CN102622609A - Method for automatically classifying three-dimensional models based on support vector machine - Google Patents

Abstract

The invention discloses a method for automatically classifying three-dimensional models based on a support vector machine. The method comprises the steps as follows: carrying out dimension reduction and characteristic decomposition on a geodesic distance matrix; creating binary classifiers for the characteristics of the three-dimensional models by using the support vector machine; and combining every two of the binary classifiers in a 'one-to-one' way by using the support vector machine to form a polynary classifier. According to the method, the three-dimensional models can be automatically classified, so that the robustness of the characteristic extraction process of the models is higher, the computing speed is higher, the characteristic extraction time is greatly shortened, and fewer three-dimension model training sample conditions can be well corresponded. The method has higher generalization performance and good expansion capability and non-linearity performance.

Description

A kind of three-dimensional model automatic classification method based on SVMs

Technical field

The present invention relates to a kind of automatic classification method of three-dimensional model.

Background technology

As after sound, image and video the 4th generation multimedia data type, three-dimensional model be the most intuitively, the multimedia messages of tool expressive force.Along with the fast development of laser scanner technique, 3 d modeling software technology and network technology, the establishment of three-dimensional model and using more and more widely, the three-dimensional model resource is more and more abundanter.The expansion of the increasing of enterprise product type and kind, product data scale makes that the sort research of three-dimensional model has important theory and engineering significance in the product design.And based on the emerging research focus of the three-dimensional model of shape classification as field of Computer Graphics, obtained to use widely in the every field such as modelling, virtual reality, analog simulation, 3D recreation, computer vision, molecular biology and three-dimensional geographic information of industrial products.

In present domestic and international disclosed document; At Z.Barutcuoglu and C.Decoro; " Hierarchical shape classification using Bayesian aggregation "; IEEE International Conference on Shape Modeling and Applications has proposed the sorting technique based on Bayesian aggregation in 2006., and the three-dimensional model in the semantic hierarchies structure is classified.In hierarchy Model, use relatively independent sorter that each class model is carried out the branch time-like, difference will take place with " father-son " relation in the hierarchical structure in the classification results of generation.In order to be consistent, a sample graphics can not only be divided into one type, only if this figure is divided into " father " class in hierarchical structure.Independently under the situation of sorter, each inconsistent probably classification results combines them, under Bayesian framework, obtains one group of classification results the most consistent then in given some that are used for an arbitrary shape descriptor.Finally utilize hierarchy to improve the precision of whole classification results.At Z.Liu, J.Mitani, Y.Fukui and S.Nishihara; " A 3D shape classifier with neural network supervision "; International Journal of Computer Applications in Technology, Vol.38, No.1-3; 2010. the middle three-dimensional model sorting technique that has proposed based on supervision type neural network, this provides a kind of three-dimensional picture sorter based on the Density Distribution of supervising the space of points this method.At first extract the feature samples of low order, train the neural network of a feedforward control to learn these characteristics then, thereby obtain an effective sorter through the Density Distribution of the characterization space of points.This sorter is divided into two stages, is respectively training stage that is used for training data and the test phase of assessing classifying quality.Not only the weight with each sample is relevant and it should be noted that the precision of sorter, and closely bound up with the hidden unit number of hiding stratum in the neural network.The hidden unit number is different, and nicety of grading also has very big difference.Therefore when training classifier, select the most appropriate hidden unit number to be necessary.

But above-mentioned two kinds of three-dimensional model sorting techniques have some not enough:

(1) the three-dimensional model sorting technique based on Bayesian aggregation mainly is to classify to the three-dimensional model that belongs in the hierarchical structure, has certain limitation, and the scope of application is less;

(2) can not corresponding non-rigid deformation based on the three-dimensional model sorting technique of neural network, in addition, nicety of grading is lower.

Summary of the invention

In order to overcome existing sorting technique classification range limitation, can't to tackle non-rigid deformation and the lower problem of precision; The present invention provides a kind of three-dimensional model automatic classification method, and this sorting technique is classified to the three-dimensional model or the cad model of generic object automatically.At first, for the characteristic of the non-rigid transformation of obtaining three-dimensional model, the geodesic line distance on any two summits of Calculation of Three Dimensional model of the present invention distributes as global characteristics through obtaining geodesic line.The present invention carries out dimensionality reduction and feature decomposition to the geodesic line distance matrix, utilizes SVMs to make up the binary classification device of three-dimensional model characteristic then, and adopts " one to one " of SVMs binary classification device to constitute the multivariate classification device in twos.The present invention can classify to three-dimensional model automatically.

The technical solution adopted for the present invention to solve the technical problems may further comprise the steps:

(1) the geodesic line distance on any two summits of Calculation of Three Dimensional model.The present invention obtains the global characteristics of each three-dimensional model gridding through the distance on characterization summit, utilizes the global characteristics training classifier that the distance feature of new input is classified.The present invention adopts the geodesic line distance on 3D grid summit to obtain the global characteristics of 3D shape, and the geodesic line distance non-rigid variation such as can not bend along with the part of a 3D shape and change, and can not change along with rigid transformation yet.The present invention converts the calculating of the geodesic line distance on any two summits on the 3D grid to the dynamic programming problems of belt restraining; Be actually from shortest path of reaching home of starting point dynamic programming; Obtain the length in this path, thereby obtain any two summit geodesic line distances.

(2) dimensionality reduction of geodesic line distance matrix and feature decomposition.Because any two summits of 3D grid can constitute the geodesic line distance matrix, the eigenwert of this matrix has been represented the global characteristics of this 3D grid, and the present invention considers this geodesic line distance matrix is carried out feature decomposition.Yet extensive Three Mesh has the above summit quantity of N=1M, will constitute the higher dimensional matrix of N*N=1M*1M, and this matrix is carried out feature decomposition needs O (N ³) computation complexity, in a rational time, can't realize at all.Therefore; The present invention has studied a kind of dimension reduction method; This method purpose is the few representative summit of sampling from the extensive summit of 3D shape; These summit geodesic lines are apart from the feature decomposition approximately equal of the low dimension matrix that constitutes with the higher dimensional matrix of all summits formation, thereby avoid higher dimensional matrix is carried out the calculating pressure of feature decomposition.Further the geodesic line distance carry out Gaussization then, its purpose is to reduce the influence of long geodesic line distance to feature decomposition, strengthens the robustness of this sorting technique, adopts the Jacobi method that low dimension matrix is carried out feature decomposition at last.

(3) utilize SVMs to make up the binary classification device of three-dimensional model characteristic.The present invention dissolves the problem of voting for a plurality of binary classification devices with many classification problems, the mode that adopts the binary classification device to make up the in twos sorter that comes from different backgrounds and possess different abilities.According to the proper vector of the sample that extracts, classify through the binary classification device, realize two class target outputs of binary classification device.The present invention makes up a binary classification device through support vector machine method, finds the solution the parameter that constrained optimization problems is confirmed SVMs through utilizing the Lagrange function, introduces the radially basic kernel function of Gauss simultaneously sample space is mapped to higher-dimension, reaches linear separability.

(4) utilize the binary classification device to be combined into the multivariate classification device.The present invention adopts " one to one " of the SVMs binary classification device that step (3) obtains to constitute the multivariate classification device in twos.Therefore,, K class training sample is made up in twos, can make up L=K (K-1)/2 training set, use SVMs binary classification device that every pair of training set is learnt respectively, produce L binary classification device for the K classification problem.In to the classification of test sample book, adopt " ballot method " to decide classification results.

The invention has the beneficial effects as follows:

The present invention has realized a kind of automatic classification method of three-dimensional model; This method can be extracted the geodesic line characteristic of three-dimensional model; Adopt support vector machine method to set up the binary classification device; Form a multivariate classification device according to " ballot method " principle by a plurality of binary classification devices of combination in twos, thereby realize the automatic classification of three-dimensional model.At first, the geodesic line distance that the present invention extracts can adapt to the rigid transformation and the non-rigid transformation of three-dimensional model, and the robustness of the characteristic extraction procedure of model is stronger, and, when the geodesic line distance calculation, adopted dynamic programming method, promoted computing velocity; Secondly, the present invention proposes the feature decomposition of a dimension reduction method efficient calculation geodesic line distance matrix, has shortened the time of feature extraction greatly; The 3rd, the present invention adopts support vector machine method as the binary classification device, and advantage is 1) can well corresponding less three-dimensional model training sample situation; 2) have stronger extensive performance, improve the classification robustness; 3) have a lot of kernel method supports, make this sorter have good expansion capacity and non-linear behaviour.Experiment showed, the three-dimensional model automatic categorizer that the present invention constitutes, have the nicety of grading height, be suitable for the wide characteristics of three-dimensional model scope.

Below in conjunction with accompanying drawing and embodiment the present invention is further specified.

Description of drawings

The general flow chart that Fig. 1 realizes for this invention;

Fig. 2 is the dimension reduction method of the geodesic line distance matrix of the present invention's proposition;

Fig. 3 is the classification process based on SVMs;

Fig. 4 is the simple expression-form of optimal classification face in the SVMs.

Embodiment

In conjunction with accompanying drawing, elaborate below the practical implementation step.

Shown in accompanying drawing 1, the present invention realizes the three-dimensional model main-process stream of classification automatically, and this general flow chart has comprised realizes each required key step of final classification.At first; A given three-dimensional grid model, the geodesic line distance on any two summits of Calculation of Three Dimensional model is carried out dimensionality reduction and feature decomposition to the geodesic line distance matrix then; Obtain the three-dimensional grid model global characteristics; This characteristic use SVMs makes up the binary classification device classifies to it, and adopts " one to one " of SVMs binary classification device to constitute the multivariate classification device in twos, utilizes this multivariate classification device can obtain classification results.At test phase, can be through the three-dimensional grid model global characteristics that obtains, be input to SVMs binary classification device and the multivariate classification device is tested.Therefore, the present invention can realize three-dimensional model is classified automatically.

In conjunction with accompanying drawing, elaborate below the practical implementation step.

One, the geodesic line distance on any two summits of Calculation of Three Dimensional model.

The present invention's hypothesis three-dimensional model to be classified is showed by polygonal mesh, and each grid is made up of according to topological relation summit, limit, polygon.The present invention obtains the global characteristics of each grid through the distance on characterization summit, utilizes the global characteristics training classifier that the distance feature of new input is classified.But; The present invention does not directly use the Euclidean distance on summit to carry out characterization, and reason is that Euclidean distance can't tackle the non-rigid deformation of 3D grid, yet; All there are certain flexible conversion such as bending in a lot of three-dimensional models; Therefore Euclidean distance will be relatively poor to the non-rigid transformation robustness, directly influence final classification results, make this sorter nicety of grading variation.Therefore, the present invention adopts the geodesic line distance on summit to obtain the global characteristics of 3D shape, and the geodesic line distance can not bend along with the part of a 3D shape and change, and this distance is constant for non-rigid transformation.

The geodesic line on any two summits distance is actually from shortest path of reaching home of starting point dynamic programming on the 3D grid.If there are any two adjacent vertexs on the path of starting point and terminal point, be respectively vi and vj, the shortest path of starting point and terminal point can be reached an optimization problem with formula table:

$\min \underset{i,j}{\mathrm{\Σ}}|v_i-v_j|$

The present invention is through finding the solution above-mentioned optimization problem, thus any 2 the geodesic line distance of Calculation of Three Dimensional grid.Method is following:

If the initial vertex is v ₀, the termination summit is v _nEach vertex v on the path of starting point between to terminal _iWriting down arrive starting point geodesic line apart from d _i, d wherein _i∈ R is v from the initial vertex ₀To any vertex v _iThe length of shortest path.v _I-1Be v _iThe neighbour's 3D grid summit that connects, its distance is weighed with Euclidean distance.The expression formula of optimization problem is following:

d ₀＝0

d _i＝min(d _i-1+||v _i-1-v _i||)

The present invention adopts dynamic programming method, utilizes iterative planning mode, guarantees that footpath, each step is the shortest, dynamic cook up net result, this method can produce the shortest path of the overall situation.This dynamic programming process utilizes width searches to realize, promptly each search travels through the k-neighbour on 3D grid summit.The present invention adopts summit, limit and polygonal neighbour's store list to realize the 3D grid topological structure; Create the neighbor lists on summit, the neighbor lists on limit, polygonal neighbor lists in the 3D grid read-in process; And; The neighbor lists on summit has comprised neighbour summit, neighbour limit, neighbour's polygon, and the neighbor lists on limit has comprised neighbour summit, neighbour limit, neighbour's polygon, and polygonal neighbor lists has comprised neighbour's polygon.Therefore k-neighbour's traversal only needs the time complexity of O (1), can guarantee that traversal speed is enough fast, thereby increase dynamic programming speed.In addition, in order further to accelerate planning speed, to tackle large-scale 3D grid, the present invention has increased by two constraint conditions in the process of dynamic programming, and the 3D grid summit of promptly satisfying this constraint condition preferentially travels through.

Article one, constraint condition does

(v _i-v _s)·(v _t-v _s)＞0

This constraint condition is arranged the planning direction (v of each dynamic programming in fact _i-v _s) and origin-to-destination direction (v _t-v _s) unanimity.This direction is the direction of preferential planning, can stop planning in case reach home, and increases the speed that this constraint condition will increase dynamic programming greatly, makes the computing velocity of any 2 geodesic line distances accelerate.

Second constraint condition does

d(v _i，v _s)≥||v _t-v _s|| ₂

This constraint condition guarantees that in ergodic process, the geodesic line on two summits is apart from d (v _i, v _s) must be greater than the Euclidean distance of terminus || v _t-v _s|| ₂Because 2 bee-lines that Euclidean distance is the space necessarily smaller or equal to 2 geodesic line distance, therefore in planning process, when also not reaching Euclidean distance, need not to judge whether arrived terminal point, can save time.

Above-mentioned steps of the present invention can be calculated any geodesic line distance fast at 2.

Two, the dimensionality reduction of geodesic line distance matrix and feature decomposition.

Geodesic line distance through any two summits of step 1) Calculation of Three Dimensional grid; Thereby constitute a higher dimensional matrix D; Wherein the index of row and column corresponding the index on 3D grid summit, each matrix element is being represented the geodesic line distance on any two 3D grid summits.Because the eigenwert of geodesic line distance matrix has been represented the global characteristics of this 3D grid, the present invention considers this geodesic line distance matrix is carried out feature decomposition.Yet extensive Three Mesh has the above summit quantity of N=1M, will constitute the higher dimensional matrix of N*N=1M*1M, and this matrix is carried out feature decomposition needs O (N ³) computation complexity, in a rational time, can't realize at all.Therefore; The present invention has studied a kind of dimension reduction method of higher-dimension geodesic line distance; This method purpose is the few representative summit of sampling from the extensive summit of 3D shape; The feature decomposition approximately equal of the higher dimensional matrix that these summit geodesic lines constitute apart from the low dimension matrix that constitutes and all summits, thus avoid higher dimensional matrix is carried out the calculating pressure of feature decomposition, accelerate training speed of the present invention greatly and moved classification speed.Shown in accompanying drawing 2, this dimension reduction method step is following:

1) calculate the mathematical expectation of all geodesic line distances, (i j) is the geodesic line distance of two vertex index i and j to d here.

d _m＝E[d(i，j)]

2) establishing the dimensionality reduction matrix is L, is initially sky.At first select a pair of vertex index (x of geodesic line apart from maximum ₁, x ₂), adding empty dimensionality reduction matrix L to, this dimensionality reduction matrix is changed to:

$L=\left[\begin{array}{cc}0& d(x_1,x_2)\\ d(x_2,x_1)& 0\end{array}\right]$

3) according to the original matrix indexed sequential, the tabulation of traversal grid vertex is with having selected the respective on summit to be appended in the matrix L in vertex index x that satisfies following two conditions and the dimensionality reduction matrix.

A) this summit x is to all vertex index x of matrix L _jGeodesic line distance greater than mathematical expectation d _m:

$d(x,x_j)>d_m,\∀j$

B) this summit x is to all summit x of matrix L _jGeodesic line maximum apart from sum:

$x=\arg \max \underset{j}{\mathrm{\Σ}}d(x,x_j)$

4) repeating step 3), any stop condition below satisfying:

A) number of vertices of matrix has surpassed setting value k.In this patent, set k=64;

B) do not had the 3D grid summit to satisfy 3) condition that sets of step.

After above-mentioned dimensionality reduction step, the dimension of original matrix D is reduced to the k value, is easy to carry out at short notice feature decomposition.Yet after having carried out the matrix dimensionality reduction, we further carry out Gaussizationes to the geodesic line distance, and its purpose is to reduce the influence of long geodesic line distance to feature decomposition, strengthen the robustness of this sorting technique.Method is following:

$d_{\mathrm{ij}}^{\′}=\exp (-d_{\mathrm{ij}}^2/2{\mathrm{\σ}}^2)$

Wherein, be d _Ij2 geodesic line distance, σ is Gauss's width, d ' _IjGeodesic line distance for Gaussization.In this patent, we define Gauss's width cs and do

σ＝max(i，j){d _ij}

The i.e. maximal value of the geodesic line distance between all summits.σ is defined as the relevant form of this data, and that last feature decomposition result is accomplished even convergent-divergent is constant, and the present invention defines this value purpose and is geodesic line apart from carrying out standardization.The present invention can learn that through the observation to lot of experiment results as long as σ is enough big, last feature decomposition is metastable about σ.

After the geodesic line distance matrix was carried out dimensionality reduction and Gaussization, the present invention carried out feature decomposition to matrix D, calculated its eigenwert.The feature decomposition formula is following:

Dv＝λv

Wherein, this patent adopts general Jacobi method to carry out feature decomposition, and eigenwert is sorted from big to small.

The vector

that the present invention constitutes eigenwert will block from the less eigenwert of setting of c and give up through blocking (cutoff) mode dimensionality reduction once more.In this patent,, set c=16 through experimental observation.Vector behind the dimensionality reduction

will be as the input feature vector of sorter of the present invention; Input feature vector through calculating each sample is trained sorter; Equally; In the actual motion; Extract this input feature vector earlier, be input to then and trained the sorter of completion that it is classified.

Three, utilize SVMs to make up the binary classification device of three-dimensional model characteristic.

The present invention dissolves many classification problems and is a plurality of binary classification device combinatorial problems.There is certain corresponding relation between many classification problems and the binary classification problems.If a problem is that multiclass can be divided, then necessarily can divide between any two types in this multiclass; Otherwise, in classification problem more than, if known its any two all right one way or the other branch then through certain combination rule, can all right one way or the otherly assign to finally realize that multiclass can divide by two.The different combinations rule has just formed different sorting algorithms, and combination rule will be set forth in step 4) in detail.The present invention proposes to adopt support vector machine method to step 2) the three-dimensional model characteristic extracted carries out binary classification.Based on the classification process of SVMs shown in accompanying drawing 3, through step 2) characteristic of extracting one group of three-dimensional grid model is as classification samples, is divided into training set and test set; SVMs of the present invention is trained; Select kernel function, and pass through the normal direction coefficient of optimal way selection sort face, and confirm the migration parameter of classifying face through the support vector set; To confirm classifying face; Form the binary classification device, be combined as the multivariate classification device through the binary classification device then, can the output category result for training set and test set.Binary classification device implementation method based on 0 SVMs is following.

Suppose for the feature samples collection (x that constitutes by three-dimensional grid model _i, y _i), wherein, i ∈ [1, n], characteristic x _i∈ R ^M, be positioned at the feature space that M ties up.y _i{+1 ,-1} is a class label to ∈.The feature samples collection can obtain the classifying face equation and is thus:

H(x)＝ω ^Tx+b＝0

Wherein ω is the vector of M dimensional feature space, is the normal direction coefficient of classifying face, and b is a scalar, is the migration parameter of classifying face.Utilize ω and b can confirm the position of classifying face.The classifying face of being constructed need significantly separate two types of samples, promptly satisfies and works as y _i=1 o'clock, H (x _i)=1, same, work as y _i=-1 o'clock, H (x _i)=-1.

Shown in accompanying drawing 4,, under the condition that two types of samples are correctly separated, make the class interval maximum based on structural risk minimization.Classifying face is located in the centre of two boundary lines, the point that defines boundaries through support vector.After support vector obtains, just no longer need other sample, can the reduced sample processing time.According to geometric knowledge, the distance of two boundary lines is 2/|| ω || ², the method that this aspect adopts promptly utilizes optimization method to obtain maximum distance, promptly minimizes

The present invention considers disturbing factor, introduces slack variable ξ and penalty coefficient C, confirms that the problem of classifying face can be converted into finding the solution of following optimal problem, introduces two constraint conditions:

y _i(ω ^Tx _i+b)≥1-ξ _i

ξ _i≥0

Under above-mentioned constraint, ask function

$\frac{1}{2}{\left|\right|\mathrm{\ω}\left|\right|}^2+C\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ξ}}_i$

Minimum value.This constrained optimization problems can be found the solution through structure Lagrange function, and structure Lagrange function is following:

$Q(\mathrm{\ω},b,\mathrm{\ξ},\mathrm{\α},\mathrm{\β})=\frac{1}{2}{\left|\right|\mathrm{\ω}\left|\right|}^2+C\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\ξ}}_i-\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_i(y_i({\mathrm{\ω}}^T{x}_i+b)-1+{\mathrm{\ξ}}_i)-\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\β}}_i{\mathrm{\ξ}}_i$

Find the solution Lagrange minimum of a function value, above-mentioned function is asked its minimum value about ω and b, this minimum value must be tried to achieve at the saddle point place.Therefore, this saddle point satisfies following condition:

$\frac{\∂Q}{\∂\mathrm{\ω}}=0,$ $\frac{\∂Q}{\∂b}=0,$ $\frac{\∂Q}{\∂\mathrm{\ξ}}=0$

α _i(y _i(ω ^Tx _i+b)-1+ξ _i)＝0

β _iξ _i＝0

α _i≥0，β _i≥0，ξ _i≥0

Find the solution and obtain:

$\mathrm{\ω}=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_i{y}_i{x}_i,$ $\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_i{y}_i=0,$ α _i+β _i＝C

Be updated in the Lagrange function, obtain:

$Q\left(\mathrm{\α}\right)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_i-\frac{1}{2}\underset{i=1,j=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_i{\mathrm{\α}}_j{y}_i{y}_j{x}_i^T{x}_j$

Alpha wherein _iSatisfy

$\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_i{y}_i=0,$ α _i≥0

Therefore, utilize the classifying face parameter of above-mentioned optimum to set up following discriminant classification function:

$H\left(x\right)=\mathrm{sign}(\underset{i,j=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_i{y}_i\left(x_i^T{x}_j\right)+b)$

Wherein,

$b=\frac{1}{\left|U\right|}\underset{i\∈U}{\mathrm{\Σ}}(y_i-{\mathrm{\ω}}^T{x}_i)$

Here U expresses support for the element number of vector set.

The present invention is according to the symbol of the value of H in the formula (x), the classification of binary classification under the judgement sample x.

The present invention has adopted nonlinear method to attempt the 3D grid characteristic is carried out binary classification, utilizes Nonlinear Vector that the 3D grid Feature Mapping is arrived high-dimensional feature space, makes its linear separability.The definition Nonlinear Vector

This vector is tieed up input feature vector x with m and is mapped to the k dimensional feature space, makes its this grouped data can linear separability at high-dimensional feature space.The respective classified discriminant function is:

$H\left(x\right)=\mathrm{sign}(\underset{i,j=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_i{y}_i({\mathrm{\Φ}}^T\left(x_i\right)\·\mathrm{\Φ}\left(x_j\right))+b)$

We consider to introduce kernel function K (x _iX) higher-dimension calculates the initiation calculation of complex and crosses problem concerning study in the solution following formula.As long as find a suitable kernel function that satisfies the Mercer condition in the input space, just can replace the inner product operation of high-dimensional feature space with this kernel function, the discriminant function of the optimal classification face of being constructed is:

$H_K\left(x\right)=\mathrm{sign}(\underset{i,j=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\α}}_i{y}_{i}K(x_i\·x)+b)$

The present invention has attempted three kinds of kernel functions commonly used, comprises radially basic kernel function of linear kernel function, Gauss and Sigmoid kernel function.Wherein the linear kernel function expression formula is following

K(x _i·x _j)＝x _i·x _j

The gaussian radial basis function expression formula is following:

$K(x_i\·x_j)=\exp \{-\frac{{\left|\right|x_i-x_j\left|\right|}^2}{2{\mathrm{\σ}}^2}\}$

Wherein σ is the variance of sample.

The expression formula of Sigmoid kernel function is following:

K(x _i·x _j)＝tanh{gx _i·x _j-h}

It constitutes the multilayer perceptron neural network, and wherein parameter g is a scale factor, and h is a displacement factor.

Find that through test the Gauss radially kernel function of base has provided classification performance preferably, therefore, the present invention adopts the kernel function of gaussian radial basis function as SVMs.

Four, utilize the binary classification device to be combined into the multivariate classification device

Because the 3D shape classification problem mainly concentrates on many classification, the binary classification device that the present invention adopts step 3) to make up is combined into a multivariate classification device.Usually, many sorting techniques mainly contain: one to one, and one-to-many and directed acyclic graph.Wherein classification is many preferably classification one to one, is applicable to practical application, and counting yield is higher, and two types of samples tend to balance, and makes discriminant classification more become to rationalizing.The present invention uses is classification one to one.For the K classification problem, K class training sample is made up in twos, can make up L=K (K-1)/2 training set, use SVMs binary classification device that every pair of training set is learnt respectively, produce L binary classification device.In to the classification of test sample book, adopt " ballot method ":,, add a ticket to such if sample x output result is judged to be such with L the binary classification device of test sample book input by K class sample architecture.All L binary classification devices to the test sample book classification after, in the K class which kind of who gets the most votes, just judge which kind of test sample book belongs to.Thereby the present invention has realized the automatic classification method of a three-dimensional model.

Effect of the present invention can further specify through following experiment.The experimental data collection is from Canadian McGill University Shape Benchmark, and this three-dimensional modeling data collection comprises 10 types of common shape altogether, comprises animal, people, machinery etc., and specific category is seen table 1.The present invention is divided into training set and test set with this data set.The training set comprises 10 types of shapes, every type of 10 models, totally 100 models.The test set comprises 10 types of shapes, every type of 10 models, totally 100 models.Training obtains the multivariate classification device on training set, the classification results of assessment multivariate classification device on test set.During training, distribute class mark separately to 10 types of shapes of training set respectively, get wherein any two types sample value and carry out training study, so just can obtain a multivariate classification device of forming by 45 binary classification devices.During test 10 types of sample values are imported this multivariate classification device successively and just can obtain all classification results.Classification results is added up, and statistics is as shown in table 1, and wherein error rate and accuracy are meant that respectively the number of the three-dimensional model that classification error and classification are correct accounts for the number percent of disaggregated model total number.

The nicety of grading of table 1 the present invention on the three-dimensional model test set

From classification results, can find out; The nicety of grading of the three-dimensional model automatic classification method that the present invention proposes reaches 86%; This has certain superiority in existing three-dimensional model sorting technique; Performance with good classification simultaneously, is tackled complicated universal model and non-rigid transformation and is had stronger robustness.Above integral body is said to be preferred implementation of the present invention; Those skilled in the art are under the prerequisite that does not break away from the principle of the invention; Can make some improvement, comprise kernel function that changes SVMs etc., scope of the present invention is appended claims and be equal to and limit.

Claims (1)

1. the three-dimensional model automatic classification method based on SVMs is characterized in that comprising the steps:

(1) obtains the global characteristics of each three-dimensional model gridding through the distance on characterization summit, utilize the global characteristics training classifier that the distance feature of new input is classified;

(2) the few representative summit of sampling from the extensive summit of 3D shape; These summit geodesic lines are apart from the feature decomposition approximately equal of the higher dimensional matrix of the low dimension matrix that constitutes and all summits formation; Further the geodesic line distance carry out Gaussization then, adopt the Jacobi method that low dimension matrix is carried out feature decomposition at last;

(3) utilize SVMs to make up the binary classification device of three-dimensional model characteristic; Make up a binary classification device through support vector machine method; Find the solution the parameter that constrained optimization problems is confirmed SVMs through utilizing the Lagrange function; Introduce the radially basic kernel function of Gauss simultaneously sample space is mapped to higher-dimension, reach linear separability; According to the proper vector of the sample that extracts, classify through the binary classification device, realize two class target outputs of binary classification device; The mode that adopts the binary classification device to make up the in twos sorter that comes from different backgrounds and possess different abilities

That (4) adopts SVMs binary classification device that step (3) obtains constitutes the multivariate classification device one to one in twos; For the K classification problem; K class training sample is made up in twos; Can make up L=K (K-1)/2 training set, use SVMs binary classification device that every pair of training set is learnt respectively, produce L binary classification device.In to the classification of test sample book, adopt the ballot method to decide classification results.

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