CN106327506B - A kind of threedimensional model dividing method merged based on probability subregion - Google Patents
A kind of threedimensional model dividing method merged based on probability subregion Download PDFInfo
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Abstract
The invention discloses a kind of threedimensional model dividing methods merged based on probability subregion, it include: that 1) over-segmentation forms a large amount of regions, 2) overdivided region is polymerize, 3) training tandem type classifier, 4) new model is split according to the tandem type classifier, merge adjacent area, obtains segmentation result.It may insure that the boundary of current initial segmentation contains the boundary finally preferably divided by a large amount of region, later, pass through Logic Regression Models, two classifiers of one tandem type of training, with to determine whether being a region by adjacent region merging technique.The theory of method of the invention based on machine learning is split triangle gridding by way of the cohesion of the region of tandem type, needs to select suitable segmentation result according to it.And the validity of the dividing method is demonstrated in the present invention, the present invention is conducive to integration characteristics, and achieves preferable effect for most types of model.
Description
Technical field
The present invention relates to threedimensional model field, in particular to a kind of threedimensional model segmentation side merged based on probability subregion
Method.
Background technique
The rapid development of computer technology creates the digital world for being opposed to real world.In this virtual generation
In boundary, by computer graphics (Computer Graphics, CG) technology, it can create as real world is even super
The marvellous scene of real world out.In such virtual world, threedimensional model occupies very important position.Threedimensional model is protected
The geological information of object in real world is stayed, and by load illumination, material, the attributes such as texture can construct true to nature later
Virtual effect.In recent years, with the development of dimensional Modeling Technology and universal, the acquisition threedimensional model of spatial digitizer
Mode compared with there is obvious development between one's early years.It can be scanned from actual model by spatial digitizer and computer vision technique
Point cloud data is obtained, by point Yun Chongjian, details post-treating and other steps obtain complete three-dimensional grid model.These are by polygon
The threedimensional model of dough sheet composition has excellent performance compared with surface model in model manufacturing, graphical display, model transformation etc.,
To at CAD (CAD), three-dimensional animation, geometric modeling is played extensively in the various works such as medical image
Effect.
With the data retrieval capabilities of growth and the application demand of growth, the processing technique of threedimensional model is allowed to become day
Gradually important research topic, including compression, divide, parametrization, and distortion of the mesh identifies, simplifies, texture mapping, denoises, and repair,
Retrieval etc..Wherein, being split to threedimensional model is a basic and important problem.Threedimensional model is divided into significant
It part can be to modeling, texture mapping, distortion of the mesh, a series of more development spaces of applications offers such as retrieval.For example, to picture
When being analyzed, picture can be usually split, and assign the information of different piece semantically, thus existed to picture
Geometric position, color are added to the prior information in many external world except texture, when in face of the task as identifying,
It can carry out more rapidly, it is more acurrate, and more complicated advanced processing.Similarly, only whole to threedimensional model for three-dimensional grid
Body is analyzed, and local information is inherently lost；And more and more application requirements carry out the part of threedimensional model
Processing, so the segmentation work to threedimensional model while in basic status but has important role.
The type of three-dimensional (3D) model is more, wherein popular is three-dimensional grid model.Three-dimensional grid model is come
It says, they are generally by triangle, quadrangle or polygon composition.Such grid configuration flexibility ratio is very high, and analogy
Line segment in X-Y scheme can approximately approach arbitrary curve, and three-dimensional grid model can also be approached all kinds of with arbitrary accuracy
Curved surface, the threedimensional model being made of them can accurately indicate sufficiently complex object very much, and in processing, by institute
Surface is polygon, can take compared to the more simple method of analytic surface, give the property that grid model is very outstanding
Matter.In these grid models, triangle gridding (Triangular Mesh) is wherein very important one kind, his surface again
All by triangular at the property on each surface is similar, is handled more easily, and for other grid models, more
Side shape can be converted to triangle, so being most basic problem to the processing of triangle gridding.In recent years to triangle gridding
Dividing method is substantially using an overall situation function, is that the point of triangle gridding or face calculate a metric, in this, as point
Cut foundation.But these algorithms by overall situation function performance due to being influenced accordingly, when functional value can not sentence model
Can not effectively it be divided when other.
Summary of the invention
The technical problem to be solved by the present invention is to propose a kind of partitioning algorithm of learning type, by extracting the triangulation network
The feature of lattice, study are split triangle gridding to suitable model.
Solve above-mentioned technical problem, the present invention provides it is a kind of based on probability subregion merge threedimensional model dividing method,
Include: that 1) over-segmentation forms a large amount of regions, 1-1) according to the triangle grid model in threedimensional model, establish figure G (V, E), wherein
V is vertex, E is side, Dist (Vi,Vj) be E on length；Dist (the V 1-2) is obtained based on weight calculationi,Vj) away from
From obtaining the adjacent triangular facet (V of every a pairi,Vj) distance；Two non-conterminous triangles 1-3) are obtained according to shortest distance algorithm
The distance in face is clustered, and a large amount of regions of over-segmentation are obtained；2) a large amount of regions are polymerize, 2-1) described a large amount of
Region is obtained in the threedimensional model in region to (p, q)；It is 2-2) similar to being obtained between (p, q) by feature vector in each region
Degree；2-3) judge whether to need to merge the region to (p, q) by establishing probabilistic model；2-4) for the probability
Model is trained band weighted regression model by all features therein to combining；3) training tandem type classifier, 3-1)
Based on machine and artificial segmenting edge, establishes boundary and recall function；3-2) according to the weight to punish the region of mistake polymerization
Value and the boundary recall function and carry out tandem type training, obtain a tandem type classifier；4) classified according to the tandem type
Device is split new model, merges adjacent area, obtains segmentation result.
Further, described
Wherein,α indicates the dihedral angle in two faces,It is defined as two faces
To the sum of the distance at the midpoint for sharing side, a, b are that weight is used to guarantee Dist (V at centeri,Vj) between [0,1].
Further, weight a, b establish the objective function of regression model as follows:
Wherein,All adjacent triangular facets are defined as to for P1,P2,...Pn,PiDistance,It is not same district
The probability in domain.
Further, the distance of two non-conterminous triangular facets is obtained according to shortest distance algorithm specifically:
Further, the cluster is K-Means clustering algorithm.
Further, the probabilistic model are as follows:
Wherein, the parameter for the linear logic regression model that ω is, φ p, q (I, R) indicate feature vector, for a three-dimensional
Model Ii, it is classified as kiA region, regional ensemble are denoted as Ri={ Ri,1,Ri,2,…Ri,ki, if N (Ri) for the institute of this model
There is adjacent region, each region is to (p, q) ∈ N (Ri) all by feature vector φ p, q (an Ii,Ri) composition.
Further, the region pair of maximum probability is polymerize in the probabilistic model, until current model IiIn no longer
There are Pg (p, q；Ii, Ri) > 0.5 region.
Further, it when training band weighted regression model, corrects mistake to obtain optimal solution by modification logarithm loss function,
The logarithm loss function are as follows:
Wherein, ε is used to avoid the occurrence of to bear infinite situation, and α indicates the weighted value to punish the region of mistake polymerization, L
Indicate the length at the edge of erasing.
Further, it establishes boundary and recalls function to α progress binary chop, function is recalled on the boundary are as follows:
Wherein,It indicates for manually dividing GiAll segmenting edges；It indicates to divide S for machineiAll points
Cut edge edge.
Further, described eigenvector include: spin image, shape diameter function, curvature, the concave-convex value in region and
Area attribute feature.
Beneficial effects of the present invention:
1) first by being a large amount of tri patch set (i.e. region) by triangulation, and assume that these are different
Region, which belongs to, should belong to different significant parts, and a large amount of region may insure that the boundary of current initial segmentation includes
The boundary finally preferably divided.Later, pass through Logic Regression Models, two classifiers of one tandem type of training, for sentencing
Whether disconnected be a region by adjacent region merging technique.By constantly merging these small regions, one can be obtained to entirety
The segmentation of model.The 3 d model library of Princeton University's offer is used in the present invention, wherein including 380 three-dimensional moulds
Type, these models share 19 seed types (people, bird, fish etc.), and the model in each type includes various postures.Experimental result
It confirms that the algorithm in the present invention can be obtained effectively to be split model.
2) dividing method in the present invention is made of the probabilistic model of a tandem type, this model is substantially a multilayer
Linear classifier, can be predicted whether in each layer of probabilistic model by adjacent region to merging into a region.In
When training, this model is successively trained in sequence, and the merging of mistake is punished by the suitable weight of dichotomy Automatic-searching.
When new threedimensional model needs to divide, the multilayered model trained can be used, it is handled.Firstly, this three-dimensional mould
Type is broken down into a large amount of region, and later, these regions gradually are merged to obtain by these regions according to this multilayered model
Final segmentation result.When obtaining result, user can check the segmentation result in each stage and select according to its needs
Suitable segmentation result.
3) the threedimensional model dividing method merged the present invention is based on probability subregion is verified by experiment, substantially can
It realizes segmentation to model, and when facing geometrical characteristic explicit model type, can be good at completing task, and for
Artificial segmentation has certain complexity, and when geometrical characteristic has the model of certain deviation, can accurately complete to divide substantially, only
There is seldom mistake.
Detailed description of the invention
Fig. 1 is that one of one embodiment of the invention is shown based on the threedimensional model dividing method process that probability subregion merges
It is intended to.
Fig. 2 (a)-Fig. 2 (d) is using the threedimensional model dividing method merged based on probability subregion in the present invention to more
A CAD model segmentation result schematic diagram.
Fig. 3 (a)-Fig. 3 (c) is using the threedimensional model dividing method merged based on probability subregion in the present invention to not
With spider model segmentation result schematic diagram.
Fig. 4 (a)-Fig. 4 (c) is using the threedimensional model dividing method merged based on probability subregion in the present invention to more
The segmentation result schematic diagram of a chair model.
Specific embodiment
To make the objectives, technical solutions, and advantages of the present invention clearer, below in conjunction with specific embodiment, and reference
Attached drawing, the present invention is described in more detail.
Fig. 1 is the threedimensional model dividing method process signal that one of one embodiment of the invention is merged based on probability subregion
Figure.
The threedimensional model dividing method that one of the present embodiment is merged based on probability subregion, comprising:
Step S1 over-segmentation forms a large amount of regions, and step S11 establishes figure G according to the triangle grid model in threedimensional model
(V, E), wherein V is vertex, E is side, Dist (Vi,Vj) be E on length；Step S12 is obtained described based on weight calculation
Dist(Vi,Vj) distance, obtain the adjacent triangular facet (V of every a pairi,Vj) distance；Step S13 is obtained according to shortest distance algorithm
Distance to two non-conterminous triangular facets is clustered, and overdivided region is obtained；Step 2 gathers the overdivided region
It closes, step S21 obtains region to (p, q) in the threedimensional model of the overdivided region；Step S22 is in each region pair
Similarity is obtained by feature vector between (p, q)；Step S23 judges whether to need the region pair by establishing probabilistic model
(p, q) is merged；Step S24 is trained cum rights by all features therein to combining for the probabilistic model
Regression model；Step S3 trains tandem type classifier, and step S31 is based on machine and artificial segmenting edge, establishes boundary and recall letter
Number；Step S32 recalls function progress tandem type training according to the weighted value for punishing the region of mistake polymerization and the boundary,
Obtain a tandem type classifier；Step S4 is split new model according to the tandem type classifier, merges adjacent region
Domain obtains segmentation result.
The principle of the present invention:
It is not a new problem that threedimensional model, which is divided into significant part,.Since the part of " significant " is to be directed to
For people, such explanation was made in terms of psychophysics: the mankind, can be to a certain extent to object when identifying shape
It is split, a complicated object can be divided into the combination of several simple objects.As a result, Hoffman etc. in 1984 once
Itd is proposed that the boundary line of element is often the minimal negative line of curvature in mankind's cognitive process, the curvature by obtaining model can be with
Realize significant segmentation.But since curvature algorithm is different, and due to various noises, lead to the segmentation result of same algorithm
There is larger difference.
The expression of 2.1 threedimensional models
Threedimensional model format has much currently popular, such as OBJ, OFF, PLY, STL etc..It is more identical to be, they
Substantially all by description point, line, face, the information such as normal create model.Three-dimensional seat a little is generally comprised in most basic model
It marks (x, y, z), dough sheet information (call number by forming the millet cake is constituted).It can completely be constructed by the two essential informations whole
A threedimensional model.Although different models can include identical information, their organizational form is slightly different.It is described below
Format OFF used herein:
OFF file is to indicate the simplest ascii text file of model, only includes the geological information of object, this and our algorithms
Target meet (our segmentation is based only upon geometrical characteristic).Each OFF file the first row is with the starting of OFF keyword, the second row
Fixed-point number a comprising model, dough sheet number b, centre is using space as separator.From the third line start recording apex coordinate, x is sat
Mark, y-coordinate, z coordinate.After having recorded vertex information, the information in start recording face.Every a line is started with the number of vertex in the face,
Triangle gridding is used in our work, therefore with 3 beginnings.The index value of separator point is done with space later (from 0 starting)
Record all the points in this face.It is worth noting that remaining point needs to look over according to outside model since any point
Sequence counterclockwise is recorded, and just can guarantee that the normal in all faces is directed to outside model in this way.
The segmentation definition of 2.2 three-dimensional grids
The segmentation of three-dimensional grid refers to is according to Attribute decompositions such as the geometry of its grid, topology, textures by polyhedron grid
Some Limited Numbers, the sub-grid each communicated with.If being defined as follows to the segmentation of Mr. Yu's original mesh S, S:
Assuming that S points are m sub- partitioning portions, it is denoted as S1, S2... Sm；All faces set of S is denoted as F { S } then their needs
Meet the following conditions:
1.
2.SkIt is connection；
3.
4.
Meet the geometry segmentation of conditions above, various pieces connection, and each part meets in human vision intentionally
The requirement of justice.
2.3 domestic and international research achievements
In the field computer graphics (Computer Graphics), mesh segmentation is always a very active research
Direction.Most algorithms are devoted to searching one and are split single grid based on geometric standard.
Early in 1991, Vincent et al. handled three using dividing ridge method (watershed segmentation)
The problem of dimension module is divided, but this dividing method the case where it is easy to appear over-segmentations, and there are sawtooth at edge；1995
Year, Herbert et al. divides threedimensional model using the region growing algorithm in image segmentation, is that the segmentation of three-dimensional grid is expanded
New thinking, to be modified followed by Many researchers using the frame that region increases realize new algorithm, such as
The algorithm that Vladislav et al. is proposed for the concavity and convexity of component；Simultaneously because to be usually present edge not smart for automatic segmentation algorithm
Really, segmentation object interrogatory is true, the problems such as over-segmentation, 1996, Krishnamurthy et al. have also been proposed by interaction come
It is split, it is artificial to participate in that segmenting edge be made more smooth, and comply fully with the judgment criteria of human vision.1997
Year, distribution form of the Wu et al. by simulation electric field on surface mesh has carried out segmentation 2000 based on physical significance,
Rossl et al. is by segmentation skeleton to achieve the purpose that parted pattern 2002, and Werghi et al. is by identification posture, according to people
Body local shape is divided；2004, G Lavoue et al. proposed the method for CAD model, and this method is by dividing
Analysis contravariant tensor has obtained multiple continuous cut zone.In the segmentation of three-dimensional grid model, the category of segmenting edge is studied
Property is a difficult point.Tsuzuki et al. proposed a kind of method in 2005, by comparing adjacent triangular facet dihedral angle and triangular facet
Piece distance is automatically completed the segmentation of three-dimensional grid model.Equally in 2005, the propositions such as Sage Katz use fuzzy clustering
The method successively divided, this method can preferably avoid over-segmentation and sawtooth border issue.2008, Yu-Kun
Lai etc. has been obtained a kind of quick and has efficiently been divided by the method for random walk (Random Walk) in expanded images segmentation
Segmentation method, this method is affected by noise smaller, and provides Interactive Segmentation and the mode divided automatically.The same year, Lior
Shapira et al. is by shape diameter function, by three-D volumes information MAP to model surface, has obtained preferable automatic segmentation
As a result.2009, various features before were organized under a learning framework by Evangelos et al. use condition random field,
Algorithm based on machine learning can be directed to wider situation, and for new validity feature, such learning framework can
Changed with being updated to expand the segmentation ability of its script.
Algorithm in the present invention is also influenced by learning framework, is designed single function and is had office to be always split
It is sex-limited, but the shortcomings that single measurement is brought can be made up by designing a segmentation framework based on machine learning, use a variety of degree
Amount makes up mutually.It is determined how in a manner of study suitably using a variety of measurements, and by the such multilayer of Adaboost
Learning framework influence, it is intended that be allowed to finally be known as effective classifier by combining weaker classifier, in this way
Thinking be verified in Viola-Jones recognition of face classifier.And it is desirable that our frame can more hold
The more features of easy integration, or even texture, the information such as color are added.
3.1 algorithm frame
Existing algorithm is directed to a certain measurement mostly and analyzes entire model, determines boundary with the value of measurement.
A kind of method of study is desirable in the present invention, to integrate the advantages of various suitable measurements are to absorb these measurements.In
In two dimensional image segmentation, there is a kind of technology to be known as super-pixel (Super Pixel).For a width picture, super-pixel algorithm will be gathered around
There is similar color, the pixel of position, the information such as texture flocks together, so that processing, analysis picture is more acurrate quick.In recent years
It is technology as SLIC come more welcome super-pixel algorithm, the adjacent a small amount of triangular facet of feature analogous location is polymerize
To facilitate subsequent processing.First, it is intended that by a model decomposition at a large amount of region.Later, for having decomposed
Model, it is intended that can these regions of merging gradually, to form our final segmentations.In order to polymerize these regions, very
Naturally we need for be regarded as in two adjacent regions the basic unit that may potentially polymerize.In the mistake for forming a large amount of regions
Cheng Zhong, each threedimensional model are actually the state for being in over-segmentation, and the triangular facet that each region is included is considerably less.And
In our final desired segmentation results, each significant part can include a large amount of triangular facet.One apparent
Problem is that it is final desired that the model one-step polymerization for initially possessing a large amount of regions directly can not be become us by a classifier
Segmentation, because their changing features are too violent for adjacent region, after our combined region, this phase
The feature distribution that feature distribution between neighbouring region is faced when being trained to different from classifier.By tandem type classifier
Inspiration, the present invention determine use a tandem type mode, gradually region is carried out using the different classifier of multilayer parameter
Merge.We will introduce " super-pixel " how formed in three dimensions first.
3.2 regions are formed
It is described below and how to form a large amount of region.For a triangle grid model S, we are considered as a figure G
Triangular facet f ∈ F { S } is considered as the vertex V in figure by (V, E), and the similarity between triangular facet, i.e. distance definition are the length of side E
Degree.The definition of length on the E of each side:
Wherein, α indicates the dihedral angle (dihedral angle) in two faces；It is defined as the center in two faces
To the sum of the distance at the midpoint on shared side, weight a, b are used to guarantee Dist (Vi,Vj) between [0,1].Next problem
It is how to obtain suitable a, b makes the measurement of distance can be very good reaction truth.We are fitted by training
Obtain a, the value of b.
3.2.1 distance training
Our Dist (Vi,Vj) value between [0,1], it can be considered as triangular facet (V by wei,Vj) belong to not
With the probability in region.Mention before for each triangle gridding we possess it is several manually divide as a result, being tied by this
Fruit it is recognised that people for triangular facet (Vi,Vj) whether should belong to the judgement that the same region is made,
It is desirable that our algorithm can learn the mark mode of the mankind, completed with this to Dist (Vi,Vj) determine
Justice.In model library, n model S is arbitrarily obtained1,S2,S3...Sn, obtain the adjacent triangular facet of the every a pair of these models.For
The adjacent triangular facet of every a pair, whether we can belong to the same region for the two triangular facets by people.If there is k people
To adjacent surface (Vi,Vj) it is made that judgement.Definition:
P_diff(Vi,Vj) illustrate that people thinks adjacent surface (Vi,Vj) adhere to the probability of different zones separately.Our sample is just
It is to randomly select all adjacent triangular facets pair in model.By a simple Logic Regression Models, we are available most
Suitable a, b weight.All adjacent triangular facets are defined to for P1,P2,...Pn,Pi, distance beBelong to different zones
Probability beThe objective function of regression model are as follows:
This function and the cost function for being log probability in logistic regression, this function be it is convex, for such
Function, gradient descent method can be used to carry out the solution of maximum value in we.We can arbitrarily set an initial parameter
After the value for calculating J (a, b) every time current gradient value can be calculated, to this gradient multiplied by certain step in value
It is long, and go to update the value of J (a, b), in this way after once iterating, the value of J (a, b) can change towards gradient direction, pass through
It repeatedly iterates, when the value of updated J (a, b) and the value of original J (a, b) are kept approximately constant, it is believed that iterate at this time
Reach convergence state, the value of parameter a, b at this time are exactly final optimum results.After a optimized, b value, we can
(V is calculatedi,Vj) distance.Gradient descent method is summarised in algorithm 1 by we:
3.2.2 dough sheet clusters
We have the distance of the adjacent triangular facet of every a pair now.Next we define two non-conterminous triangular facets
Distance:
Using shortest distance algorithm, can obtain in a model, the distance in any two face.Obtaining these data
In the case of, the cluster for carrying out dough sheet can be started.A large amount of region is formed based on the clustering algorithm of K-Means using one to make
For the initial part of subsequent algorithm.Since initial center of the K-Means algorithm to cluster is more sensitive, so using triangular facet
Area obtains the initial cluster center on model by Monte Carlo as weight.Since we are actually less concerned about this
The available accuracy clustered a bit only desires to obtain many region, the state in over-segmentation is allowed to, so by cluster
Quantity is set to 2000.More number of clusters are also possible, but the rank that corresponding calculation amount will increase, and assemble later
Section is also more.2000 clusters can play ideal result in our experiment.
The merging algorithm of 3.3 greed
Now, for a threedimensional model Ii, we are classified as kiA region, regional ensemble are denoted as Ri={ Ri,1,
Ri,2,…Ri,ki, if N (Ri) be this model all adjacent regions.Each region is to (p, q) ∈ N (Ri) all by one
A feature vector φ p, q (Ii,Ri) composition.This feature vector illustrates the similarity between each region pair, according to this spy
Vector is levied to determine whether to merge in the two regions.
Region is combined (p, q) using a probabilistic model to represent whether by we:
Wherein, the parameter for the linear logic regression model that w is.(and the dimension of feature vector φ p, q (I, R) are identical) if
Pg(p,q；I, R) value be greater than 0.5, then Ri, p, Ri, q have bigger possibility to condense together.It is being previously mentioned, will use
Multistage model carrys out gradually combined region.In each stage, it would be desirable to merge a certain number of regions.
It is possible that one-time calculation, which goes out institute combined region in need, but such may cause merging process and do not connect
It is continuous, and need to obtain final merging process by a complicated optimization process.So relatively simple using one
Mode: the region pair of greedy polymerization maximum probability, until current model IiIn no longer there is Pg (p, q；Ii, Ri) > 0.5
Region.A bit for needing to illustrate, after we are to zone of convergency Rp and Rq, we will not be considered further that within a stage.
Using the new region that the two regions are combined into as the object (because their feature has changed) of combined region.
The region pair for merging maximum probability is continued to search in remaining all areas pair.Because very coarse being separated from one
Begin, in the middle the region very more comprising quantity, it can be ensured that we still can effectively be divided after combined region.In
After the merging in one stage, model I has a new area distribution.This new area distribution will be used as next stage
Initial input carry out the merging of next step.Algorithm is summarised in algorithm 2 by we:
3.4 training band weighted regression models
We indicate Pg (p, q using linear model；I,R).Meanwhile the result that possessor's work point is cut.Due to not giving this
Some true any classification informations of segmentation result, they are merely representative of two regions to whether belonging to a part.Utilize these
The data of true segmentation can add label to Ν (Ri).For arbitrary people work segmentation result Gi, Ri, p are labeled as
With the maximum label in the overlapping region Gi.Next, for any one region to Ri, p and PRi, q, if their label is
It is identical, then we defineOtherwiseIt will be used to the model I of training1,I2,…INIn region pair spy
Seek peace their label combines, we obtain { < φi,yi>}.It, can be by their all features pair for all models
It combines, is trained using these samples.
In general, logistic regression, which is commonly used, minimizes logarithm loss to be trained, but in the present case simply
Good effect cannot be but obtained using logarithm loss, because this loss function can symmetrically punish that two kinds of mistakes (obtain
Biggish calculated value), excessively and underestimate the size of Pg, for 2000 regions, only very least a portion of region in them
0.5 is less than to the value of Pg, other most of regions are to should be put together.We pass through modification logarithm loss function
To correct mistake: for mistake the region pair being aggregating item we factor alpha is multiplied by before loss.Further, I
Be also multiplied by before loss function erasing edge length L.It is multiplied by this scale and is used to reflect the merging longer region in boundary
The region that should bear shorter than boundary is more punished.It is as follows that we define loss function:
Wherein, ε is the value of a very little, bears infinite situation for avoiding the occurrence of.This loss function is still convex,
So common gradient descent method can be used to obtain optimal solution.In the training process, there are one critically important parameter alphas.
Select a suitable α very crucial to final prediction.Derive from such idea to the selection of α: the effect of α is punishment mistake
The region of polymerization, value is bigger, and for the region quantity merged in entire merging process with regard to smaller, classifier tends to nonjoinder area
Domain, but we simultaneously but want to the combined region as much as possible under conditions of not wrong combined region.Then this
Function (Boundary Recall) is recalled with regard to inspiring us to define a boundary, he is capable of detecting when under current cutting state
With the similarity of true segmentation, we can be by this similarity function come to α progress binary chop in this way.Recall letter in boundary
Number (Boundary Recall) should in this way before being searched, first be calculated and do not close in the current generation as α is incremented by
And value r is recalled on boundary before.During finding α, it is intended that the back boundary of this stage merging is recalled value and is not less than
r-p；The model for being used to training is randomly divided into two parts, I by ustrainAnd Itrue。
A biggish number is first arranged in we, and to guarantee the value of α between, next we are carried out using dichotomy
It searches.When determining α, we use ItrainIt trains to obtain the parameter of current linear model, next uses ItrueVerify ours
Boundary recalls whether value meets the requirements.In this way by repeatedly searching, suitable α value can be chosen.
3.5 cascade models are trained and function is recalled on boundary
A upper section is mentioned, and it is critically important for selection α that function is recalled on boundary.We define boundary in this way and recall function:
Wherein,It indicates for manually dividing GiAll segmenting edges；It indicates to divide S for machineiAll points
Cut edge edge；If for a certain GiIn segmenting edge, can be in SiIn find and it distance be less than ε segmenting edge, Wo Menke
It to think that this segmenting edge can be detected, and is recorded, finally counts GiIn ratio shared by the edge that is detected
Example, and be averaged available boundary in all models and recall value.
After having boundary to recall function, in conjunction with binary chop, we can find suitable in a stage for classifier
Parameter.But when being trained with the loss function of such cum rights, in general polymerization can stopped very early, in this way
It can be left the region not polymerizeing largely.Reason is to have used the strategy of a kind of very " careful " when setting α, as far as possible
The zone of convergency for avoiding mistake, also inevitably leading to some regions that should polymerize in this way, there is no polymerize.Then polymerization process, but
Be feature between current region pair can not be further continued for using.There is merging between region, formd new region,
It thus needs to extract feature again in new region.And it is of note that feature invalid between zonule, or
Perhaps it can be played a role in large area.It extracts feature over larger areas again in this way, and is carried out with identical step
Training, polymerization obtains bigger region again, but such polymerization can still stop.Then continue to train third classifier,
And so on.
In fact, the process of such a cascade classifier of training and other cascade classifiers be it is much like, than
Such as in Viola-Jones face detector or Adaboost.The difference is that during tandem type training,
Function, the parameter value that algorithm can automatically be optimized are recalled by weight α and boundary, rather than passes through and manually adjusts threshold
Value, this advantage also help our algorithm that can train the number of plies more deeper classifier.For as Adaboost
Tandem type classifier, the trained number of plies the deep more Weak Classifier group can be combined into strong classifier.
This algorithm can effectively use training sample, in each stage, ItrainAnd ItrueIntersection is sky, in this way can be with
Avoid the case where over-fitting occur when selecting α to greatest extent.Also, we adopt the two subsets in each stage
Sample is all completely independent, so can have to data in the feature that each stage is extracted to a more healthy and stronger prediction.And
And after training has carried out some stages, since region quantity has greatly reduced, even if the mould that we choose in sampling
Type is similar in the last stage therewith, and due to the variation significantly of feature, the risk for over-fitting occur also can be reduced accordingly.
The region merging technique of 3.6 tandem types
After training the classifier of a tandem type according to the method described before, so that it may with it come to new
Model is split.When a new model needs to divide, it is broken down into tandem type area after a large amount of region is used as first
The initial segmentation that domain merges.Later, it is only necessary to which a stage for needing to be split is set.In each stage, according to before
The model learnt has some regions that will be merged, the result that next stage will use a upper phase zone to merge as
Input.It so goes on, will eventually get a reasonable segmentation result.
4.1 data set
Possess numerous data sets different from image segmentation, without suitable 3 d model library, is more dividing a few years ago
Cutting work all is that some threedimensional models are carried out.In 2009, Princeton University issued their 3 d model library,
Possess 380 models, and each model has carried out manual segmentation by several volunteers.We using these manual segmentations as
The target that we learn, to each model, we take the average value of volunteer's manual segmentation as two triangular facets whether
Belong to the measurement of the same area.In this way, this measurement can be normalized to the value of [0,1], and can be regarded as the two three
Edged surface belongs to the probability of the same area.While the publication of this model library, some measurement threedimensional model segmentation knots are also disclosed
The standard of fruit.
4.2 local feature description
Above, it repeatedly mentions, during cascading training, it will extract the feature between region.These features
The geometrical property in the region pair based on place.The extraction of geometrical characteristic can be directly related to whether our segmentations succeed, because
Each stage, trained classifier are a relatively simple linear classifier, and the classification capacity of itself is limited, if
The feature of extraction cannot explicitly show the difference between region, then it is likely used only to current task is exactly linearly inseparable
, it is desirable that feature between extended area pair can be enriched to obtain as far as possible.It is worth noting that due to using a letter
Single linear classifier, it is desirable to be supplemented in classifier and newly be characterized in very easily, not needing the algorithm frame to us
Make any change, it is only necessary to new feature and calculation be added at feature extracting.But there is no selections to add
Enter excessive feature, it is desirable to classified with some features as efficient as possible, such processing speed faster, and due to making
It is the classifier of the tandem type of a multilayer, to the classifying quality of each layer of classifier, there is no very high requirement (phases
For single-layer model).
The feature used is more based on local message, so some global characteristics that entire model is described
Description is not applicable in our algorithm.For description of model, more research work are directed to model index
Work.In recent years, with the development of model index, researcher proposes new problem, it is how special according to some in model library
Fixed component carrys out search model.Then, a large amount of local feature description's algorithm is suggested.It is known as spinning present invention uses one kind
The character representation method of image.Spin image is a kind of simple and healthy and strong local shape factor algorithm.Spin image (Spin
Image idea) is in fact very simple, the vertex of normal vector is had for one, by the way that the point in model is projected the top
The profile of this vertex surrounding vertex is sketched the contours of in point tangent plane.The size of adjustable tangent plane adjusts.
Spin image, to obtain the local feature description of smaller area or large area.Positioned at the vertex of different location, such as
Our spin image size of fruit is suitable, can obtain apparent profile difference.It should be noted that in different models
More similar spin image may also can be obtained, this shows two different models, their local geometric features may also
It is similar.In our experiment, for model It, its prime area isi,1,Ri,2...,Ri,n, we are by the center in region
Sampled point of the position as free image, in this way each model can obtain n (n=2000 in our experiment) spin figures
Picture, these spin images reflect the local geometric features of corresponding region.For our model library, possess 380 moulds altogether
Type, entire model library meeting let us obtain 380*2000=7.6*105A spin image.For these images that spin, we will
They cluster, and the number of cluster is set as 1500, although this is an empirical numerical value, in some experiments
Show that such cluster number can suitably represent these free images.After cluster, we can assign certainly to region
Revolve the feature of image.We have the spin image of 1500 types at present, are labeled as T1,T2,...,T1500, then for every
Each region of one model can construct the feature of one 1500 dimension, Feature (t to them1,t1,...t1500), ti
Value be the region include TiThe number of the spin image of seed type, for a region pair, we can compare they itself
The similitude of Feature.When merging two regions, when more new feature, it is only necessary to simply by theirs
Feature stacks up.Such structure can analogize to the bag of words in text analyzing, for the description class in a region
Like the description for a paragraph, the feature in region is exactly the quantity for the spin image type for including in this region, such as same
The feature of a paragraph is just included in the quantity of the keyword in this paragraph.
4.22 shape diameter functions (Shape Diameter Function)
Shape diameter function is the mode that another describes three-dimensional grid local feature.Shape diameter function (SDF) is directed to
A point on three-dimensional grid model is calculated, can be so fine that be projected as one by the three-dimensional shape information in space locating for the shop
A characteristic value is projected on two-dimensional surface the description of threedimensional model volume.Assuming that P is a point on three-dimensional grid,
We do a cone along this normal direction, and the corner angle of cone is variable element.It is worth noting that circular cone
The apex angle of body has apparent influence to the value of SDF, too sensitive to local feature if the value at angle is too small, if apex angle value is too
Greatly, such as 180 ° very close, the SDF value being calculated in this way can not can show well because of excessive noise and mistake
It is most important to choose a suitable angle for local feature.In our experiment, our unified apex angles of choosing are 120 °, this
The SDF value that sample can guarantee can effectively reflect the geometrical characteristic of current triangular facet.We can be on this cone
Sampling obtains some rays, these rays are extended, and allows them to pass through inside grid and intersects until with the grid other end, we
The Euclidean distance for recording these rays and grid intersection point is averaged the SDF value that can be obtained by point P.Further, Wo Menke
It is normalized with all SDF values to model I, normalized value is defined as:
Wherein,It is the SDF value that each in model is put, α is a normalized parameter, in our reality
α=4 are all used in testing.
We extract the center of gravity of all triangular facets, and to their SDF value of each center of gravity calculation and conduct is normalized
The characteristic attribute of each triangular facet.When operating to region, we can be by SDF value that the region is included to count
The form of histogram shows.We set 50 sections, and normalized SDF value is likely to be in these sections, for an area
Domain, we can count the SDF value for the triangular facet that this region includes.Between region pair, we can be according to two regions
SDF Data-Statistics histogram carry out similarity system design.Combined region to when, operation is also very simple, we only need
Again statistics is to obtain the SDF Data-Statistics histogram of new region.
4.2.3 curvature (curvature)
It is having been previously mentioned, the cognition of people is based on using the minimal negative line of curvature as the boundary line of segmentation.This result
Inspire us by curvature to adding some features between region pair.Negative cruvature line is a useful feature, is frequently located in two
Exceedingly band among a convex part.And for most of objects, convex part, which often represents one, to be had and cannot continue
A possibility that entirety of segmentation, excessive position is divided there are meaning between the two parts, is very big.In addition to this, for vertex
Curvature, there are also another metric forms: Gaussian curvature.The Gaussian curvature on vertex is defined as the product of storekeeper's curvature, product
Size can effectively reflect model surface in the bending degree of apex, in this way for detection plane have very big benefit.
In our experiment, for a region pair, we extract the curvature value of their boundaries, calculate separately minimum negative cruvature
Average value and their Gaussian curvature are as one of feature.
4.2.4 the concave-convex value (convexity value) in region
It is previously mentioned, a significant part be often it is convex, this inspire we go detection will be after two region merging techniques
Whether new region meets this characteristic.Take one kind described in the paper for grid bumps value (convexity
Value measurement).It can be explained on 2 dimensional planes for the time being, for a polygon, first calculating all tops of polygon
The convex closure that point is constituted, later for constituting each side of polygon, we can calculate the midpoint of this edge to the distance of convex closure,
It is exactly the concave-convex value of this polygon that these distances, which are sought weighted average according to the length on side,.Two-dimensional result is extended into three-dimensional
On, for region R, the triangular facet collection in the R of region is combined into F { R }, and the vertex set of R is P { R }, can be in the hope of region R by P { R }
Convex closure CR, then the concave-convex value of region R is defined as follows:
Wherein, area (f) is the area of face f, dist (f, CR) be face f center arrive along the face normal extension and convex closure
The distance of intersection point.By the calculating of bumps value, it can be effectively prevented and non-convex part appearance occur.
4.2.5 area attribute feature
Feature more than can obtain preferable effect in the training process substantially, but in actual test, hair
Now will appear a kind of situation: the region for having some very littles can not be polymerize, although the region adjacent with them is by them
It is fully wrapped around live.Reason is that there is no make constraint to the size in two regions of region centering.If one in two regions
Fully wrapped around firmly another region in region, then lesser region should actually belong to biggish region.So in addition feature
During, the characteristic that should be not only confined on zone boundary, should also region-of-interest itself geometrical property, such as area
The size in domain, the perimeter of zone boundary, convex closure volume etc..
In embodiment, it is trained using 200 models, and is trained on remaining model, absolutely mostly
In number situation, this dividing method can obtain good as a result, being using in the present invention as shown in Fig. 2 (a)-Fig. 2 (d)
Threedimensional model dividing method based on the merging of probability subregion is to multiple CAD model segmentation result schematic diagrames.Fig. 3 (a)-Fig. 3 (c)
Shown is using the threedimensional model dividing method merged based on probability subregion in the present invention to different spider model segmentation results
Schematic diagram.It is using the threedimensional model dividing method pair merged based on probability subregion in the present invention shown in Fig. 4 (a)-Fig. 4 (c)
The segmentation result schematic diagram of multiple chair models.
More than it should be understood by those ordinary skilled in the art that:, described is only specific embodiments of the present invention, and
It is not used in the limitation present invention, all within the spirits and principles of the present invention, any modification, equivalent substitution, improvement and etc. done,
It should be included within protection scope of the present invention.
Claims (8)
1. a kind of threedimensional model dividing method merged based on probability subregion, characterized by comprising:
1) over-segmentation forms a large amount of regions,
1-1) according to the triangle grid model in threedimensional model, figure G (V, E) is established, wherein V is vertex, E is side, Dist (Vi,
Vj) value between [0,1], be regarded as triangular facet (Vi,Vj) belong to the probability of different zones；
Dist (the V 1-2) is obtained based on weight calculationi,Vj) distance, obtain the adjacent triangular facet (V of every a pairi,Vj) away from
From；
It 1-3) is clustered according to the distance that shortest distance algorithm obtains two non-conterminous triangular facets, obtains overdivided region；
2) overdivided region is polymerize,
Region 2-1) is obtained in the threedimensional model of the overdivided region to (p, q)；
Similarity 2-2) is obtained by feature vector between (p, q) in each region；
2-3) judge whether to need to merge the region to (p, q) by establishing probabilistic model；
2-4) for the probabilistic model, by all features therein to combining, it is trained band weighted regression model；
3) training tandem type classifier,
It 3-1) is based on machine and artificial segmenting edge, boundary is established and recalls function；
Function progress tandem type training 3-2) is recalled according to the weighted value for punishing the region of mistake polymerization and the boundary, is obtained
To a tandem type classifier；
4) new model is split according to the tandem type classifier, merges adjacent area, obtains segmentation result.
2. threedimensional model dividing method according to claim 1, which is characterized in that described
Wherein,α indicates the dihedral angle in two faces,The center for being defined as two faces is arrived
The sum of the distance at the midpoint on shared side, a, b are that weight is used to guarantee Dist (Vi,Vj) between [0,1].
3. threedimensional model dividing method according to claim 2, which is characterized in that weight a, b is established as follows
The objective function of regression model:
Wherein, the distance for defining all adjacent triangular facets pair isThe probability for belonging to different zones is
4. threedimensional model dividing method according to claim 1, which is characterized in that obtain two according to shortest distance algorithm
The distance of non-conterminous triangular facet specifically:
5. threedimensional model dividing method according to claim 1, which is characterized in that the cluster is that K-Means cluster is calculated
Method.
6. threedimensional model dividing method according to claim 1, which is characterized in that the probabilistic model are as follows:
Wherein, ω is the parameter of linear logic regression model, and φ p, q (I, R) indicate feature vector, for a threedimensional model Ii,
It is classified as kiA region, regional ensemble are denoted as Ri={ Ri,1,Ri,2,…Ri,ki, if N (Ri) it is all adjacent of this model
Region, each region is to (p, q) ∈ N (Ri) all by feature vector φ p, q (an Ii,Ri) composition.
7. threedimensional model dividing method according to claim 6, which is characterized in that greedy in the probabilistic model to gather
The region pair of maximum probability is closed, until current model IiIn no longer there is Pg (p, q；Ii,RiThe region of) > 0.5.
8. threedimensional model dividing method according to claim 6, which is characterized in that establish boundary and recall function to α progress
Function is recalled on binary chop, the boundary are as follows:
Wherein,It indicates for manually dividing GiAll segmenting edge regions；It indicates to divide S for machineiAll points
Fringe region is cut, if for a certain GiIn segmenting edge, can be in SiIn find with it distance be less than ε segmenting edge, then
Think that this segmenting edge can be detected, and recorded, finally counts GiIn ratio shared by the edge that is detected,
And be averaged available boundary in all models and recall value, distance (p, q) is any two region between (p, q)
Distance.
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