnormal point deletion on corona model, edge portions be all often it is more irregular, rough,
The quality of the Mosaic face of subsequent builds is influenced whether in this way.Therefore, it is necessary to carry out Laplce to the edge for scanning corona model
Smoothly.I.e. for each vertex v on edge linei, on edge line all there are two vertex it is adjacent thereto, if it is respectively vj
And vk, by vjAnd vkThe average value of coordinate is as viNew coordinate position；When the new coordinate position each vertex on edge line
After all calculating, all of which is moved on respective new coordinate position.
104, secondary registration is carried out to treated at smooth edge scanning corona model and CBCT tooth models.
Since abnormal point can influence the registration effect of corona and root of the tooth, so in order to promote registration effect, it is abnormal in removal
After putting and carrying out smooth edge processing, secondary registration can be carried out to scanning corona model and CBCT tooth models, to ensure two
The precision of aligned in position between person.The specific implementation of wherein secondary registration is identical as the careful registration in step 101,
This is repeated no more.
105, to after secondary registration scanning corona model and CBCT tooth models in the relatively small model of density carry out
Density increase is handled, so that the density contrast of two models is no more than pre-set density difference range.
When the density difference of two models larger (such as a model is twice or more of another model), subsequently obtain
The problem of Mosaic face obtained can cause grid lines to intersect because point is one-to-many to appearance, and mesh topology does not meet demand.For
It avoids that the problem occurs, first the relatively small model of density in the two can be handled into line density increase, so that two moulds
The density contrast of type is no more than pre-set density difference range.
The increased specific implementation of density can be：Using loop algorithms to the scanning corona mould after the secondary registration
The relatively small model of density carries out tessellation in type and CBCT tooth models, so that grid increases, density increases.
106, using geodesic curve split plot design, the corona part on density treated CBCT tooth models is removed, is obtained
CBCT root models.
Before it will scan corona model and CBCT tooth models are merged, need the tooth on CBCT tooth models first
Crown moieties remove, to obtain CBCT tooth models.Specifically, can first be found out on CBCT tooth models and scanning corona model
On the nearest vertex of edge point, the geodesic curve path that these vertex are formed between any two, as on CBCT tooth models
CBCT tooth models are divided into two parts, and the closer part model of range sweep corona model are deleted by cut-off rule, are obtained
Obtain the CBCT root models far from scanning corona model.
107, using default bridging algorithm, bridges in cascade is carried out to the scanning corona model and the CBCT root models
It connects.
After obtaining CBCT root models, the edge of the edge point and CBCT root models of corona model can will be scanned
Point is divided into multigroup point set, then by presetting bridging algorithm, splices respectively to each group of point set, obtains multiple splicings
Face realizes that corona is merged with the preliminary of root of the tooth.
108, the hole obtained after being bridged to multistage is repaired, and carries out Mesh smoothing processing, obtains fusion results.
Due to when carrying out multistage bridge joint to two models, not spliced between bridge section and bridge section, so carrying out
It will appear several holes after multistage bridge joint to need to repair.After carrying out hole repair, in order to enable the hole filled up can melt
Enter the grid on periphery without seeming lofty, Mesh smoothing processing can be carried out again, to obtain final fusion results.Wherein
The method for carrying out fairing processing to grid can be average curvature optical flow method.
The method of corona and fusion of roots provided in an embodiment of the present invention can be obtained dividing from CBCT tooth models
It before root model, is first registrated, abnormal point deletion, smooth edge, secondary registration is then carried out, to exclude abnormal point to matching
The influence of quasi- effect, then to after secondary registration scanning corona model and CBCT tooth models in the relatively small model of density into
Line density increase is handled, so that the density contrast of two models is no more than pre-set density difference range, to avoid the spelling being subsequently generated
The phenomenon that there are grid lines to intersect for junction, mesh topology does not meet demand.Geodesic curve split plot design is being utilized, from CBCT teeth
After segmentation obtains CBCT root models in model, using default bridging algorithm, to scanning corona model and CBCT root models
Multistage bridge joint is carried out, and the hole by being obtained after being bridged to multistage is repaired, then carries out Mesh smoothing processing, melted
Close result.Splice since corona edge is divided into multiple segments by multistage bridge joint, the complexity of each segment is opposite
It is relatively low, so this connecting method is not influenced by corona edge complexity, for opposite bezier surface splicing method, this
Invention can be higher in corona edge complexity, ensures the corona fusion of roots effect of high robust.
Further, according to method shown in FIG. 1, an alternative embodiment of the invention additionally provides a kind of corona and root of the tooth
The method of fusion, as shown in Fig. 2, the method includes：
201, scanning corona model and CBCT tooth models are registrated.
202, the abnormal point on the scanning corona model is deleted.
It should be noted that the embodiment of the present invention is not limited the execution sequence of step 201 and step 202.It can be first
Step 201 is executed, then executes step 202；Step 202 can also be first carried out, then executes step 201；Can also both hold simultaneously
Row.
203, smooth edge processing is carried out to the scanning corona model after suppressing exception point.
204, secondary registration is carried out to treated at smooth edge scanning corona model and CBCT tooth models.
205, to after secondary registration scanning corona model and CBCT tooth models in the relatively small model of density carry out
Density increase is handled, so that the density contrast of two models is no more than pre-set density difference range.
206, using geodesic curve split plot design, the corona part on density treated CBCT tooth models is removed, is obtained
CBCT root models.
Specifically, elder generation for two edge points adjacent on scanning corona model, is found on CBCT tooth models and it
Two nearest consecutive points of distance；Then the geodesic curve path of two consecutive points found is calculated, and by the geodesic curve path
On vertex be added segmentation point set；It has traversed again on the scanning corona model after all edge points, has deleted the segmentation
All vertex in point set obtain two parts region；It will finally be deleted with the region of the scanning corona model relative close,
Obtain the CBCT root models.
207, using default bridging algorithm, bridges in cascade is carried out to the scanning corona model and the CBCT root models
It connects.
Specifically, can first determine scanning corona model upper edge point and CBCT root models upper edge point it
Between point correspondence；It is then based on the point correspondence, using Hermite function interpolations, is obtained adjacent in each bridge section
Interpolation point between edge point；It is finally directed to each bridge section, triangulation processing is carried out to interpolation point and edge point, obtains multistage
Bridge curved surface.
Wherein it is determined that the specific implementation of point correspondence can be：With the scanning corona model edge and described
The proximity pair at CBCT root models edge be starting point, for each edge point on the scanning corona model, find and
Edge point in its nearest CBCT root model is as corresponding points.
Using Hermite function interpolations, the specific implementation side of interpolation point of the adjacent edge between putting in each bridge section is obtained
Formula can be：
According to the continuous curve parametric equation C of 2 single orders1(u) and C2(u), the tangential vector field T of two curves is utilized1
(u) and T2(u) it obtains：
S (u, v)=C1(u)F1(v)+C2(u)F2(v)+T1(u)F3(v)+T2(u)F4(v)
Again by solving S (u, v), interpolation point (u, v) is obtained.
In formula, S (u, v) is interpolation curve C1(u) and C2(u) Hermite interpolation curved surfaces；F1(v), F2(v), F3(v), F4
(v) it is three rank Hermite basic functions.Wherein,
F1(v)=(1-v)2(1+2v)
F2(v)=v2(3-2v)
F3(v)=v (v-1)2
F4(v)=v2(v-1)
208, the hole obtained after being bridged to multistage is repaired.
After carrying out multistage bridge joint, first identify which region belongs to hole, then carrying out triangulation to hole realizes hole
It repairs in hole.Wherein, the method for identifying hole can be：First judge whether the number that opposite side belongs to triangle gridding is 1, if 1, then
It determines when front is a part for hole；Then will include when specific region in front is determined as hole.
209, the position on increased vertex when hole is repaired in adjustment, so that the grid obtained after adjustment meets specific trellis
Topological structure.
When due to carrying out triangulation operation to repair hole, need first to add vertex, then by connecting vertex
Realize triangulation at triangle, thus the vertex position of addition may be undesirable and lead to the mesh topology after subdivision not
Meet specific trellis topological structure.Therefore, it is necessary to adjust the position on increased vertex, preset so that the grid after adjustment meets
Topological structure.
210, Mesh smoothing processing is carried out to the model after adjustment, obtains fusion results.
Further, according to above method embodiment, an alternative embodiment of the invention additionally provides a kind of corona and tooth
The device of root fusion, as shown in figure 3, described device includes mainly：
Registration unit 31 is registrated for that will scan corona model and CBCT tooth models；
Deleting unit 32, for deleting the abnormal point on the scanning corona model；
Smoothing processing unit 33, for carrying out smooth edge processing to the scanning corona model after suppressing exception point；
The registration unit 31 is additionally operable to carry out treated at smooth edge scanning corona model and CBCT tooth models
Secondary registration；
Density processing unit 34, for after secondary registration scanning corona model and CBCT tooth models in density it is opposite
Smaller model is handled into line density increase, so that the density contrast of two models is no more than pre-set density difference range；
Removal unit 35, for utilizing geodesic curve split plot design, by the crown portion on density treated CBCT tooth models
Divide removal, obtains CBCT root models；
Bridge-jointing unit 36 presets bridging algorithm, to the scanning corona model and the CBCT root models for utilizing
Carry out multistage bridge joint；
Unit 37 is repaired, the hole for being obtained after being bridged to multistage is repaired；
Fairing unit 38 obtains fusion results for carrying out Mesh smoothing processing.
Optionally, density processing unit 34, for utilizing loop algorithms to the scanning corona model after the secondary registration
Tessellation is carried out with the relatively small model of density in CBCT tooth models.
Optionally, as shown in figure 4, the removal unit 35 includes：
Searching module 351, for after being handled into line density, for two edge points adjacent on scanning corona model,
Two consecutive points nearest with its distance are found on CBCT tooth models；
First computing module 352, the geodesic curve path for calculating find two consecutive points；
Add module 353, for segmentation point set to be added in the vertex on the geodesic curve path；
Removing module 354 deletes the cut-point for having traversed on the scanning corona model after all edge points
All vertex in set obtain two parts region；
The removing module 354 is additionally operable to delete with the region of the scanning corona model relative close, described in acquisition
CBCT root models.
Optionally, as shown in figure 4, the bridge-jointing unit 36 includes：
Determining module 361, for determining scanning corona model upper edge point and CBCT root models upper edge
Point correspondence between point；
Second computing module 362, for obtaining each bridge using Hermite function interpolations based on the point correspondence
Interpolation point of the adjacent edge between point in section；
Subdivision module 363 carries out triangulation processing for being directed to each bridge section to interpolation point and edge point.
Optionally, the determining module 361, for the scanning corona model edge and CBCT root models side
The proximity pair on edge is that starting point finds the CBCT tooth nearest with it for each edge point on the scanning corona model
Edge point on root model is as corresponding points.
Optionally, as shown in figure 4, described device further includes：
Adjustment unit 39 after the hole for being obtained after being bridged to multistage is repaired, is carrying out at Mesh smoothing
Before reason, the position on increased vertex when hole is repaired in adjustment, so that the grid obtained after adjustment meets specific trellis topology
Structure.
The device of corona and fusion of roots provided in an embodiment of the present invention can be obtained dividing from CBCT tooth models
It before root model, is first registrated, abnormal point deletion, smooth edge, secondary registration is then carried out, to exclude abnormal point to matching
The influence of quasi- effect, then to after secondary registration scanning corona model and CBCT tooth models in the relatively small model of density into
Line density increase is handled, so that the density contrast of two models is no more than pre-set density difference range, to avoid the spelling being subsequently generated
The phenomenon that there are grid lines to intersect for junction, mesh topology does not meet demand.Geodesic curve split plot design is being utilized, from CBCT teeth
After segmentation obtains CBCT root models in model, using default bridging algorithm, to scanning corona model and CBCT root models
Multistage bridge joint is carried out, and the hole by being obtained after being bridged to multistage is repaired, then carries out Mesh smoothing processing, melted
Close result.Splice since corona edge is divided into multiple segments by multistage bridge joint, the complexity of each segment is opposite
It is relatively low, so this connecting method is not influenced by corona edge complexity, for opposite bezier surface splicing method, this
Invention can be higher in corona edge complexity, ensures the corona fusion of roots effect of high robust.
An embodiment of the present invention provides a kind of storage medium, the storage medium includes the program of storage, wherein described
The method that equipment program controls the storage medium when running where executes corona and fusion of roots as described above.
Storage medium may include the volatile memory in computer-readable medium, random access memory (RAM)
With the forms such as Nonvolatile memory, such as read-only memory (ROM) or flash memory (flashRAM), memory includes at least one storage
Chip.
The instruction stored in storage medium provided in an embodiment of the present invention can be obtained dividing from CBCT tooth models
It before root model, is first registrated, abnormal point deletion, smooth edge, secondary registration is then carried out, to exclude abnormal point to matching
The influence of quasi- effect, then to after secondary registration scanning corona model and CBCT tooth models in the relatively small model of density into
Line density increase is handled, so that the density contrast of two models is no more than pre-set density difference range, to avoid the spelling being subsequently generated
The phenomenon that there are grid lines to intersect for junction, mesh topology does not meet demand.Geodesic curve split plot design is being utilized, from CBCT teeth
After segmentation obtains CBCT root models in model, using default bridging algorithm, to scanning corona model and CBCT root models
Multistage bridge joint is carried out, and the hole by being obtained after being bridged to multistage is repaired, then carries out Mesh smoothing processing, melted
Close result.Splice since corona edge is divided into multiple segments by multistage bridge joint, the complexity of each segment is opposite
It is relatively low, so this connecting method is not influenced by corona edge complexity, for opposite bezier surface splicing method, this
Invention can be higher in corona edge complexity, ensures the corona fusion of roots effect of high robust.
An embodiment of the present invention provides the device of a kind of corona and fusion of roots, described device includes storage medium and processing
Device；
The processor is adapted for carrying out each instruction；
The storage medium is suitable for storing a plurality of instruction；
The method that described instruction is suitable for being loaded by the processor and executing corona and fusion of roots as described above.
Include kernel in processor, is gone in storage medium to transfer corresponding program unit by kernel.Kernel can be arranged one
It is a or more, the fusion accuracy of corona and root of the tooth is improved by adjusting kernel parameter, to improve the robustness of fusion.
The device of corona and fusion of roots provided in an embodiment of the present invention can be obtained dividing from CBCT tooth models
It before root model, is first registrated, abnormal point deletion, smooth edge, secondary registration is then carried out, to exclude abnormal point to matching
The influence of quasi- effect, then to after secondary registration scanning corona model and CBCT tooth models in the relatively small model of density into
Line density increase is handled, so that the density contrast of two models is no more than pre-set density difference range, to avoid the spelling being subsequently generated
The phenomenon that there are grid lines to intersect for junction, mesh topology does not meet demand.Geodesic curve split plot design is being utilized, from CBCT teeth
After segmentation obtains CBCT root models in model, using default bridging algorithm, to scanning corona model and CBCT root models
Multistage bridge joint is carried out, and the hole by being obtained after being bridged to multistage is repaired, then carries out Mesh smoothing processing, melted
Close result.Splice since corona edge is divided into multiple segments by multistage bridge joint, the complexity of each segment is opposite
It is relatively low, so this connecting method is not influenced by corona edge complexity, for opposite bezier surface splicing method, this
Invention can be higher in corona edge complexity, ensures the corona fusion of roots effect of high robust.
Present invention also provides a kind of computer program products, when being executed on the device in corona and fusion of roots, fit
In the program code for executing initialization there are as below methods step：
Scanning corona model and CBCT tooth models are registrated；
Delete the abnormal point on the scanning corona model；
Smooth edge processing is carried out to the scanning corona model after suppressing exception point；
Secondary registration is carried out to treated at smooth edge scanning corona model and CBCT tooth models；
To after secondary registration scanning corona model and CBCT tooth models in the relatively small model of density into line density
Increase is handled, so that the density contrast of two models is no more than pre-set density difference range；
Using geodesic curve split plot design, the corona part on density treated CBCT tooth models is removed, CBCT is obtained
Root model；
Using default bridging algorithm, multistage bridge joint is carried out to the scanning corona model and the CBCT root models；
The hole obtained after being bridged to multistage is repaired, and carries out Mesh smoothing processing, obtains fusion results.
It should be understood by those skilled in the art that, embodiments herein can be provided as method, system or computer program
Product.Therefore, complete hardware embodiment, complete software embodiment or reality combining software and hardware aspects can be used in the application
Apply the form of example.Moreover, the application can be used in one or more wherein include computer usable program code computer
The computer program production implemented in usable storage medium (including but not limited to magnetic disk storage, CD-ROM, optical memory etc.)
The form of product.
The application is with reference to method, the flow of equipment (system) and computer program product according to the embodiment of the present application
Figure and/or block diagram describe.It should be understood that can be realized by computer program instructions every first-class in flowchart and/or the block diagram
The combination of flow and/or box in journey and/or box and flowchart and/or the block diagram.These computer programs can be provided
Instruct the processor of all-purpose computer, special purpose computer, Embedded Processor or other programmable data processing devices to produce
A raw machine so that the instruction executed by computer or the processor of other programmable data processing devices is generated for real
The device for the function of being specified in present one flow of flow chart or one box of multiple flows and/or block diagram or multiple boxes.
These computer program instructions, which may also be stored in, can guide computer or other programmable data processing devices with spy
Determine in the computer-readable memory that mode works so that instruction generation stored in the computer readable memory includes referring to
Enable the manufacture of device, the command device realize in one flow of flow chart or multiple flows and/or one box of block diagram or
The function of being specified in multiple boxes.
These computer program instructions also can be loaded onto a computer or other programmable data processing device so that count
Series of operation steps are executed on calculation machine or other programmable devices to generate computer implemented processing, in computer or
The instruction executed on other programmable devices is provided for realizing in one flow of flow chart or multiple flows and/or block diagram one
The step of function of being specified in a box or multiple boxes.
In a typical configuration, computing device includes one or more processors (CPU), input/output interface, net
Network interface and memory.
Memory may include computer-readable medium in volatile memory, random access memory (RAM) and
The forms such as Nonvolatile memory, such as read-only memory (ROM) or flash memory (flash RAM).Memory is computer-readable medium
Example.
Computer-readable medium includes permanent and non-permanent, removable and non-removable media can be by any method
Or technology realizes information storage.Information can be computer-readable instruction, data structure, the module of program or other data.
The example of the storage medium of computer includes, but are not limited to phase transition internal memory (PRAM), static RAM (SRAM), moves
State random access memory (DRAM), other kinds of random access memory (RAM), read-only memory (ROM), electric erasable
Programmable read only memory (EEPROM), fast flash memory bank or other memory techniques, read-only disc read only memory (CD-ROM) (CD-ROM),
Digital versatile disc (DVD) or other optical storages, magnetic tape cassette, tape magnetic disk storage or other magnetic storage apparatus
Or any other non-transmission medium, it can be used for storage and can be accessed by a computing device information.As defined in this article, it calculates
Machine readable medium does not include temporary computer readable media (transitory media), such as data-signal and carrier wave of modulation.
It should also be noted that, the terms "include", "comprise" or its any other variant are intended to nonexcludability
Including so that process, method, commodity or equipment including a series of elements include not only those elements, but also wrap
Include other elements that are not explicitly listed, or further include for this process, method, commodity or equipment intrinsic want
Element.In the absence of more restrictions, the element limited by sentence "including a ...", it is not excluded that including element
There is also other identical elements in process, method, commodity or equipment.
It will be understood by those skilled in the art that embodiments herein can be provided as method, system or computer program product.
Therefore, complete hardware embodiment, complete software embodiment or embodiment combining software and hardware aspects can be used in the application
Form.It is deposited moreover, the application can be used to can be used in the computer that one or more wherein includes computer usable program code
The shape for the computer program product implemented on storage media (including but not limited to magnetic disk storage, CD-ROM, optical memory etc.)
Formula.
It these are only embodiments herein, be not intended to limit this application.To those skilled in the art,
The application can have various modifications and variations.It is all within spirit herein and principle made by any modification, equivalent replacement,
Improve etc., it should be included within the scope of claims hereof.
Claims (10)
1. a kind of method of corona and fusion of roots, which is characterized in that the method includes：
Scanning corona model and CBCT tooth models are registrated；
Delete the abnormal point on the scanning corona model；
Smooth edge processing is carried out to the scanning corona model after suppressing exception point；
Secondary registration is carried out to treated at smooth edge scanning corona model and CBCT tooth models；
To after secondary registration scanning corona model and CBCT tooth models in the relatively small model of density into line density increase
Processing, so that the density contrast of two models is no more than pre-set density difference range；
Using geodesic curve split plot design, the corona part on density treated CBCT tooth models is removed, CBCT roots of the tooth are obtained
Model；
Using default bridging algorithm, multistage bridge joint is carried out to the scanning corona model and the CBCT root models；
The hole obtained after being bridged to multistage is repaired, and carries out Mesh smoothing processing, obtains fusion results.
2. according to the method described in claim 1, it is characterized in that, to the scanning corona model and CBCT teeth after secondary registration
The relatively small model of density includes into line density increase processing in model：
Using loop algorithms to after the secondary registration scanning corona model and CBCT tooth models in density it is relatively small
Model carries out tessellation.
3. according to the method described in claim 1, it is characterized in that, using geodesic curve split plot design, by density treated CBCT
Corona part removal on tooth model, obtaining CBCT root models includes：
After being handled into line density, for two edge points adjacent on scanning corona model, found on CBCT tooth models
Two nearest consecutive points with its distance；
The geodesic curve path of two consecutive points found is calculated, and segmentation point set is added in the vertex on the geodesic curve path
It closes；
It has traversed on the scanning corona model after all edge points, has deleted all vertex in the segmentation point set, obtain
Obtain two parts region；
It will be deleted with the region of the scanning corona model relative close, obtain the CBCT root models.
4. according to the method described in claim 1, it is characterized in that, using bridging algorithm is preset, to the scanning corona model
Carrying out multistage bridge joint with the CBCT root models includes：
Determine the point correspondence between the scanning corona model upper edge point and CBCT root models upper edge point；
Based on the point correspondence, using Hermite function interpolations, interpolation of the adjacent edge between putting in each bridge section is obtained
Point；
For each bridge section, triangulation processing is carried out to interpolation point and edge point.
5. according to the method described in claim 4, it is characterized in that, determine scanning corona model upper edge point with it is described
Point correspondence between the point of CBCT root models upper edge includes：
Using the proximity pair at the scanning corona model edge and CBCT root models edge as starting point, swept for described
Each edge point on corona model is retouched, finds the edge point in the CBCT root models nearest with it as corresponding points.
6. method according to any one of claims 1-5, which is characterized in that the hole obtained after being bridged to multistage into
After row repairing, before carrying out Mesh smoothing processing, the method further includes：
The position on increased vertex when adjustment repairing hole, so that the grid obtained after adjustment meets specific trellis topology knot
Structure.
7. the device of a kind of corona and fusion of roots, which is characterized in that described device includes：
Registration unit is registrated for that will scan corona model and CBCT tooth models；
Deleting unit, for deleting the abnormal point on the scanning corona model；
Smoothing processing unit, for carrying out smooth edge processing to the scanning corona model after suppressing exception point；
The registration unit is additionally operable to carry out secondary match to treated at smooth edge scanning corona model and CBCT tooth models
It is accurate；
Density processing unit, for after secondary registration scanning corona model and CBCT tooth models in density it is relatively small
Model is handled into line density increase, so that the density contrast of two models is no more than pre-set density difference range；
Removal unit removes the corona part on density treated CBCT tooth models for utilizing geodesic curve split plot design,
Obtain CBCT root models；
Bridge-jointing unit, for using bridging algorithm is preset, being carried out to the scanning corona model and the CBCT root models more
Section bridge joint；
Unit is repaired, the hole for being obtained after being bridged to multistage is repaired；
Fairing unit obtains fusion results for carrying out Mesh smoothing processing.
8. according to the device described in claim 7, which is characterized in that described device further includes：
Adjustment unit, after the hole for being obtained after being bridged to multistage is repaired, before carrying out Mesh smoothing processing,
The position on increased vertex when adjustment repairing hole, so that the grid obtained after adjustment meets specific trellis topological structure.
9. a kind of storage medium, which is characterized in that the storage medium includes the program of storage, wherein run in described program
When control the storage medium where equipment perform claim require 1 to the corona and root of the tooth described in any one of claim 6
The method of fusion.
10. the device of a kind of corona and fusion of roots, which is characterized in that described device includes storage medium and processor；
The processor is adapted for carrying out each instruction；
The storage medium is suitable for storing a plurality of instruction；
Described instruction is suitable for being loaded by the processor and being executed as described in any one of claim 1 to claim 6
The method of corona and fusion of roots.
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111402155A (en) * | 2020-03-10 | 2020-07-10 | 西安科技大学 | Improved crown model edge smoothing processing method based on noise classification and fitting |
| US11026767B1 (en) | 2020-07-23 | 2021-06-08 | Oxilio Ltd | Systems and methods for planning an orthodontic treatment |
| CN112927358A (en) * | 2021-03-10 | 2021-06-08 | 杭州美齐科技有限公司 | Automatic complete tooth reconstruction method based on multi-mode data registration |
| CN113516784A (en) * | 2021-07-27 | 2021-10-19 | 四川九洲电器集团有限责任公司 | Tooth segmentation modeling method and device |
| CN116468848A (en) * | 2023-03-08 | 2023-07-21 | 雅客智慧（北京）科技有限公司 | Three-dimensional tooth model reconstruction method, three-dimensional tooth model reconstruction device, electronic equipment and storage medium |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20050019732A1 (en) * | 2003-07-23 | 2005-01-27 | Orametrix, Inc. | Automatic crown and gingiva detection from three-dimensional virtual model of teeth |
| CN105447908A (en) * | 2015-12-04 | 2016-03-30 | 山东山大华天软件有限公司 | Dentition model generation method based on oral cavity scanning data and CBCT (Cone Beam Computed Tomography) data |
| CN105761252A (en) * | 2016-02-02 | 2016-07-13 | 北京正齐口腔医疗技术有限公司 | Image segmentation method and device |
| CN106327535A (en) * | 2016-08-16 | 2017-01-11 | 苏州迪凯尔医疗科技有限公司 | CBCT tooth root and intraoral scanning dental crown fusion method |
-
2018
- 2018-03-26 CN CN201810252814.2A patent/CN108335318A/en active Pending
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20050019732A1 (en) * | 2003-07-23 | 2005-01-27 | Orametrix, Inc. | Automatic crown and gingiva detection from three-dimensional virtual model of teeth |
| CN105447908A (en) * | 2015-12-04 | 2016-03-30 | 山东山大华天软件有限公司 | Dentition model generation method based on oral cavity scanning data and CBCT (Cone Beam Computed Tomography) data |
| CN105761252A (en) * | 2016-02-02 | 2016-07-13 | 北京正齐口腔医疗技术有限公司 | Image segmentation method and device |
| CN106327535A (en) * | 2016-08-16 | 2017-01-11 | 苏州迪凯尔医疗科技有限公司 | CBCT tooth root and intraoral scanning dental crown fusion method |
Non-Patent Citations (2)
| Title |
|---|
| XIAOMENG WEI 等: "Automatic Mesh Fusion for Dental Crowns and Roots in a Computer-aided Orthodontics System", 《2015 8TH INTERNATIONAL CONFERENCE ON BIOMEDICAL ENGINEERING AND INFORMATICS》 * |
| 赵一姣 等: "一种基于曲率连续算法的冠、根三维数据融合方法", 《北京大学学报（医学版）》 * |
Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111402155A (en) * | 2020-03-10 | 2020-07-10 | 西安科技大学 | Improved crown model edge smoothing processing method based on noise classification and fitting |
| CN111402155B (en) * | 2020-03-10 | 2022-06-21 | 江西都莱美科技有限公司 | Improved crown model edge smoothing processing method based on noise classification and fitting |
| US11026767B1 (en) | 2020-07-23 | 2021-06-08 | Oxilio Ltd | Systems and methods for planning an orthodontic treatment |
| CN112927358A (en) * | 2021-03-10 | 2021-06-08 | 杭州美齐科技有限公司 | Automatic complete tooth reconstruction method based on multi-mode data registration |
| CN113516784A (en) * | 2021-07-27 | 2021-10-19 | 四川九洲电器集团有限责任公司 | Tooth segmentation modeling method and device |
| CN113516784B (en) * | 2021-07-27 | 2023-05-23 | 四川九洲电器集团有限责任公司 | Tooth segmentation modeling method and device |
| CN116468848A (en) * | 2023-03-08 | 2023-07-21 | 雅客智慧（北京）科技有限公司 | Three-dimensional tooth model reconstruction method, three-dimensional tooth model reconstruction device, electronic equipment and storage medium |
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