CN105261062B - A kind of personage's segmentation modeling method - Google Patents

A kind of personage's segmentation modeling method Download PDF

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CN105261062B
CN105261062B CN201510628199.7A CN201510628199A CN105261062B CN 105261062 B CN105261062 B CN 105261062B CN 201510628199 A CN201510628199 A CN 201510628199A CN 105261062 B CN105261062 B CN 105261062B
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personage
head model
model
head
vertex
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CN105261062A (en
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陆佃杰
刘弘
张克
张桂娟
郑向伟
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Shandong Normal University
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Abstract

The present invention relates to a kind of person model method for reconstructing, disclose a kind of personage's segmentation modeling method, including use the cloud data of spatial digitizer acquisition personage's head point, build personage's head model;Personage's head model of structure is pre-processed, pretreated personage's head model is obtained;Method is simplified using the edge contraction based on side curvature and area error to simplify pretreated personage's head model, and carries out the minutia of reservation personage's head model using interactive approach;Obtained personage's head model is matched and merged with the Human torso in trunk database, complete manikin is finally obtained.The method increase the efficiency of modeling, increase the diversity of model, have very high application value in group emulates.

Description

A kind of personage's segmentation modeling method
Technical field
The present invention relates to a kind of modeling method more particularly to a kind of personage's segmentation modeling methods.
Background technology
Computer group animation is because have the characteristics that accurate, intelligence and strong operability, in animation animation, network game Making, traffic administration, crowd evacuation and disaster escape etc. achieve good effect.How three are carried out to true human body It is a significant challenge that current group Animation Simulating faces that dimension, which is modeled and is applied in group animation,.
Traditional Stereo face recognition is usually using structure light or laser scanner, although high-precision individual character can be obtained Change three-dimensional (3 D) manikin, but it is of high cost and complicated for operation.The Kinect device that Microsoft releases utilizes infrared technique, Neng Goushi The fast acquiring of the lower three-dimensional information of existing low cost.This breakthrough has greatly pushed some to use the application of 3-D technology, such as base In the human action identification of Kinect, bone modeling, recognition of face, scene three-dimensional reconstruction etc., all become the research of related field Hot spot.Kinect depth cameras are also often used for as scanner fast in real time with its feature at low cost and easy to operate Personalized three-dimensional (3 D) manikin is built fastly.
But since the model point cloud density of Kinect scannings is too big, the three-dimensional (3 D) manikin by its structure is difficult by widely Using.For example, in crowd simulation scene, since crowd size is huge, it is desirable that human body real-time rendering speed is fast.If directly will The three-dimensional (3 D) manikin of Kinect scannings is applied in group's emulation, the effect that can undoubtedly increase overhead, reduce crowd simulation Rate.Therefore how simplified model and how the minutia of reserving model, and obtain one it is simple and similar to master mould height The model of degree is a meaningful problem.
Invention content
In order to solve the disadvantage that the prior art, the present invention provide a kind of personage's segmentation modeling method.This method is set based on 3D The standby head model for obtaining the realistic personalization of head high-precision, using the edge contraction letter based on side curvature and area error Change method, and interactive mode is used to retain the minutia of head model, then select suitable body model and head mould Type merges automatically, rebuilds a complete person model.
To achieve the above object, the present invention uses following technical scheme:
A kind of personage's segmentation modeling method, including:
Step (1):The cloud data of personage's head point are acquired using spatial digitizer, build personage's head model;
Step (2):Personage's head model of structure is pre-processed, pretreated personage's head model is obtained;
Step (3):Method is simplified using the edge contraction based on side curvature and area error to simplify pretreated personage Head model, and interactive approach is used to carry out the minutia for retaining personage's head model;
Step (4):Personage's head model that step (3) is obtained and the Human torso in trunk database into Row matching and fusion, finally obtain complete manikin.
Pretreated detailed process is in the step (2):
Step (2.1):By on the topology map to figure for building personage's head model, people is removed using the method for graph theory Fragment in object head model obtains personage's head model of removal fragment;
Step (2.2):Judge to whether there is loophole in personage's head model of removal fragment, and if it exists, then using support The Hierarchical Approach of radial basis function repairs personage's head model, the people after being repaired to loophole using Laplace method Object head model is smoothed;
If loophole is not present, personage's head model of no loophole is smoothed using Laplace method.
The detailed process of the step (2.1) is:
Step (2.1.1):By on the topology map to figure for building personage's head model, personage's head model is initialized Topological structure;
Step (2.1.2):Using the extreme saturation method traversing graph G of figure, retain maximum connected graph Gmax
Step (2.1.3):Pass through GmaxPersonage's head model is reconstructed, realizes the removal fragment processing of personage's head model.
Personage's head model is repaired using the Hierarchical Approach of support radial basis function in the step (2.2) Process is:
It obtains several points at random in personage's head model, and obtains the corresponding normal vector of each point simultaneously, by people The surface conversion of object head model is at implicit surfaces;
The surface vertices set of personage's head model is fitted to a parallelepiped, then surface vertices set and The grouping of surface vertices set is recursively sub-divided into the big quadrants such as 8, constructs stratification point set;
Multi-level interpolation is carried out using different Interpolation-Radix-Functions to the stratification point set different levels of structure, is finally realized Recovery to personage's head model.
In the step (2.2) using Laplace method come the process of smoothing processing personage's head model for:
The three-dimensional position on vertex in personage's head model is moved to the position of centre of gravity of surrounding vertex using Laplace method It is dynamic, so that vertex is minimized with surrounding vertex gap;
Personage head is recalculated according to the location information of surrounding vertex for each point on personage's head model The spatial position of respective point to carry out personage's head model smooth on model.
Use in the step (3) process of the minutia of interactive approach reservation personage's head model for:
Step (3.1):According to the set of the reservation regional edge in personage's head model, the collapse cost on non-reserved side is calculated And the average value of non-reserved edge contraction cost;
Step (3.2):Need the average value that the collapse cost on the side retained is equal to non-reserved edge contraction cost average with this The product of the random weight of value, the collapse cost sequence on the side retained as needed, carries out edge contraction operation from small to large.
The collapse cost be equal to personage's head model in reservation region it is non-reserved while while curvature with retain region Middle the sum of the area error deleted behind the non-reserved side of this.
The process that step (4) personage's head model is merged with Human torso is:
Step (4.1):It is determined respective fusion respectively according to the boundary edge of personage's head model and Human torso Region determines personage's head model integration region F1With Human torso integration region F2, and it is respectively mapped to two-dimensional space H1, H2
Step (4.2):By two-dimensional space H1, H2Merge, obtains two-dimensional space Hc;Using FCF methods to two-dimensional space HcIn Each point blend surface F is reconstructedc, obtain the curved surface that personage's head model is merged with Human torso;
Step (4.3):Automatic fusion personage's head is carried out according to the curved surface that personage's head model is merged with Human torso Portion's model and Human torso construct hierarchy manikin.
3D scanners are Kinect 3D scanners in the step (1).
Using FCF methods to two-dimensional space H in the step (4.2)cIn each point blend surface F is reconstructedcMistake Cheng Wei:
First, blend surface F is calculatedcVertex vcRespectively in F1On coordinate v1And in F2On coordinate v2
Then, according to vc=f (s) v1+(1-f(s))v2, obtain blend surface FcVertex vcCoordinate, wherein f (s) tables Show the non-homogeneous spline curve interpolation algorithms of b three times.
Beneficial effects of the present invention are:
(1) present invention obtains the head model of the realistic personalization of head high-precision using 3D equipment, using based on The edge contraction of side curvature and area error simplifies method, and the details spy for effectively remaining model is protected using interactive mode Sign;
(2) maximum difference is the minutia on head between person model, especially in group emulates, on trunk Detailed information seem it is not so important, and to group personage distinguish most apparent position be on head, so this method Using the Method Modeling of head and trunk segmentation based on Kinect, selects suitable body model to be merged with head model, rebuild One complete person model, using FCF fusion methods, the automatic fusion between implementation model can not only simplify operation, and And the efficiency of modeling can also be improved, increase the diversity of model, there is very high application value in group emulates.
Description of the drawings
Fig. 1 is personage's segmentation modeling method flow diagram of the present invention;
Fig. 2 a) it is the personage's head model removed before fragment;
Fig. 2 b) it is the personage's head model removed after fragment;
Fig. 3 a) it is original personage's head model;
Fig. 3 b) it is the personage's head model repaired after loophole;
Fig. 4 a) it is smooth preceding personage's head model;
Fig. 4 b) be it is smooth after personage's head model;
Fig. 5 a) it is side curvature estimation schematic diagram;
Fig. 5 b) it is that area error calculates schematic diagram;
Fig. 6 a) it is 20921 points, original personage's head model of 41261 tri patch;
Fig. 6 b) be simplified rate be 80% personage's head model;
Fig. 6 c) be simplified rate be 90% personage's head model;
Fig. 6 d) be simplified rate be 95% personage's head model;
Fig. 7 a) it is the fusion flow chart that personage's head model is merged with Human torso;
Fig. 7 b) it is improved FCF functions;
Fig. 8 is the syncretizing effect figure that personage's head model is merged with Human torso.
Specific implementation mode
The present invention will be further described with embodiment below in conjunction with the accompanying drawings:
As shown in Figure 1, a kind of personage's segmentation modeling method, including:
Step (1):The cloud data of personage's head point are acquired using spatial digitizer, build personage's head model;
Step (2):Personage's head model of structure is pre-processed, pretreated personage's head model is obtained;
Step (3):Method is simplified using the edge contraction based on side curvature and area error to simplify pretreated personage Head model, and interactive approach is used to carry out the minutia for retaining personage's head model;
Step (4):Personage's head model that step (3) is obtained and the Human torso in trunk database into Row matching and fusion, finally obtain complete manikin.
The manikin for obtaining different accuracy in this way can build stratification human body model data using these manikins Library.Wherein, 3D scanners can select Kinect 3D scanners or other scanners in step (1).Using Kinect as deep Video camera is spent, there is the advantages that easy to operate, easily realization, using flexible, can be good at rebuilding high-precision personage head mould Type.
By taking Kinect 3D scanners as an example:
Kinect 3D scanners are used in step (1), are compiled using C++ on Microsoft Visual Studio platforms Journey acquires head point cloud data.
Step (2) is pretreatment operation, and main purpose is the fragment removed on personage's head model, when repairing data acquires It is possible that the loophole occurred, is smoothed personage's head model.
The detailed process of step (2) includes:
Step (2.1):The fragment on personage's head model is removed, by the topology map of personage's head model to figure On, unnecessary fragment in model is removed using the method for graph theory, process is:
Step (2.1.1):It is leted others have a look at using chart the topological structure of object head model, initializes the topology of personage's head model Structure G={ V, F, L }, V indicate that the point set of personage's head model, F indicate that the set in personage's head model face, L indicate personage's head The set on portion model side;
Step (2.1.2):Using the extreme saturation method traversing graph G of figure, maximum connected graph is to need what is retained to open up Structure is flutterred, it is G to enable maximum connected graphmax
Step (2.1.3):Pass through GmaxPersonage's head model is reconstructed, realizes the operation of removal fragment, such as Fig. 2 a) it is removal Personage's head model before fragment, Fig. 2 b) it is the personage's head model removed after fragment.
Step (2.2):Judge to whether there is loophole in personage's head model of removal fragment, and if it exists, then using support The Hierarchical Approach of radial basis function restores personage's head model, reverts to implicit surface, and reconstruction model is general using drawing Lars method is smoothed personage's head model after loophole reparation;
If loophole is not present, personage's head model of no loophole is smoothed using Laplace method.
The specific implementation that model is restored using the Hierarchical Approach of Compactly supported radial basis function in step (2.2) Cheng Wei:
Assuming that P={ piIt is the N number of scattered points obtained at random in a model, and the corresponding normal direction of each point is obtained simultaneously Measure ni;Threedimensional model surface conversion at Implicitly function be defined as F (x), wherein zero level integrates F (x)=0 as the table of grid model Face, F (x) <Inside 0 region expression model, F (x) >0 region is outside model;
To model surface vertex piDetermine a local orthogonal coordinate system (ui,vi,wi), wherein wiPositive direction and piNormal direction The direction of amount is identical.Define Implicitly function gi(x)=wi-h(ui,vi) approach vertex piThe basic configuration of surrounding small neighbourhood.
Wherein, h (u, v) ≡ Au2+2Buv+CV2Expression approaches vertex p with quadratic surfaceiCircumferential shape, in h (u, v) is Number A, B and C are obtained using least square method, are obtained by solution formula (1).
In formula (1), φσ(r)=(1-r)4+ (4r+1) is Wendaland Compact supports RBF, and r indicates that variable, σ are Support radius.
According to threedimensional model surface mesh vertex set P, threedimensional model surface is turned using basic function RBFs according to formula (2) Turn to implicit surfaces F (x), wherein λiCoefficient in order to control.
Calculate control coefrficient λi.By each vertex piFormula (3) can be obtained by bringing formula (2) into
It can be obtained according to formula (3)
In formula (4), known to right side.Therefore one is can be obtained about λiSparse vectors, can using iterative method To solve the sparse vectors, unknown number λ can getiValue;
The λ i being calculated are brought into formula (2), you can it is hidden to obtain its according to the threedimensional model surface vertices collection P of input Formula toroidal function;
Build stratification point set { PN=P ..., P2,P1}.P is fitted to a parallelepiped first, then it and Its grouping is recursively sub-divided into the big quadrants such as 8.Point set P is polymerize by the parallelepiped based on Octree;For each There are the points inside P for a cell, and by equalizing and normalizing calculating, and a unit normal of P is distributed to barycenter;
Multi-level interpolation.Build stratification point set { PN=P ..., P2,P1After, it is defined first by recursively mode Interpolation-Radix-Function, such as formula (5):
fk(x)=- 1, k=0
(5)
fk(x)=fk-1(x)+ok(x), k=1,2 ..., N
Wherein work as fk(x)=0 interpolation P whenk, ok(x) it is penalty function, calculation formula is (6):
Partial approximation toroidal function giIt (x) can be by PkUsing least square fitting;Weights ciBy solving linear equation GroupIt obtains, c is solved using pretreatment bi-Conjugate Gradient Methodi.Wherein support radius sigmak+1k/ 2, σ1=aL, L are the length of boundary diagonal of a parallelogram, and parameter a makes the octant of bounding box always by a radius sigma1Ball Covering, effect is best when finding a=0.75 in multiple practice.Usually subdivision level n passes through σ0And σ1It determines, and works asWhen can obtain relatively good result.Such as Fig. 3 a) be archetype, Fig. 3 b) it is by Model Reconstruction Design sketch afterwards, it is evident that repaired the loophole of model.
Wherein, model is smoothed using Laplace method.
The three-dimensional position on vertex is moved to the position of centre of gravity of surrounding vertex, vertex is made to be minimized with surrounding vertex gap. The spatial position of the point is recalculated according to the location information of surrounding vertex for each point on model.Laplce is flat Shown in sliding formula such as formula (7):
N is the number of vertices around current point,For the new coordinate on i-th of vertex.Such as Fig. 4 a) be smoothing processing before Model, Fig. 4 b) design sketch that is that treated, it is evident that the smoothing processing to model is realized by the method.
Wherein, in step (3) while the edge contraction of curvature and area error simplify method while curvature and area error calculating Method is as follows:
Such as Fig. 5 a) shown in, the calculation of side curvature is:
Wherein l=&#124;&#124;q-p&#124;&#124;, indicate the distance between point q and point p, hi=d { vi, e }, indicate point viTo the distance of side e, β indicates a coefficient, n1, n2Face (v is indicated respectively1, q, p) and knead dough (v2, p, q) normal vector, α indicate two normal vectors folder Angle.
Such as Fig. 5 b) shown in, the calculation of area error is:
If the angle of triangle rotating is θ, then by deleting error Q caused by a face ttFor:
Qt=lt×θ (9)
Wherein lt=(A1+A2)/2, A1For triangle t=(v0,v1,v2) area, A2For triangle t'=(v, v1,v2) Area.Enable θ=1-ntnt', wherein ntThe normal vector of expression face t, nt′The normal vector of expression face t '.It then deletes caused by the e of side Area error EaFor:
Wherein P is and v0The set of connected all tri patch.
In conclusion the calculation formula of edge contraction cost is formula (11):
E=Ec+Es (11)
Wherein, use in step (3) process of the minutia of interactive approach reservation personage's head model for:
Step (3.1):The collection for making us the reservation regional edge in object head model is combined into P={ ei', wherein i=0,1, 2 ..., c, c indicate the total number for retaining side;Calculate the collapse cost E on non-reserved sidejAnd non-reserved edge contraction cost is averaged ValueWherein j indicates the non-reserved side of j-th strip;N indicates the total number on non-reserved side;
Step (3.2):It enablesWhereinIndicate the collapse cost on the side for needing to retain, (rand ()+0.3) indicates the random weight of E;It is sorted according to collapse cost, carries out edge contraction operation from small to large.
Such as Fig. 6 a) it is archetype, there are 20921 points, 41261 tri patch.Fig. 6 b), Fig. 6 c), Fig. 6 d) and using this The simplification method of the reserving model detail characteristic proposed in invention, remains the minutia of eye and nose.Fig. 6 b) have 3640 points, 7986 tri patch, the rate that simplifies are 80%;Fig. 6 c) there are 1916 points, 3799 tri patch, the rate of simplification is 90%;Fig. 6 d) there are 1014 points, 1995 tri patch, the rate that simplifies is 95%.By Fig. 6 b)~Fig. 6 d) it can be seen that this hair The method of reserving model detail characteristic in bright has been effectively kept the minutia of model.
Model Fusion process such as Fig. 7 a) shown in, the process that step (4) personage's head model is merged with Human torso For:
Step (4.1):It is determined respective fusion respectively according to the boundary edge of personage's head model and Human torso Region determines integration region F1, F2, and it is mapped to two-dimensional space H1, H2
Step (4.2):By H1, H2Merge, obtains Hc;Using FCF methods to HcIn each point blend surface is reconstructed Fc, obtain the curved surface that personage's head model is merged with Human torso;
Step (4.3):Automatic fusion personage's head is carried out according to the curved surface that personage's head model is merged with Human torso Portion's model and Human torso construct hierarchy manikin.
Wherein, HcIncluding two class vertex:One kind is directly by F1, F2The original vertex of coming is inherited, another kind of is to pass through friendship Fork calculates newly-generated point.Such as Fig. 7 b), this method changes the s in non-homogeneous b spline curve interpolation algorithm f (s) three times Into the fusion for Controlling model.
FcVertex vcCoordinate be:
vc=f (s) v1+(1-f(s))v2
Wherein, v1Indicate vcIn F1On coordinate, v2Indicate vcIn F2On coordinate, s=1-l/L, l be point arrive HcLower boundary Distance, L be up-and-down boundary distance.
As shown in figure 8, the automatic fusion between model is realized using the fusion method in the present invention, it will not after fusion The minutia of model is lost, and very smooth after the fusion of primary side circle border region.Fusion method based on boundary edge, model The size of integration region be controllable, the new vertex generated because of fusion is little to the complexity effect of model, can be with It ignores, as there is 3740 points before Fig. 8 Model Fusions, 3934 points after fusion have only generated less than 200 points.The present invention Fusion method will not be excessive change model complexity, the Size estimation before still can making model that it be kept to merge.
Finally, stratification human body model data library is constructed and applied in group's emulation.The people of 600 people can be simulated The scene of group's emergency evacuation in teaching building.Using LOD methods, fine manikin is used when view distance is less than 40 (having 43261 tri patch) (has 3216 triangles when view distance is more than 40 less than 100 using the model of medium accuracy Dough sheet), use coarse model (there are 1046 tri patch) when view distance is more than 100.It is used in scene most multiple Miscellaneous model.It is 22FPS wherein to use the average frame per second of LOD methods, and the frame per second of most complex model is used there was only 7.5FPS.It can See in group emulates structure stratification model library can effective lifting system performance.
Personage's modeling method proposed by the present invention based on the realistic personalizations of Kinect can rebuild high realism Personalized person model, and modeling speed can be improved, increase model diversity.The personage of method reconstruct in through the invention Model not only has the very high sense of reality, but also model complexity is low, the LOD person models built using the method in the present invention Database can effectively improve the efficiency of crowd evacuation.
Above-mentioned, although the foregoing specific embodiments of the present invention is described with reference to the accompanying drawings, not protects model to the present invention The limitation enclosed, those skilled in the art should understand that, based on the technical solutions of the present invention, those skilled in the art are not Need to make the creative labor the various modifications or changes that can be made still within protection scope of the present invention.

Claims (7)

1. a kind of personage's segmentation modeling method, which is characterized in that including:
Step (1):The cloud data of personage's head point are acquired using spatial digitizer, build personage's head model;
Step (2):Personage's head model of structure is pre-processed, pretreated personage's head model is obtained;
Step (3):Method is simplified using the edge contraction based on side curvature and area error to simplify pretreated personage head Model, and using the minutia of interactive approach reservation personage's head model;
Step (4):The personage's head model obtained to step (3) and the Human torso progress in trunk database Match and merge, finally obtains complete manikin;
3D scanners are Kinect 3D scanners in the step (1);
Pretreated detailed process is in the step (2):
Step (2.1):By on the topology map to figure for building personage's head model, personage's head is removed using the method for graph theory Fragment in portion's model obtains personage's head model of removal fragment;
Step (2.2):Judge to whether there is loophole in personage's head model of removal fragment, and if it exists, then radial using support The Hierarchical Approach of basic function repairs personage's head model, personage's head after being repaired to loophole using Laplace method Portion's model is smoothed;
If loophole is not present, personage's head model of no loophole is smoothed using Laplace method;
The detailed process of the step (2.1) is:
Step (2.1.1):By on the topology map to figure for building personage's head model, initialization personage's head model is opened up Flutter structure;
Step (2.1.2):Using the extreme saturation method traversing graph G of figure, retain maximum connected graph Gmax
Step (2.1.3):Pass through GmaxPersonage's head model is reconstructed, realizes the removal fragment processing of personage's head model;
In the step (2.2) using Laplace method come the process of smoothing processing personage's head model for:
The three-dimensional position on vertex in personage's head model is moved to the position of centre of gravity of surrounding vertex using Laplace method, is made Vertex is minimized with surrounding vertex gap;
Personage's head model is recalculated according to the location information of surrounding vertex for each point on personage's head model The spatial position of upper respective point to carry out personage's head model smooth.
2. a kind of personage's segmentation modeling method as described in claim 1, which is characterized in that using branch in the step (2.2) The process repaired to personage's head model of Hierarchical Approach of support radial basis function is:
It obtains several points at random in personage's head model, and obtains the corresponding normal vector of each point simultaneously, by personage's head The surface conversion of portion's model is at implicit surfaces;
The surface vertices set of personage's head model is fitted to a parallelepiped, then surface vertices set and surface The grouping of vertex set is recursively sub-divided into the big quadrants such as 8, constructs stratification point set;
Multi-level interpolation is carried out using different Interpolation-Radix-Functions to the stratification point set different levels of structure, is finally realized to people The recovery of object head model.
3. a kind of personage's segmentation modeling method as described in claim 1, which is characterized in that using interaction in the step (3) The process of minutia that formula method retains personage's head model is:
Step (3.1):According to the set of the reservation regional edge in personage's head model, calculate non-reserved side collapse cost and The average value of non-reserved edge contraction cost;
Step (3.2):The collapse cost on the side retained is needed to be equal to the average value and the average value of non-reserved edge contraction cost The product of random weight, the collapse cost sequence on the side retained as needed, carries out edge contraction operation from small to large.
4. a kind of personage's segmentation modeling method as claimed in claim 3, which is characterized in that the collapse cost is equal to personage's head Reservation region in portion's model it is non-reserved while while curvature with retain the area error after deleting the non-reserved side of this in region The sum of.
5. a kind of personage's segmentation modeling method as described in claim 1, which is characterized in that step (4) personage head mould The process that type is merged with Human torso is:
Step (4.1):It determines respective integration region respectively according to the boundary edge of personage's head model and Human torso, determines Personage's head model integration region F1With Human torso integration region F2, and it is respectively mapped to two-dimensional space H1, H2
Step (4.2):By two-dimensional space H1, H2Merge, obtains two-dimensional space Hc;Using FCF methods by two-dimensional space HcIn it is each A point reconstruct blend surface Fc, obtain the curved surface that personage's head model is merged with Human torso;
Step (4.3):According to the curved surface that personage's head model is merged with Human torso, it is automatic merge personage's head model with Human torso constructs hierarchy manikin.
6. a kind of personage's segmentation modeling method as described in claim 1, which is characterized in that 3D scanners in the step (1) For Kinect 3D scanners.
7. a kind of personage's segmentation modeling method as claimed in claim 6, which is characterized in that use FCF in the step (4.2) Method is to two-dimensional space HcIn each point blend surface F is reconstructedcProcess be:
First, blend surface F is calculatedcVertex vcRespectively in F1On coordinate v1And in F2On coordinate v2
Then, according to vc=f (s) v1+(1-f(s))v2, obtain blend surface FcVertex vcCoordinate, wherein f (s) indicate it is non- Uniform b spline curve interpolations algorithm three times.
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