CN104966088B - Based on small echo in groups-variation interconnection vector machine fracture surface image recognition methods - Google Patents
Based on small echo in groups-variation interconnection vector machine fracture surface image recognition methods Download PDFInfo
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Abstract
The invention discloses one kind being based on small echo-variation interconnection vector machine fracture surface image recognition methods in groups, first, using small echo in groups (Grouplet) conversion process fracture surface image, Grouplet is calculated separately to Grouplet coefficients and reconciles entropy, Grouplet kurtosis and Grouplet average energies this 3 feature vectors, then, characteristic feeding variation interconnection vector machine (VRVM) grader is identified.This method characteristic is to absorb all advantages of small echo in groups and variation interconnection vector machine, compared with existing image-recognizing method, the method of proposition has apparent advantage in terms of image recognition, not only increase the discrimination of image, and recognition speed is significantly improved, and with the increase of training samples number, this Heterosis must be more apparent, has broad application prospects in image procossing.
Description
Technical field
The present invention relates to the methods of image procossing, more particularly to a kind of based on small echo-variation interconnection vector machine metal in groups
Fracture surface image recognition methods.
Background technology
In all kinds of failures of mechanized equipment, harm maximum main with fracture failure, the diagnosis and analysis of fracture failure
One of the research topic that always people pay much attention to, and the pattern recognition and classification of fracture surface image is to carry out fracture defect intelligence
Change the critical problem of analysis.It, can be effectively since wavelet transformation has good localization property simultaneously in time domain and frequency domain
The texture information for extracting fracture surface image, currently, having become the main method of Metal Fracture Surface Images feature extraction[1-5].However, with
The research for problem is goed deep into, and deficiency of the small wave converting method in Metal Fracture Surface Images processing is also fully exposed, due to small
The support Interval of wave base is square, cannot effectively approach unusual linearity curve；Wavelet transformation can only obtain the limited direction of image
Information cannot fully utilize the geometry regularity of image itself.In addition, how the wavelet basis and parameter in wavelet transformation select
There is great influence to Metal Fracture Surface Images identification, and how to select best wavelet basis and parameter, currently, it is any according to
According to.
Therefore, for based on wavelet transformation in metal fracture method the existing deficiency in terms of Metal Fracture Surface Images identification,
There is an urgent need to seek new Metal Fracture Surface Images recognition methods.For this purpose, extra small wave analysis thought is introduced into gold by doctor Li Zhinong
Belong in fracture surface image processing, and has made intensive studies[6-9].Wen Xian [6,7]In conjunction with the respective excellent of contourlet transformation and RVM
Point, proposes a kind of aviation component fracture apperance recognition methods based on Contourlet-RVM, i.e., with contourlet transformation into
Row feature extraction is identified metal fracture pattern using RVM as grader.Meanwhile by the method for proposition with
Contourlet-SVM recognition methods compares and analyzes.Wen Xian [8,9]Bandelet transformation is applied to Metal Fracture Surface Images
In processing, it is proposed that the Metal Fracture Surface Images recognition methods based on Bandelet transformation, and carried out experimental verification.However, with
The drawbacks of research for problem is goed deep into, more existing super wavelet analysis method also gradually displays, and such as works as the several of image
When what structure is more complicated, Bandlet map table diagram pictures be not it is fine, reason be geometry stream calculation inaccuracy and
It is more difficult to approach.For contourlet transformation as wavelet transformation, there are a common deficiencies, that is, lack translation invariant
Property, pseudo- Gibbs phenomenons nearby are will produce in the singular point (edge or texture) of processing image, the image after reconstruct is attached in singular point
Closely it is alternately present the larger vibration of amplitude up and down.In addition, the low frequency transform (LP decomposition) of contourlet transformation has redundancy,
Its redundancy is 4/3.Based on this, need to propose that new x-let changes bring deficiency existing for solution existing method.
Small echo (Grouplet) transformation in groups is Mallat[10]A kind of completely new Image Multiscale point proposed in 2009
Analysis technology can realize a kind of two dimensional image processing fast algorithm by Haar transform, and superior function is significantly better than existing
Wavelet analysis method and other directional wavelets.The transformation breaches the limitation of multi-scale image decomposition, can be at any time
It is spatially converted, possesses the ability of the change base according to image texture structure adaptive, to preferably sparse
Expression ability, greater flexibility and more superior performance.Since Grouplet converts brand-new theoretical looks and original
Application characteristic, the especially advantage in processing texture information rich image have begun to cause the country as soon as the transformation proposes
The strong interest of outer scholar[10-19].Peyr é are in Wen Xian [11]In propose a kind of dynamic based on tight frame Grouplet transformation
Texture synthesis method；In Wen Xian [12]In propose it is a kind of using Grouplet become bring synthesis and repair natural image side
Method.Maalouf[13-15]It is changed in Grouplet changes and has done a few thing, such as document;14]It gives a kind of based on Grouplet
The image quality evaluating method of transformation, Wen Xian [15]Propose a kind of color image super resolution calculation converted based on Grouplet
Method.Takahirof[16]It is shunk using hard color and Grouplet changes is brought to Image Denoising by Use.Wei[17]Propose a kind of audiovisual
Grouplet methods, and carried out verification experimental verification.At home, University Of Shantou Yan Jing culture and education is awarded[18,19]It is changed in Grouplet changes
A few thing is done, in conjunction with greedy algorithm (Greedy algorithm) and dynamic programming algorithm (Dynamic Programming
Algorithm) tailoring process of associated domain is improved, proposes a kind of new AGT (Advanced Grouplet
Transform it) converts, avoids occurring a case where streamline is cut into multistage streamline during cutting out associated domain.
Currently, the research of Grouplet transformation is only in theoretical research, image repair is only limited in image procossing
De-noising is converted with Grouplet.By consulting important database both at home and abroad, do not find Grouplet transformation in engineering and
Application in material science, that is to say, that Grouplet transformation is still a blank in engineering and material science research.It is based on
This, is in 2014, our seminars[20~22]Grouplet transformation is introduced into fracture credit analysis, it is proposed that be based on
The recognition methods of Grouplet-RVM, the method for proposition is with Grouplet average energies, Grouplet reconciliation entropys and Grouplet
The kurtosis amount of being characterized, RVM are identifier, and are successfully applied in Metal Fracture Surface Images identification.The experimental results showed that with small
Wave-RVM recognition methods compares, and the method for proposition, which overcomes small echo-RVM recognition methods, can only obtain the limited direction letter of image
Breath, achieves higher discrimination.Compare with Grouplet-SVM recognition methods, Grouplet-RVM recognition methods and
Grouplet-SVM recognition methods has equally good discrimination, this is because the required supporting vector quantity of Grouplet-RVM
Much less is wanted, is not limited by Mercer theorems in the selection of kernel function, arbitrary kernel function can be built.It is therefore proposed
The recognition speed of method be substantially better than Grouplet-SVM recognition methods, it is this excellent in particular with the increase of training sample
Gesture is more apparent.
However, with the further further investigation of problem, it has been found that the calculation amount of Grouplet-RVM recognition methods is also
It is very big, it is necessary in the case where ensuring discrimination, recognition speed can be increased substantiallyThis is to have very much in engineering
Meaning.Under the promotion of this background, the present invention is on the basis of Grouplet-RVM recognition methods, it is proposed that a kind of new
Grouplet-VRVM (small echo-variation interconnection vector machine in groups) recognition methods, meanwhile, by the method and Grouplet- of proposition
RVM recognition methods has carried out comparative analysis, the validity for the method that experiment show proposes.
Invention content
Based on above-mentioned background technology, the technical problem to be solved by the invention is to provide one kind based on small echo-variation in groups
Interconnection vector machine fracture surface image recognition methods, using Grouplet reconcile entropy, Grouplet average energies, Grouplet kurtosis as
Characteristic quantity, VRVM are applied to as identifier in Metal Fracture Surface Images identification, are keeping identical discrimination, substantially
Degree improves training speed.
The present invention takes following technical scheme to realize above-mentioned purpose.Based on small echo in groups-variation interconnection vector machine fracture figure
As recognition methods, using Grouplet conversion process fracture surface images, to Grouplet coefficients calculate separately Grouplet reconcile entropy,
Then Grouplet kurtosis and Grouplet average energies characteristic feeding VRVM graders are identified, detailed process
It is as follows：
1) Grouplet transformation is carried out to fracture surface image, obtains the Grouplet coefficient subbands of image；
2) be directed to each frequency band output Grouplet coefficients calculated, obtain based on Grouplet reconcile entropy,
The fracture surface image characteristic of Grouplet average energies and Grouplet kurtosis；
Grouplet local entropies：
Grouplet overall situation entropys：
Grouplet reconciliation entropys：
Grouplet kurtosis：
Grouplet average energies：
Wherein：X is the Grouplet coefficients of each frequency band after Grouplet transformation, and M × N is the band scale size,
M, n correspond to the row and column of the frequency band；
P × q is the scale size after all Grouplet coefficients synthesis, and p, q are corresponding row and column；
I, j respectively represent the row and column of the band image；X is the Grouplet coefficients of the frequency band；For the frequency band
The mean value of Grouplet coefficients；σ is standard deviation.
3) fracture surface image characteristic is divided into two parts：A part of fracture surface image characteristic is established for training
VRVM identification models；The characteristic of another part fracture surface image is used for testing classification, is sent into the identification model having had built up
Middle carry out Classification and Identification.
Formula is calculated by three feature vectors above it is found that the Grouplet reconciliation entropys proposed had both reflected the part of image
Texture information, and reflect global Global Information.The Grouplet average energies of proposition are the flat of fracture surface image texture information
Reflect, since Grouplet average energies, Grouplet reconciliation entropys are the quadratic relations of Grouplet coefficients, proposition
Grouplet kurtosis is the biquadratic relationship of Grouplet coefficients, therefore, Grouplet kurtosis ratio Grouplet average energies,
Grouplet reconciliation entropys can more reflect small textural characteristics variation, more sensitive to textural characteristics, be conducive to the spy of fracture surface image
Sign extraction.
The present invention inherits all advantages of small echo in groups and variation interconnection vector machine, with the metal fracture figure based on small echo
As recognition methods compares, limited directional information can only be captured by overcoming this method, cannot efficiently extract the edge of image
The defect of information；Compared with the image-recognizing method based on contourlet transformation, overcomes this method and lack translation invariant
Property and low frequency decompose) redundancy；Compared with the image-recognizing method converted based on Bandelet, this method is overcome several
The limitation what is indicated makes it that can not efficiently indicate that irregular geometry of milli in natural texture structure；With
Grouplet-RVM recognition methods compares, and in the case where ensureing that discrimination does not reduce, recognition speed is greatly improved, and
And with the increase of training samples number, this advantage equally shows more apparent.
The beneficial effects are mainly as follows following four aspects：
1, compared with the image-recognizing method based on wavelet transformation, overcome can only be captured based on wavelet transformation it is limited
Directional information cannot efficiently extract the defect of the marginal information of image；
2, compared with the image-recognizing method based on contourlet transformation, contourlet transformation and wavelet transformation one
Sample, there are a common deficiencies, that is, lack translation invariance, can nearby be produced in the singular point (edge or texture) of processing image
Raw puppet Gibbs phenomenons, the image after reconstruct are alternately present the larger vibration of amplitude up and down near singular point.In addition,
The low frequency transform (LP decomposition) of contourlet transformation has redundancy, redundancy 4/3；.And the present invention overcomes well
This disadvantage of contourlet transformation；
3, compared with the image-recognizing method converted based on Bandelet, although Bandlet can indicate " wheel well
It is wide " figure, but since " piecemeal " in Bandlet algorithms causes the geometry that it can not indicate that relevance is very long in image well
Structure, while the straight line in its support Interval is approximate and not ideal enough for the processing of intersection.These aspects cause
Its limitation on geometric representation makes it that can not efficiently not indicate that irregular geometry knot of milli in natural texture structure
Structure.And the present invention then compensates for this disadvantage；
4, the method proposed inherits all of the transformation of small echo (Grouplet) in groups and variation interconnection vector machine (VRVM)
Advantage, compared with current state-of-the-art Grouplet-RVM recognition methods, invention introduces a kind of improvement interconnection vector machines
Algorithm will calculate more complicated convolution integral operation and be changed to relatively simple logarithm and operation in interconnection vector machine, thus
In the case of ensureing that discrimination does not reduce, recognition speed is greatly improved, and with the increase of training samples number, it is this
Advantage equally shows more apparent.
This method has broad application prospects in image procossing.
Description of the drawings
Fig. 1 is the flow chart of Grouplet-VRVM recognition methods of the present invention；
Fig. 2 is the recognition result schematic diagram of Grouplet average energies-VRVM；
Fig. 3 is the recognition result schematic diagram of Grouplet reconciliation entropys-VRVM；
Fig. 4 is the recognition result schematic diagram of Grouplet kurtosis-VRVM；
In figure：△ cleavage fractures；Dimpled fracture；Zero intergranular fracture.
Specific implementation mode
Below in conjunction with attached drawing, implementation principle and engineer application example, the invention will be further described.Referring to Fig. 1 to Fig. 4.
1, the feature extracting method based on Grouplet transformation
The good localization property of wavelet transformation so that this method has good application prospect in image procossing.
Wavelet coefficient is made to tend not to the textural characteristics for being used directly to indicate image however, the shifting of wavelet coefficient becomes characteristic, therefore,
When image characteristics extraction, usually wavelet coefficient and comentropy are combined, the distribution using the energy sequence of each scale of small echo replaces
The probability distribution of signal, to reflect that the textural characteristics of image, this entropy are known as little Bo Shang [13,14], expression formula is
In formula：piFor opposite wavelet energy, i.e. energy under i-th of scale accounts for the ratio between gross energy.The Wavelet Entropy energy of image
Enough reflection image information number, value is bigger, illustrates that detailed information is abundanter.Break to metal currently, Wavelet Entropy has become
Mouth image carries out the main method of feature extraction.
However, the research with problem is goed deep into, it is found that the Metal Fracture Surface Images feature extraction based on wavelet transformation exists very
Big deficiency is mainly shown as that the support Interval of wavelet transformation is square, and in image processing applications, wavelet transformation can only obtain
The information in the limited direction on the lateral of image, longitudinal direction and diagonal line is taken, therefore singular curve can not be approached well.
The texture information of image can not be extracted when handling the Metal Fracture Surface Images with complex texture well.
It is applied to the deficiency of Metal Fracture Surface Images feature extraction for Wavelet Entropy, Grouplet transformation is introduced by the present invention
It in Metal Fracture Surface Images analysis, and is combined with comentropy, it is proposed that the concept of Grouplet local entropies and Grouplet overall situation entropys.
Its local entropy HcIt is defined as
Here, x is the Grouplet coefficients of each frequency band after Grouplet transformation, and M × N is the band scale size,
M, n correspond to the row and column of the frequency band.
Since local entropy cannot reflect the contact between each frequency band coefficient, for this purpose, Grouplet changes have been also contemplated herein
Global entropy H after changingi, global entropy is the entropy found out after image frequency band coefficient all after Grouplet is converted integrates,
It is defined as follows
Wherein, p × q is the scale size after all Grouplet coefficients synthesis, and p, q are corresponding row and column.
Local entropy stresses the local grain information representation of image, is that the details of each frequency band coefficient embodies.Global entropy is then noted
Weight Global Information, is the synthesis of all frequency band coefficients.Therefore, it is more comprehensively accurate local entropy to can combine to global entropy
Acquisition image information, local entropy and global entropy are asked into harmonic average herein, Grouplet is obtained and reconciles entropy, expression formula is
Since Grouplet reconciliation entropys combine the comentropy and local entropy of fracture surface image, the local detail of image is contained
The whole texture information of information and image can more comprehensively express the area between the fracture surface image of several different texture features
Not.The Grouplet coefficients distribution more sparse compared to small echo so that the Grouplet reconciliation entropy differences of different fracture surface images
Obviously, the difference between different fracture surface images can be more reflected than Wavelet Entropy.
Kurtosis is the numerical statistic amount of a reflection signal distributions characteristic, for describing sign mutation component severe degree
Scalar is normalized fourth central square.Here, kurtosis is introduced into Metal Fracture Surface Images, converts, carry in conjunction with Grouplet
Go out the concept of Grouplet kurtosis, is used for Metal Fracture Surface Images feature extraction.Grouplet kurtosis is defined as
In above formula, M × N is the size of band image, and i, j respectively represent the row and column of the band image；X is the frequency band
Grouplet coefficients；For the mean value of frequency band Grouplet coefficients；σ is standard deviation, and calculating formula is as follows
Meanwhile giving the definition of Grouplet average energies
By formula (5) and formula (7) it is found that Grouplet average energies are the average reflections of fracture surface image texture information, due to
Grouplet average energies are the quadratic relations of Grouplet coefficients, and Grouplet kurtosis is 4 powers of Grouplet coefficients
Relationship, therefore, Grouplet kurtosis ratio Grouplet average energies can more reflect small textural characteristics variation, to textural characteristics
It is more sensitive, be conducive to the feature extraction of fracture surface image.
By formula (4), (5), (7) it is found that Grouplet reconcile entropy, Grouplet kurtosis and Grouplet average energies this three
In the calculating of a characteristic quantity, it is important to determine Grouplet coefficients.
Different from traditional wavelet, the correlation computations of associated domain are introduced in Grouplet transformation.It is M for size
The fracture surface image of × N is defined the two-dimensional grid G of M × N first0, the point in grid corresponds to the pixel of image, in G0It is interior
One group of sub-grid G can be marked offj.By Haar transform, in each scale 2jOn, it is complementary after being decomposed and intersection is not present
Sub-grid Gj+1WithIt will be eachPoint be associated with m ∈ Gj+1Point on, can thus be preserved in each scale
The position relationship of each point in sub-grid, the distance between these points are exactly relating value, are stored inIn, AjIt is exactly
Associated domain.
For low frequency coefficient aJ(i.e. mean coefficient) and high frequency coefficient dj(i.e. detail coefficients), Grouplet transformation calculations go out
Standardization details between two associations are average[19]：
New weighted average is respectively[19]：
New weighted valueIt calculates as follows：
These values are stored in：
In formula (11), m ∈ Gj.In out to out 2JOn, mean coefficient is normalized：
Each scale detail coefficients of fracture surface image are calculated by formula (8)-(12)Mean coefficient aJ[m]And associated domain
CoefficientFracture is found out herein by each scale detail coefficients and mean coefficient of the Grouplet transformation to fracture surface image
Each category feature of image.By above-mentioned various it is recognised that Grouplet transformation contains each hierachical decomposition coefficient and these rulers
Association domain coefficient on degree, making while handling image to the calculating of associated domain also can reservation figure to the greatest extent
The texture structure of picture.Fracture surface image coefficient based on Grouplet transformation possesses the details abundanter than wavelet coefficient and indicates,
Opposite wavelet transformation can only can compare wavelet transformation from horizontal, vertical and diagonal approximating curve, Grouplet transformation
Singular curve is more effectively approached, the geometry regularity of fracture surface image is more fully utilized.
2, variation interconnection vector machine (VRVM) identification model and algorithm：
In traditional probabilistic model, stochastic variable can be divided into observation data D and non-viewing variable θ[23].Wherein, it observes
The marginal probability density of data D is：
P (D)=∫ P (D, θ) d θ； (13)
The integral and calculating of usual formula (13) is complex, and a similar distribution Q (θ) is incorporated herein to improve answering for calculating
Miscellaneous degree.For parameter θ, the integral and calculating form of the marginal probability density of this non-viewing data can be improved to first carry out
Then Logarithmic calculation is added again, that is, formula (13) is write as：
LnP (D)=L (Q)+KL(Q|P)； (14)
In formula：
Wherein, the similar distribution Q (θ) of use is probability density P (D, θ) and Posterior distrbutionp KL(Q|P the relative entropy between)
Range difference：
Here, KL(Q|) >=0, and L (Q)+K PL(Q|P) it is being independently distributed for Q, therefore maximizes L (Q) and be equivalent to minimum
KL(Q|P), convolution (15), (16), Q (θ) are exactly P (θ |D APPROXIMATE DISTRIBUTION).By this approximation method, one is selected
Suitable distribution Q, can be so that entire calculating process be simplified, it is therefore desirable to construct a simple Q distribution.
According to formula (13) and in view of the variant { θ of parameter θiCan then be defined as：
Wherein：
Wherein, < lnP (D, θ) >k≠iIt is Qk(θk) it is distributed the expectation of (wherein k ≠ i).Easy proof obtains, if probability
Model is expressed as a node of each factor in a directed acyclic graph, then Qi(θi) it is dependent on the variable shape of Q distributions
Formula[23]。
The right half part of formula (18) depends on Qk≠iAny time, the left-half of formula (18) is the condition distribution of conjugation,
So the required Q of standard profilek≠iMoment is easy to get[23,24].At the time of being easily found iteration initialization, then by following
Ring iterative more newly arrives to obtain final value.
More complicated than regressive case in the case of classification, there is no the hierarchical structures being completely conjugated in the case.It gives
The marginal probability for going out input data is：
ln P(T|X)=ln ∫ ∫ P (T|X,ω)P(ω|α)P(α)dωdα； (19)
Convolution (18), improved interconnection vector machine can be approximated to be：
The calculating process of above formula is obviously too complicated, to simplify operation, according to document[25]In analysis method introduce following formula：
In formula, z=(2t-1) y, λ (ξ)=(1/4 ξ) tanh (ξ/2), ξ is the parameter of a variation, and formula (21) are substituted into
In identification model,
It can obtain：
In formula,And meet condition P (T|X, ω)/F (T, X, ω, ξ) >=1 is equal to ln P
(T|X, ω)/F (T, X, ω, ξ) >=0, formula (22) is substituted into formula (20), is obtained：
Function Q on the right of optimized-type (23)ω(ω) and Qα(α) and parameter ξ={ ξn, optimum results Qω(ω) is generated
One normal distribution form：
Qω(ω)=N (ω |m,S)； (24)
Parameter in formula is respectivelyAnd A=
diag(am)。
The result that optimization generates makes Qα(α) is to obey gamma to be distributed：
Variational parameter ξnEstimated value again be calculated by following formula：
Same method obtains：
L=< lnF>+<lnP(ω|α)>+<lnP(α)>-<lnQw(ω)>-<lnQa(α)>； (27)
Wherein：
It will be apparent that in the identification model of entire VRVM, by the deformation improvement to complicated calculations form, calculating is optimized
Speed, it is clear that by logarithm and operation come to substitute convolution algorithm be simple and feasible.
3, small echo-variation interconnection vector machine (Grouplet-VRVM) recognition methods in groups：
Metal fracture recognition methods (abbreviation Grouplet-VRVM) based on Grouplet-VRVM is as shown in Figure 1.Control
Fig. 1 illustrates this method.The detailed process of this method is as follows：
1) Grouplet transformation is carried out to images to be recognized, each scale details of fracture surface image is calculated by formula (8)-(12)
CoefficientMean coefficient aJ[m]Be associated with domain coefficient
2) be directed to each frequency band output Grouplet coefficients calculated, obtain based on Grouplet reconcile entropy,
The other fracture surface image characteristic of Grouplet average energies, three type of Grouplet kurtosis.Grouplet reconciliations entropy,
Grouplet average energies, the calculating formula of Grouplet kurtosis are shown in formula (4), (5), (7).
3) characteristic of fracture surface image is divided into two parts, a part of fracture surface image characteristic is established for training
VRVM identification models；The characteristic of another part fracture surface image is used for testing classification, is sent into the identification model having had built up
Middle carry out Classification and Identification.
4, engineer application example：
100 cleavage fractures, 100 dimpled fractures are had chosen herein, and 22 intergranular fractures, size is 256 × 256.
In order to verify proposition method validity, here, by the method for proposition also with Grouplet-RVM, Grouplet-SVM identify
Method has carried out comparative analysis.
The VRVM recognition effect comparative analyses of the feature vector of 4.1 different Grouplet coefficients：
Fig. 2, Fig. 3, Fig. 4 be respectively extracted fracture surface image Grouplet average energies, Grouplet reconciliation entropy,
Three kinds of characteristics of Grouplet kurtosis, are sequentially inputted to the recognition result being trained in RVM identifiers.
By Fig. 2, Fig. 3 and Fig. 4 it is found that there are 18 fracture surface images using Grouplet average energy-VRVM recognition methods
It is misjudged, discrimination 83.78%.There are 17 fracture surface images misjudged using Grouplet reconciliation entropy-VRVM recognition methods,
Discrimination is 84.68%.Using Grouplet kurtosis-VRVM recognition methods, after identification, there is 1 cleavage fracture misjudged
For dimpled fracture, 5 intergranular fractures are mistaken for dimpled fracture, discrimination 94.59%.Image based on Grouplet kurtosis
Recognition methods is substantially better than the image-recognizing method based on Grouplet average energies, Grouplet reconciliation entropys.
These three recognition methods are using identical identifier, except that the characteristic parameter used is different, respectively
It is Grouplet average energies, Grouplet reconciliations entropy, Grouplet kurtosis.By formula (4), (5), (7) it is found that Grouplet is flat
Equal energy and Grouplet reconciliation entropys are 2 power relationships of Grouplet coefficients, and Grouplet kurtosis is the 4 of Grouplet coefficients
Power relationship.Obviously, in terms of reflecting metal fracture textural characteristics variation, Grouplet kurtosis ratio Grouplet average energies,
Grouplet reconciliation entropys are more sensitive.When metal fracture textural characteristics vary slightly, the characteristic value of Grouplet kurtosis will have
Significant changes, be probably Grouplet average energies, Grouplet reconcile entropy changing features nearly a hundred times, therefore,
Grouplet kurtosis is particularly suited for the feature of extraction Metal Fracture Surface Images.
The recognition methods comparative analysis of 4.2 Grouplet-VRVM and Grouplet-RVM, Grouplet-SVM
These three recognition methods of Grouplet-VRVM, Grouplet-RVM and Grouplet-SVM are using identical
Characteristic utilizes the characteristic of Grouplet transformation extraction fracture surface images, the difference is that the grader used is not
Together.In Grouplet-VRVM recognition methods, using variation interconnection vector machine, in Grouplet-RVM recognition methods,
Using traditional interconnection vector machine, and in Grouplet-SVM recognition methods, using support vector machines.These three
The recognition result of method is as shown in table 1.
1 three kinds of recognition methods identification recognition effect comparisons of table
As shown in Table 1, these three recognition methods all achieve satisfied separating effect.In particular by Grouplet kurtosis
When as feature vector, discrimination reaches 94.59%.For using identical feature vector, the identification between this three's method
Rate gap is simultaneously little.However, the recognition speed of these three methods has apparent difference, as shown in table 2.
2 three kinds of recognition methods identification recognition time comparisons of table
As shown in Table 2, the training time of Grouplet-VRVM, Grouplet-RVM recognition methods is far fewer than Grouplet-
SVM recognition methods.In to the identification of 222 fracture surface images in total, Grouplet-VRVM recognition times are 1.87s,
Grouplet-RVM recognition times are 2.11s, and are averaged recognition time based on Grouplet-SVM as 12.75s, are
7 times or so the time required to Grouplet-VRVM recognition methods, 6 times or so the time required to Grouplet-RVM recognition methods.
This is because the supporting vector quantity of Grouplet-SVM recognition methods is with the linear growth of the increase of training sample, excessive
Supporting vector does not only result in Grouplet-SVM recognition methods and there is a possibility that overfitting, and the training time is caused to increase
Add, recognition speed reduces, and kernel function will also meet Mercer conditions.And relative to Grouplet-SVM recognition methods,
Grouplet-VRVM, Grouplet-RVM recognition methods have better generalization ability, and solution is more sparse, apply to point
When class problem, a kind of probability metrics can be provided to the ownership of classification, and required supporting vector quantity wants much less, in core
It is not limited by Mercer theorems in the selection of function, arbitrary kernel function can be built.In particular with carrying for training sample
It rises, the recognition speed advantage of Grouplet-VRVM, Grouplet-RVM recognition methods is more apparent.
By table 2 it is also found that the opposite Grouplet-RVM recognition methods of Grouplet-VRVM recognition methods is in training
Between on decrease, this is because in Grouplet-VRVM recognition methods, by the association of Grouplet-RVM recognition methods to
More complicated convolution integral operation is calculated in amount machine and is changed to relatively simple logarithm and operation, thus greatly reduces RVM's
Calculation amount.Therefore, Grouplet-VRVM recognition methods still has certain advantage, and with the increase of training samples number,
This Heterosis must be also more apparent.
It follows that the present invention provides a kind of very outstanding image-recognizing methods, not only there is very high identification to imitate
Rate, moreover, recognition speed is also significantly improved.The method of proposition is before image processing field has wide application
Scape.
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Claims (1)
1. small echo-variation interconnection vector machine fracture surface image recognition methods in groups is based on, using Grouplet conversion process fracture figures
Picture obtains the Grouplet coefficient subbands of image；It is calculated, is obtained for the Grouplet coefficients of each frequency band output
The fracture surface image characteristic of Grouplet reconciliations entropy, Grouplet average energies and Grouplet kurtosis；Then, VRVM is established
Fracture surface image identification model；In traditional probabilistic model, stochastic variable can be divided into observation data D and non-viewing variable θ；Its
In, the marginal probability density of observation data D is：P (D)=∫ P (D, θ) d θ；
It is characterized in that, when establishing VRVM fracture surface image identification models, by the side of the non-viewing data of traditional probabilistic model
The integral and calculating form of edge probability density is changed to first carry out Logarithmic calculation, then is added, and then, selects a suitable distribution Q
(θ) improves the complexity of calculating；For this purpose, for parameter θ, above formula is write as：
LnP (D)=L (Q)+KL(Q|P)；
In formula：
Wherein, the similar distribution Q (θ) of use is probability density P (D, θ) and Posterior distrbutionp KL(Q|P the relative entropy distance between)
Difference：
Here, KL(Q|) >=0, and L (Q)+K PL(Q|P) it is being independently distributed for Q, therefore maximizes the K that L (Q) is equivalent to minimumL
(Q|P), in conjunction with above formula L (Q) and KL(Q|P expression formula), Q (θ) are exactly P (θ |D APPROXIMATE DISTRIBUTION)；In view of P (D)=∫ P
Variant { the θ of (D, θ) d θ and parameter θi, Q (θ) may be defined as：
Wherein：
Wherein, < lnP (D, θ) >k≠iIt is Qk(θk) distribution expectation, wherein k ≠ i；
Then, it updates to obtain final value by loop iteration；
For the grader of fracture surface image, the marginal probability for providing input data is：
lnP(T|X)=ln ∫ ∫ P (T|X,ω)P(ω|α)P(α)dωdα；
According to above thinking, improved interconnection vector machine can approximation obtain：
lnP(T|X) >=L=<lnF>+<lnP(ω|α)>+<lnP(α)>-<lnQw(ω)>-<lnQa(α)>；
Wherein：
In this way, completing the foundation of VRVM fracture surface image identification models；
Finally, it is input to foundation using the Grouplet of extraction reconciliations entropy, Grouplet average energies, Grouplet kurtosis
It is trained and identifies in VRVM fracture surface image identification models.
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