CN105488541A - Natural feature point identification method based on machine learning in augmented reality system - Google Patents

Abstract

The invention provides a natural feature point identification method based on machine learning in an augmented reality system. The method comprises the steps of selecting the front image of a planar object as a target image; simulating the target image under combined observation conditions by perspective transformation to synthesize a sample image; collecting feature points and feature vectors in the sample image to serve as a training sample for machine learning; modeling for the feature vectors of the natural feature points of the target image through machine learning; dividing the plurality of natural feature points in the target image into different categories of the same quantity according to the modeling result, and respectively judging whether each feature point in a scene image belongs to any category.

Description

Based on the natural feature points recognition methods of machine learning in augmented reality system

Technical field

The present invention relates to the natural feature points recognition methods based on machine learning in a kind of augmented reality system.

Background technology

In recent years along with the develop rapidly of the technology such as computer vision, optics, display, development for augmented reality provides strong technical support, but as the three-dimensional registration technology of one of augmented reality system core technology, never tremendous breakthrough, precision is not high enough governs the Application and Development that augmented reality is applied to outdoor system always in registration, can say that three-dimensional registration is directly connected to the success or not of an augmented reality system, thus also just have very important reality and far reaching significance to the three-dimensional registration algorithm research in augmented reality.

A kind of register method based on physical feature is proposed in prior art.At initial phase, the image getting two width different visual angles, as with reference to frame, mates the Corner Feature of reference frame, and uses the method based on mark to carry out Accurate Calibration.At real time phase, compare by present frame and former frame the wide baseline matching problem solving unique point, and calculate the basic transformation matrix between present frame and reference frame with two View Algorithm.Then using these initial estimation as the starting point of nonlinear optimization, deviation is retrained as cost function using two views of characteristic point position and three-view diagram, minimize this cost function to estimate the position of camera, finally make calculating more stable with the method for similar Kalman filtering.

The register method based on texture is also proposed in prior art.The method is also utilize mark to carry out tracking initiation, and the object needing ex ante analysis tracked, and extract feature based on texture as matching template, all the other processes are with basically identical based on the method identified.

The physical feature tracking technique based on backprojection reconstruction is also been proposed in prior art.The method is formed primarily of two steps: embed and play up.Wherein embed and comprise appointment 4 points to set up the world coordinate system at dummy object place.Use Kanade-Lucas-Tomasi (being called for short KLT) feature detection to follow the trail of physical feature corresponding in real-time video when playing up.These features are normalized and carry out estimated projection matrix as input.The method without the need to predefined Datum identifier and outdoor AR system can be applied to.People employ the Fern sorting technique simplified of feature descriptor Sift leading at present in typical AR application.Wherein using planar grains object known in advance as tracking target, establish training dataset, directly utilize shooting built-in on current mobile phone to carry out a video capture, achieve the real-time follow-up that 6DOF frequency is 20Hz.

But it is not high that the method for above-mentioned prior art generally mates accuracy, or process is complicated and cause characteristic matching slower.

Summary of the invention

Technical matters to be solved by this invention is for there is above-mentioned defect in prior art, natural feature points recognition methods based on machine learning in a kind of augmented reality is provided, initial matching point is less, coupling accuracy is higher to reach, the object of the accurate tracking that is conducive to target image and registration.

In order to realize above-mentioned technical purpose, according to the present invention, providing the natural feature points recognition methods based on machine learning in a kind of augmented reality system, comprising:

First step: choose the front image of a width planar object as target image;

Second step: utilize perspective transform to simulate the target image under combination observation condition, to synthesize sample image;

Third step: to collect in the sample image of synthesis unique point and proper vector as the training sample of machine learning;

4th step: modeling is carried out to the proper vector of the natural feature points of target image by machine learning;

5th step: according to modeling result using the different classification of the multiple natural feature points in target image as respective numbers, judges whether each unique point in scene image belongs to arbitrary classification respectively.

Preferably, described combination observation condition comprise angle and/or distance and/or illumination.

Preferably, second step comprises:

The perspective transformation matrix of target image local coordinate to the projection of imaging plane is expressed as:

p＝CM, $M=\left[\begin{array}{cc}R& T\\ 0& 1\end{array}\right]$

Wherein, C is camera internal parameter, and M is external parameter matrix, and R is rotation matrix, and it adopts the Eulerian angle in three-dimensional graphics and robot kinematics to be expressed as R=R _yaw, R _pitch, R _roll; T=[T _xt _yt _z] be translation vector; Wherein R _yaw, R _pitchdetermine the angle between camera and target image plane normal, R _rollillustrate the rotation of target image in imaging plane, T _zcarry out the vertical range representing target and camera photocentre, it is as scale factor, T _xrepresent the horizontal cross distance of camera and target image plane, T _yrepresent the horizontal fore-and-aft distance of camera and target image plane; When camera internal parameter C is constant, by external parameter R _yaw, R _pitch, R _roll, T _x, T _y, T _zsample uniformly, to simulate the observation image of target image under different angles, distance, illumination and combination thereof as composograph.

Preferably, in the sample image of the collection synthesis in third step, unique point and proper vector comprise as the training sample of machine learning and perform following step for each sample image:

Calculate unique point K and the proper vector D thereof of target image I;

Upgrade perspective transformation matrix P (t);

Sample image I (t)=P (t) * I is synthesized according to perspective transformation matrix P (t);

Calculate the unique point K (t) of sample image I (t) and corresponding proper vector D (t) thereof;

Carry out matching characteristic point according to geometrical constraint K (t)=P (t) * K+ μ, wherein μ is the error that feature extraction algorithm is introduced, and wherein " * " represents multiplication symbol;

The unique point of coupling is added training sample data collection.

Preferably, also comprise at third step and further Screening Treatment is carried out to training sample; Described Screening Treatment comprises the uniqueness adopting Autocorrelation Detection unique point, to get rid of the similar features point in the similar or iteron region in sample image from the unique point of sample image.

Preferably, described Screening Treatment comprises: make I ₀=I is target image, I _t=p _ti is t width sample image, p _tfor perspective transformation matrix, K _t,i, L _t,i, D _t,i, N _tbe respectively sample image I _tunique point, unique point coordinate, proper vector and unique point number, i, j are unique point sequence number; As t=0, p ₀=E is unit matrix, I ₀=I, the Autocorrelation Detection of unique point calculates the proper vector distance U of any two unique points _i,j=| D _{0, i}-D _{0, j}|, i, j ∈ 0,1,2...N ₀; U at that time _i,jduring < ε, refuse the i-th, j unique point sequence number as class label, refuse this unique point K simultaneously _{0, i}and refusal unique point K _{0, i}match point on training image as training sample, wherein, N ₀the number of representation feature point, ε is proper vector distance threshold; The unique point set of this Autocorrelation Detection is expressed as SetK=<K _{0, i}| U _i,j> ε, i, j ∈ 0,1,2...N ₀, i ≠ j>; From unique point set by screening the unique point of the larger predetermined quantity of selected characteristic vector spacing as training sample data collection.

Preferably, the reproducibility detecting unique point is also comprised at third step;

Wherein, unique point K is calculated _{0, i}at sample image I _tin reproducibility formula

In formula, ε, μ are the error that feature extraction algorithm is introduced, D _t,jbe the proper vector of t width sample image, D _{0, i}for the vector of projection properties point, dist (D _t,j, D _{0, i}) be D _t,jwith D _{0, i}distance, L _t,jrepresent the unique point coordinate of t width sample image, L _{0, i}for projection properties point coordinate, | L _t,j-p _tl _{0, i}| represent the distance of the unique point of sample image and projection; As unique point K _{0, i}meet time, keeping characteristics point K _{0, i}and match point is as training sample; As unique point K _{0, i}do not meet time, by unique point K _{0, i}get rid of from training sample set; Wherein T is the sum of sample image, and ω is reproducibility coefficient.

Preferably, third step also comprise utilize gauss hybrid models get rid of error hiding;

Wherein, by statistical nature point K _iproper vector set by the proper vector set of the N number of unique point on target image as Gaussian Mixture Distribution Model

$p(D;a_k,S_k,{\mathrm{\&pi;}}_k)=\underset{k=0}{\overset{N-1}{\&Sigma;}}{\mathrm{\&pi;}}_k{p}_k\left(D\right);$

In formula, D represents vector set, a _k, S _k, π _krepresent Mean Matrix, covariance matrix respectively, ratio that each single Gauss model accounts in mixture model, π _k>=0, φ (D; a _ks _k) representing the probability distributing density function of data, d is the dimension of proper vector, will in proper vector as the sampled point of Density Estimator, maximize formula estimated parameter θ by expectation value:

$\mathrm{\&theta;}=\underset{\mathrm{\&theta;}}{\mathrm{argmax}}\left(L\right(D,\mathrm{\&theta;}\left)\right);$

$L(D,\mathrm{\&theta;})=\log p(D,\mathrm{\&theta;})=\underset{i=1}{\overset{N}{\&Sigma;}}log\left(\underset{k=0}{\overset{N}{\&Sigma;}}{\mathrm{\&pi;}}_k{p}_k\right(D\left)\right),\mathrm{\&theta;}=\{a_k,S_k,{\mathrm{\&pi;}}_k\};$

L (D, θ) represents expectation value or average;

According to gauss hybrid models, obtain unique point K and K _ithe probability of coupling is expressed as follows:

The foundation that whether coupling is correct using above-mentioned new probability formula as judging characteristic, when time, if then think that unique point K does not meet K _idistributed model, now, K is got rid of from training sample.

Compared with prior art, present invention employs the unique point founding mathematical models that a large amount of samples is each target image.Making the sampling feature vectors in same classification have certain unchangeability according to the suitable feature of selection is the principle constructing effective sorter, mapping relations one by one between proper vector are converted into the classification problem in pattern-recognition by the present invention, the speed of characteristic matching is further increased under the prerequisite ensureing accuracy, and the real-time follow-up achieved on this basis planar target and pose estimation.

At proper vector matching stage, the present invention using the coupling of unique point proper vector as classification problem, propose the feature matching method based on machine learning, mapping relations one by one between proper vector are converted into the classification problem in pattern-recognition, instead of the arest neighbors coupling of proper vector, thus computation burden is transferred to the training stage from real time phase.Experiment shows that method of the present invention is set relative to traditional KD and BBF method has the advantage that feature identification is accurate, robustness is high.

Accompanying drawing explanation

By reference to the accompanying drawings, and by reference to detailed description below, will more easily there is more complete understanding to the present invention and more easily understand its adjoint advantage and feature, wherein:

Fig. 1 schematically shows the process flow diagram based on the natural feature points recognition methods of machine learning in augmented reality system according to the preferred embodiment of the invention.

It should be noted that, accompanying drawing is for illustration of the present invention, and unrestricted the present invention.Note, represent that the accompanying drawing of structure may not be draw in proportion.Further, in accompanying drawing, identical or similar element indicates identical or similar label.

Embodiment

In order to make content of the present invention clearly with understandable, below in conjunction with specific embodiments and the drawings, content of the present invention is described in detail.

Fig. 1 schematically shows the process flow diagram based on the natural feature points recognition methods of machine learning in augmented reality system according to the preferred embodiment of the invention.

As shown in Figure 1, be included in augmented reality system based on the natural feature points recognition methods of machine learning in augmented reality system according to the preferred embodiment of the invention and perform following step:

First step S1: choose the front image of a width planar object as target image;

Second step S2: utilize perspective transform to simulate the target image under combination observation condition, to synthesize sample image; Wherein, combine observation condition comprise angle and/or distance and/or illumination.

Particularly, in second step S2, target image local coordinate can be expressed as to the perspective transformation matrix of the projection of imaging plane:

p＝CM, $M=\left[\begin{array}{cc}R& T\\ 0& 1\end{array}\right]$

Wherein, C is camera internal parameter, and M is external parameter matrix, and R is rotation matrix, and it adopts the Eulerian angle in three-dimensional graphics and robot kinematics to be expressed as R=R _yaw, R _pitch, R _roll; T=[T _xt _yt _z] be translation vector; Wherein R _yaw, R _pitchdetermine the angle between camera and target image plane normal, R _rollillustrate the rotation of target image in imaging plane, T _zcarry out the vertical range representing target and camera photocentre, it is as scale factor, T _xrepresent the horizontal cross distance of camera and target image plane, T _yrepresent the horizontal fore-and-aft distance of camera and target image plane; When camera internal parameter C is constant, by external parameter R _yaw, R _pitch, R _roll, T _x, T _y, T _zsample uniformly, to simulate the observation image of target image under different angles, distance, illumination and combination thereof as composograph.

Third step S3: to collect in the sample image of synthesis unique point and proper vector as the training sample of machine learning;

In the sample image of such as, collection synthesis particularly, in third step S3, unique point and proper vector can comprise as the training sample of machine learning and perform following step for each sample image:

Calculate unique point K and the proper vector D thereof of target image I;

Upgrade perspective transformation matrix P (t);

Sample image I (t)=P (t) * I is synthesized according to perspective transformation matrix P (t);

Calculate the unique point K (t) of sample image I (t) and corresponding proper vector D (t) thereof;

Carry out matching characteristic point according to geometrical constraint K (t)=P (t) * K+ μ, wherein μ is the error that feature extraction algorithm is introduced, and wherein " * " represents multiplication symbol;

The unique point of coupling is added training sample data collection.

Preferably, also comprise at third step S3 and further Screening Treatment is carried out to training sample.Described Screening Treatment comprises the uniqueness adopting Autocorrelation Detection unique point, to get rid of the similar features point in the similar or iteron region in sample image from the unique point of sample image, to improve the accuracy of sorter.

Such as, I is made ₀=I is former target image, I _t=p _ti is t width sample image, p _tfor perspective transformation matrix, K _t,i, L _t,i, D _t,i, N _tbe respectively sample image I _tunique point, unique point coordinate, proper vector and unique point number, i, j are unique point sequence number; As t=0, p ₀=E is unit matrix, I ₀=I, the Autocorrelation Detection of unique point calculates the proper vector distance U of any two unique points _i,j=| D _{0, i}-D _{0, j}|, i, j ∈ 0,1,2...N ₀; U at that time _i,jduring < ε, refuse the i-th, j unique point sequence number as class label, refuse this unique point K simultaneously _{0, i}and refusal unique point K _{0, i}match point on training image as training sample, wherein, N ₀the number of representation feature point, ε is proper vector distance threshold; The unique point set of this Autocorrelation Detection is expressed as SetK=<K _{0, i}| U _i,j> ε, i, j ∈ 0,1,2...N ₀, i ≠ j>; By the unique point that this unique point set selected characteristic vector spacing is larger, similar features point can be got rid of like this to improve the accuracy of sorter (such as, from unique point set by screening the unique point of the larger predetermined quantity of selected characteristic vector spacing, as training sample data collection).

In addition, preferably, the reproducibility detecting unique point is also comprised at third step S3.

Particularly, unique point K is calculated _{0, i}at sample image I _tin reproducibility formula

In formula, ε, μ are the error that feature extraction algorithm is introduced, D _t,jbe the proper vector of t width sample image, D _{0, i}for the vector of projection properties point, dist (D _t,j, D _{0, i}) be D _t,jwith D _{0, i}distance, L _t,jrepresent the unique point coordinate of t width sample image, L _{0, i}for projection properties point coordinate, | L _t,j-p _tl _{0, i}| represent the distance of the unique point of sample image and projection; As unique point K _{0, i}meet time, think unique point K _{0, i}there is higher reproducibility, keeping characteristics point K _{0, i}and match point is as training sample; Otherwise, the unique point of lower reproducibility is got rid of from training sample set; Wherein T is the sum of sample image, and ω is reproducibility coefficient.

Preferably, also comprise at third step S3 and utilize gauss hybrid models to get rid of error hiding, particularly:

By statistical nature point K _iproper vector set by the proper vector set of the N number of unique point on target image as Gaussian Mixture Distribution Model

$p(D;a_k,S_k,{\mathrm{\&pi;}}_k)=\underset{k=0}{\overset{N-1}{\&Sigma;}}{\mathrm{\&pi;}}_k{p}_k\left(D\right)---(1-2)$

In formula, D represents vector set, a _k, S _k, π _krepresent Mean Matrix, covariance matrix respectively, ratio that each single Gauss model accounts in mixture model, π _k>=0, φ (D; a _ks _k) representing the probability distributing density function of data, d is the dimension of proper vector, will in proper vector as the sampled point of Density Estimator, maximize formula estimated parameter θ by expectation value:

$\mathrm{\&theta;}=\underset{\mathrm{\&theta;}}{\mathrm{argmax}}\left(L\right(D,\mathrm{\&theta;}\left)\right)---(1-4)$

$L(D,\mathrm{\&theta;})=\log p(D,\mathrm{\&theta;})=\underset{i=1}{\overset{N}{\&Sigma;}}log\left(\underset{k=0}{\overset{N}{\&Sigma;}}{\mathrm{\&pi;}}_k{p}_k\right(D\left)\right),\mathrm{\&theta;}=\{a_k,S_k,{\mathrm{\&pi;}}_k\}---(1-5)$

L (D, θ) represents expectation value or average;

According to gauss hybrid models, unique point K and K _ithe probability of coupling can be expressed as follows:

The foundation that whether coupling is correct using above-mentioned new probability formula (1-6) as judging characteristic, when time, if then think that unique point K does not meet K _idistributed model, now, K is got rid of from training sample, to improve the accuracy of sorter.

4th step S4: modeling is carried out to the proper vector of the natural feature points of target image by machine learning;

5th step S5: according to modeling result using the different classification of the multiple natural feature points in target image as respective numbers, judges whether each unique point in scene image belongs to arbitrary classification respectively.

Such as, t is made to be unique point in scene image, class (t) for sorter be class (t) ∈ {-1 to the response function of the unique point t in scene image, 0,1...n-1}, wherein 0,1,2 ... n-1 represents the classification sequence number of the target image characteristics point that the unique point t in target image characteristics point and scene image matches, and-1 represents do not have the unique point t in target image characteristics point and scene image to match; Wherein n, m are positive integer.

, there is not general optimal classification device in theoretical without free lunch according to machine learning.In practical problems, various sorter has his own strong points in computing velocity, memory space requirement etc.Therefore the present invention tests various sorter (decision tree, random tree, support vector machine, k nearest neighbor etc.), to select the best approach of the most applicable Feature Points Matching.

In fact, invention removes similar features point (such as, be 640*480 and details can detect 1000-1500 unique point usually compared with on the image of horn of plenty in a width resolution, and the present invention is about 150-200 by the unique point number being retained as classification after the screening of training sample), decrease interference, thus improve coupling accuracy, and tracking and the registration of target image can be completed more accurately.

In a particular application, conplane prerequisite is according to pinhole camera model and target signature point, the present invention uses the homography matrix H estimating between two width images based on the method for RANSAC, and using homography matrix H as judging characteristic Point matching whether foundation, the offset error of unique point coordinate is taken as 1.5 pixels (now experiment test effect is better).

It should be noted that, unless stated otherwise or point out, otherwise the term " first " in instructions, " second ", " the 3rd " etc. describe only for distinguishing each assembly, element, step etc. in instructions, instead of for representing logical relation between each assembly, element, step or ordinal relation etc.

Be understandable that, although the present invention with preferred embodiment disclose as above, but above-described embodiment and be not used to limit the present invention.For any those of ordinary skill in the art, do not departing under technical solution of the present invention ambit, the technology contents of above-mentioned announcement all can be utilized to make many possible variations and modification to technical solution of the present invention, or be revised as the Equivalent embodiments of equivalent variations.Therefore, every content not departing from technical solution of the present invention, according to technical spirit of the present invention to any simple modification made for any of the above embodiments, equivalent variations and modification, all still belongs in the scope of technical solution of the present invention protection.

Claims (8)

1. in augmented reality system based on a natural feature points recognition methods for machine learning, it is characterized in that comprising:

First step: choose the front image of a width planar object as target image;

Second step: utilize perspective transform to simulate the target image under combination observation condition, to synthesize sample image;

Third step: to collect in the sample image of synthesis unique point and proper vector as the training sample of machine learning;

4th step: modeling is carried out to the proper vector of the natural feature points of target image by machine learning;

5th step: according to modeling result using the different classification of the multiple natural feature points in target image as respective numbers, judges whether each unique point in scene image belongs to arbitrary classification respectively.

2. method according to claim 1, is characterized in that, combination observation condition comprise angle and/or distance and/or illumination.

3. method according to claim 1 and 2, is characterized in that, comprises at second step:

The perspective transformation matrix of target image local coordinate to the projection of imaging plane is expressed as:

$p=CM,M=\left[\begin{array}{cc}R& T\\ 0& 1\end{array}\right]$

Wherein, C is camera internal parameter, and M is external parameter matrix, and R is rotation matrix, and it adopts the Eulerian angle in three-dimensional graphics and robot kinematics to be expressed as R=R _yaw, R _pitch, R _roll; T=[T _xt _yt _z] be translation vector; Wherein R _yaw, R _pitchdetermine the angle between camera and target image plane normal, R _rollillustrate the rotation of target image in imaging plane, T _zcarry out the vertical range representing target and camera photocentre, it is as scale factor, T _xrepresent the horizontal cross distance of camera and target image plane, T _yrepresent the horizontal fore-and-aft distance of camera and target image plane; When camera internal parameter C is constant, by external parameter R _yaw, R _pitch, R _roll, T _x, T _y, T _zsample uniformly, to simulate the observation image of target image under different angles, distance, illumination and combination thereof as composograph.

4. method according to claim 1 and 2, is characterized in that, in the sample image of collection in third step synthesis, unique point and proper vector comprise as the training sample of machine learning and perform following step for each sample image:

Calculate unique point K and the proper vector D thereof of target image I;

Upgrade perspective transformation matrix P (t);

Sample image I (t)=P (t) * I is synthesized according to perspective transformation matrix P (t);

Calculate the unique point K (t) of sample image I (t) and corresponding proper vector D (t) thereof;

Carry out matching characteristic point according to geometrical constraint K (t)=P (t) * K+ μ, wherein μ is the error that feature extraction algorithm is introduced, and wherein " * " represents multiplication symbol;

The unique point of coupling is added training sample data collection.

5. method according to claim 1 and 2, is characterized in that, also comprises carry out Screening Treatment to training sample further at third step; Described Screening Treatment comprises the uniqueness adopting Autocorrelation Detection unique point, to get rid of the similar features point in the similar or iteron region in sample image from the unique point of sample image.

6. method according to claim 5, is characterized in that, described Screening Treatment comprises: make I ₀=I is target image, I _t=p _ti is t width sample image, p _tfor perspective transformation matrix, K _t,i, L _t,i, D _t,i, N _tbe respectively sample image I _tunique point, unique point coordinate, proper vector and unique point number, i, j are unique point sequence number; As t=0, p ₀=E is unit matrix, I ₀=I, the Autocorrelation Detection of unique point calculates the proper vector distance U of any two unique points _i,j=| D _{0, i}-D _{0, j}|, i, j ∈ 0,1,2...N ₀; U at that time _i,jduring < ε, refuse the i-th, j unique point sequence number as class label, refuse this unique point K simultaneously _{0, i}and refusal unique point K _{0, i}match point on training image as training sample, wherein, N ₀the number of representation feature point, ε is proper vector distance threshold; The unique point set of this Autocorrelation Detection is expressed as SetK=<K _{0, i}| U _i,j> ε, i, j ∈ 0,1,2...N ₀, i ≠ j>; From unique point set by screening the unique point of the larger predetermined quantity of selected characteristic vector spacing as training sample data collection.

7. method according to claim 1 and 2, is characterized in that, also comprises the reproducibility detecting unique point at third step;

Wherein, unique point K is calculated _{0, i}at sample image I _tin reproducibility formula

In formula, ε, μ are the error that feature extraction algorithm is introduced, D _t,jbe the proper vector of t width sample image, D _{0, i}for the vector of projection properties point, dist (D _t,j, D _{0, i}) be D _t,jwith D _{0, i}distance, L _t,jrepresent the unique point coordinate of t width sample image, L _{0, i}for projection properties point coordinate, | L _t,j-p _tl _{0, i}| represent the distance of the unique point of sample image and projection; As unique point K _{0, i}meet time, keeping characteristics point K _{0, i}and match point is as training sample; As unique point K _{0, i}do not meet time, by unique point K _{0, i}get rid of from training sample set; Wherein T is the sum of sample image, and ω is reproducibility coefficient.

8. method according to claim 1 and 2, is characterized in that, also comprises utilize gauss hybrid models to get rid of error hiding at third step;

Wherein, by statistical nature point K _iproper vector set by the proper vector set of the N number of unique point on target image as Gaussian Mixture Distribution Model

$p(D;a_k,S_k,{\mathrm{\&pi;}}_k)=\underset{k=0}{\overset{N-1}{\&Sigma;}}{\mathrm{\&pi;}}_k{p}_k\left(D\right);$

In formula, D represents vector set, a _k, S _k, π _krepresent Mean Matrix, covariance matrix respectively, ratio that each single Gauss model accounts in mixture model, π _k>=0, φ (D; a _ks _k) representing the probability distributing density function of data, d is the dimension of proper vector, will in proper vector as the sampled point of Density Estimator, maximize formula estimated parameter θ by expectation value:

$\mathrm{\&theta;}=\underset{\mathrm{\&theta;}}{\mathrm{argmax}}\left(L\right(D,\mathrm{\&theta;}\left)\right);$

$L(D,\mathrm{\&theta;})=\log p(D,\mathrm{\&theta;})=\underset{i=1}{\overset{N}{\&Sigma;}}log\left(\underset{k=0}{\overset{N}{\&Sigma;}}{\mathrm{\&pi;}}_k{p}_k\right(D\left)\right),\mathrm{\&theta;}=\{a_k,S_k,{\mathrm{\&pi;}}_k\};$

L (D, θ) represents expectation value or average;

According to gauss hybrid models, obtain unique point K and K _ithe probability of coupling is expressed as follows:

The foundation that whether coupling is correct using above-mentioned new probability formula as judging characteristic, when time, if then think that unique point K does not meet K _idistributed model, now, K is got rid of from training sample.