CN109657690B - Image texture feature extraction and identification method based on multivariate logarithm Gaussian mixture model - Google Patents

Image texture feature extraction and identification method based on multivariate logarithm Gaussian mixture model Download PDF

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CN109657690B
CN109657690B CN201811575477.7A CN201811575477A CN109657690B CN 109657690 B CN109657690 B CN 109657690B CN 201811575477 A CN201811575477 A CN 201811575477A CN 109657690 B CN109657690 B CN 109657690B
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陈熙
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Guizhou Education University
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G06V10/40—Extraction of image or video features
    • G06V10/46—Descriptors for shape, contour or point-related descriptors, e.g. scale invariant feature transform [SIFT] or bags of words [BoW]; Salient regional features
    • G06V10/462—Salient features, e.g. scale invariant feature transforms [SIFT]
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Abstract

The invention relates to an image texture feature extraction and identification method based on a multivariate logarithmic Gaussian mixture model, and belongs to the technical field of pattern identification. Firstly, filtering a texture image by adopting a Gaussian two-dimensional Gabor filter, and constructing a logarithmic Gaussian random vector; performing parameter modeling on a logarithmic Gaussian random vector by adopting a multivariate logarithmic Gaussian probability model; performing parameter modeling on the logarithmic Gaussian random vector by adopting a plurality of multivariate logarithmic Gaussian probability models; estimating parameters theta related to the multivariate logarithmic Gaussian probability hybrid model obtained by parameter modeling by adopting the expectation maximization to obtain the multivariate logarithmic Gaussian probability hybrid model; and finally, calculating the probability that the texture image to be classified belongs to the multivariable logarithm Gaussian mixture model of various images, wherein the probability is the basis of classification. The method can effectively identify the texture image with the statistical characteristics of non-Gaussian and thick trailing.

Description

Image texture feature extraction and identification method based on multivariate logarithm Gaussian mixture model
Technical Field
The invention relates to an image texture feature extraction and identification method based on a multivariate logarithm Gaussian mixture model, and belongs to the technical field of pattern identification.
Background
Texture is an important feature of images and is widely applied to the fields of pattern recognition and computer vision. Texture statistics is an important method for texture recognition, and current texture statistical models can be divided into gaussian statistical models and non-gaussian statistical models. The two-dimensional Gabor filter is an effective image texture feature extraction method. Research on two-dimensional Gabor filters has focused mainly on two-dimensional Gabor filter parameter selection, fast computation, and a wide variety of applications. At present, a very small amount of statistical characteristics of results obtained after Gabor filtering of working research images exist, and a Gaussian probability model is mainly adopted for research, wherein the statistical characteristics comprise mean values, covariance, probability density and the like.
By performing statistical analysis on the result of the Gabor filtering of the texture image, the distribution of the Gabor filtering is found not to be subjected to Gaussian distribution, but to have thick trailing non-Gaussian characteristics, so that a non-Gaussian model, namely a logarithmic Gaussian model, is adopted to perform statistical modeling on the result of the Gabor filtering of the texture image.
Disclosure of Invention
The invention provides an image texture feature extraction and identification method based on a multivariate logarithm Gaussian mixture model, which is used for solving the problem of extraction and identification of texture image features with thick trailing features in texture statistical distribution. Aiming at the defect that the traditional Gaussian mixture model cannot model thick-trailing statistical distribution, the image texture feature extraction and identification method based on the multivariate logarithm Gaussian mixture model can model thick-trailing statistical distribution, and the texture image identification rate is high.
The technical scheme of the invention is as follows: a multivariate logarithm Gaussian mixture model-based image texture feature extraction and identification method comprises the following specific steps:
step1, firstly, filtering a texture image by adopting a Gaussian two-dimensional Gabor filter, and constructing a logarithmic Gaussian random vector;
the definition of Step1.1, gaussian two-dimensional Gabor filter is as follows:
Figure BDA0001916624130000011
wherein
Figure BDA0001916624130000021
k v ＝k max /f v ，
Figure BDA0001916624130000022
k max Is the maximum frequency, typically k max ＝π/2，
Figure BDA0001916624130000023
The scale parameter v takes the value v = 0.., 4, and the direction parameter μ takes the values μ =0,1,2,3, z = (h, s) and | | z | = (h, s) 2 +s 2 ) H, s denote the coordinates of a gaussian two-dimensional Gabor filter, where i denotes the imaginary unit; the parameter sigma determines the bandwidth of the Gauss two-dimensional Gabor filter, and the value is 2 pi;
step1.2, assuming that the texture image is represented as I (h, s), and h, s also represent the coordinates of the image, the result obtained after filtering by using the gaussian two-dimensional Gabor filter is represented as a complex matrix: r u,v (h,s)＝ψ μ,v (h, s) I (h, s); step step1.1 refers to z = (h, s), so ψ μ,v (h, s) is psi μ,v (z), I (h, s) represents an image, I (h, s) and psi μ,v In (h, s), h and s respectively represent an abscissa and an ordinate;
step1.3, constructing a logarithmic Gaussian random vector X;
let abs (R) u,v (h, s)) represents the resulting complex matrix R obtained after filtering u,v The modulus of (h, s), i.e. the amplitude of the filtering result, vector Hist (abs (R)) u,v (h, s))) represents abs (R u,v (h, s)) histogram vector from Hist (abs (R) u,v (h, s))) to construct a logarithmic gaussian random variable X u,v The logarithmic Gaussian random vector X is composed of logarithmic Gaussian random variables X u,v To construct a log-gaussian random vector X containing 40 log-gaussian random variables as:
Figure BDA0001916624130000024
wherein, if histogram vector Hist (abs (R)) u,v (h, s))) is 128, a log gaussian random vector X formed by the texture image after Gabor filtering and histogram vector calculation corresponds to 128 sample vectors with the length of 40; wherein, the 1 st sample of all random variables in the logarithmic Gaussian random vector X forms the 1 st sample vector, the 2 nd sample of all random variables in the logarithmic Gaussian random vector X forms the 2 nd sample vector, and so on; the 128 th sample of all random variables in the log-gaussian random vector X constitutes the 128 th sample vector. The extraction of the texture image features refers to the logarithmic Gaussian random vector obtained in the step Step1.3.
Further, when the texture recognition is actually performed by using the method provided by the invention, all random variables do not need to be selected when the logarithmic gaussian random vector X is selected in step1.3, and a subset of the random vector X in the formula (2) is actually selected.
Step2, performing parameter modeling on the logarithmic Gaussian random vector X by adopting a multivariate logarithmic Gaussian probability model to obtain a logarithmic Gaussian probability function model of the parameterized logarithmic Gaussian random vector X;
assuming that there is a gaussian random vector Y: [ Y ] 0,0 ,Y 0,1 ,...,Y 0,4 ,Y 1,0 ,Y 1,1 ,...,Y 1,4 ,...,Y 7,0 ,Y 7,1 ,...,Y 7,4 ]The mean vector and covariance are respectively mu and sigma, and X is defined according to the logarithm Gaussian random variable u,v ＝exp(Y u,v ) Then, the log gaussian probability function model of the log gaussian random vector X is:
Figure BDA0001916624130000031
f X (x) And can be written as: f. of X (x) = f (X | θ), where the parameter θ represents the mean vector μ and covariance matrix Σ in the logarithmic gaussian random vector X probability density function; x is a radical of a fluorine atom 1 ,x 2 ,...,x 40 Is 40 random variables of a logarithmic gaussian random vector X.
Step3, performing parameter modeling on the logarithmic Gaussian random vector X by adopting a plurality of multivariate logarithmic Gaussian probability models to obtain a parameterized multivariate logarithmic Gaussian probability mixture model, wherein the model is as follows:
Figure BDA0001916624130000032
in this model, the parameter Θ = (ω =) is present 1 ,ω 2 ,…,ω M ,θ 1 ,θ 2 ,…,θ M ) Wherein
Figure BDA0001916624130000033
ω i Representing the mixing coefficient, theta, of the ith multivariate logarithmic Gaussian probability mixture model i Representing the mean vector μ in the ith multivariate logarithmic Gaussian probability model i Sum covariance matrix Σ i ；p i (x|θ i ) Representing the probability of image X in the ith multivariate log-gaussian probability model, the number of M multivariate log-gaussian probability models, and p (X | Θ) also representing the multivariate log-gaussian probability mixture model of the log-gaussian random vector X.
Step4, estimating parameters theta related in the multivariate logarithmic Gaussian probability mixture model obtained by parameter modeling by adopting the expectation maximization to obtain the multivariate logarithmic Gaussian probability mixture model;
the main steps of the estimation are as follows:
step4.1, initializing theta to be theta 0 ，
Figure BDA0001916624130000034
Step4.2, let t =1, the following cycle is started:
Figure BDA0001916624130000041
Figure BDA0001916624130000042
Figure BDA0001916624130000043
Figure BDA0001916624130000044
Figure BDA0001916624130000045
t＝t+1
when the parameter theta t When the change is not large or the preset cycle step number is reached, the cycle is stopped;
in the above cycle, t is a cycle variable, x j N sample vectors are used in the cycle for parameter estimation, wherein the j sample vector is a logarithm Gaussian random vector X; through the circulation, the parameter theta can be obtained, so that a multivariate logarithmic Gaussian probability mixture model p (x | theta) in a formula (4) is obtained;
Figure BDA0001916624130000046
represents omega in the process of t-1 iteration l A value of (d);
Figure BDA00019166241300000412
represents theta in the t-1 th iteration process l A value of (d); theta t-1 Representing the value of theta in the t-1 iteration process;
Figure BDA0001916624130000048
represents the mu in the t-1 iteration process l A value of (d);
Figure BDA0001916624130000049
representing Σ in the t-th iteration l A value of (d); p (l | x) j ,Θ t-1 ) An intermediate variable during the t-1 th iteration is shown.
The step Step4.1 comprises the following steps:
step4.1.1, initialize theta 0 Then, clustering a certain type of samples to be classified by adopting a fuzzy C-means clustering algorithm, taking the formed clustering number A as the number M of the models in the multivariate log Gaussian probability mixed model, and then calculating the mean vector of each cluster to initialize the expected vector corresponding to the multivariate log Gaussian probability model;
step4.1.2, assume that a cluster contains x 1 ,x 2 ,…,x t A sample, then matrix
Figure BDA00019166241300000410
Initializing a covariance matrix corresponding to a multivariate logarithmic Gaussian probability model; mixing coefficient omega of ith multivariate logarithmic Gaussian probability mixture model i (i =1,2, \ 8230;, M) is initialized to
Figure BDA00019166241300000411
The criterion for the end of the iteration is | Θ t -Θ t-1 |/|Θ t-1 The | is less than 0.1 or the iteration number reaches 40.
And Step5, finally, calculating the probability that the texture image to be classified belongs to the multivariable logarithm Gaussian mixture model of various images, wherein the probability is the basis of classification.
Assuming that the texture images to be identified and classified have c classes, extracting a part of image from each class of texture image, and then obtaining a multivariate logarithmic Gaussian probability mixture model of each class of texture image by using the method introduced in Step4, wherein the multivariate logarithmic Gaussian probability mixture model is respectively expressed as p (x | theta) 1 ),p(x|Θ 2 ),…,p(x|Θ c ) (ii) a For a sample image x to be classified, its corresponding Gabor histogram is 128 40-dimensional vectors, denoted as x 1 ,x 2 ,…,x 128 The classification of the image x is then completed by the following method steps:
(1) And calculating
Figure BDA0001916624130000051
Wherein "c" represents the total number of categories of the image; p (theta) m ) Is the probability of class m, let p (Θ) 1 )＝p(Θ 2 )＝…＝p(Θ c )＝1/c，
Figure BDA0001916624130000052
Representing a vector x i The probability of (d); p (x) i |Θ m ) Representing a vector x i Probability of belonging to class m;
(2) If p (theta) m I x) is p (Θ) 1 |x),p(Θ 2 |x),…,p(Θ c | x), the class of image x is class m, where p (Θ) m | x) represents the probability that image x belongs to the mth multivariate log gaussian mixture probability model.
Log gaussian probability density is a probability density function developed from gaussian probability density with thick tail. The two-dimensional Gabor filtering results of the images under specific scales and directions are modeled by adopting logarithmic Gaussian random variables, then the filtering results of the texture images under different scales and different directions can be modeled by adopting a plurality of logarithmic Gaussian random variables, so that a logarithmic Gaussian random vector related to the two-dimensional Gabor filtering results is constructed, and the statistical characteristics of the texture images can be better described by modeling the vector by adopting a multivariate logarithmic Gaussian mixture model.
The multivariate logarithm Gaussian mixture model modeling is carried out on the two-dimensional Gabor filtering result of the texture image, which is a new application of the two-dimensional Gabor filter and a new development of the Gaussian mixture model texture modeling. Experiments in the aspect of texture recognition show that the multivariate logarithmic Gaussian mixture model modeling on the two-dimensional Gabor filtering result of the texture image is superior to the traditional Gaussian mixture model texture modeling method.
The invention has the beneficial effects that:
1. according to the method, non-Gaussian and thick-trailing statistical modeling is carried out on the Gaussian two-dimensional Gabor filtering result of the texture image, the modeling method is a multivariable logarithmic Gaussian mixture model, and the defect that the traditional Gaussian mixture model cannot model thick-trailing statistical characteristics is overcome;
2. when multivariate logarithmic Gaussian distribution modeling is carried out on the texture image Gauss two-dimensional Gabor filtering result, part of logarithmic Gaussian random variables are selected, the identification precision of the texture image is improved, and meanwhile, the complexity and the calculated amount of modeling are reduced;
3. in the matching identification stage, the algorithm adopted by the invention is simple and convenient to calculate, and can realize real-time image matching identification.
Drawings
FIG. 1 is a schematic block diagram of the step of extracting image texture features based on multivariate logarithmic Gaussian mixture model in the present invention;
wherein, the MLGMM 1 ,MLGMM 2 ,…,MLGMM C Respectively representing the 1 st sample, the 2 nd sample, \ 9476, the multivariate logarithmic Gaussian mixture model established by the c-th sample, theta 1 ,Θ 2 ，…,Θ C Is a model 1,2, \ 8230, parameter of C;
FIG. 2 (a) is a sample image representative of 4 types of textures in a Brodatz texture database used in the present invention, from left to right, bark, beach sand, wood grain, and Plastic bubbles; FIG. 2 (b) is a representative sample image of class 4 textures in the USPTex texture database used in the present invention;
FIG. 3 is the average recognition rate (%) of the algorithm in the case of different numbers of training samples in the USPTex texture database in example 1 of the present invention;
FIG. 4 is the average recognition rate (%) of the algorithm in example 2 of the present invention under different numbers of training samples in the Brodatz texture database.
The icons in fig. 3 and 4 are as follows:
Figure BDA0001916624130000061
represents the algorithm "Steerable Sub-Gaussian Modeling" proposed by G Tzagkarakis et al 2008;
Figure BDA0001916624130000062
represents the algorithm "Multivariate Generalized Gaussian Mixture Model" proposed by KN Kumar in 2015;
Figure BDA0001916624130000063
representing the multi-variable logarithm Gaussian mixed probability model algorithm provided by the invention;
Figure BDA0001916624130000064
represents the "Gaussian mixture model" algorithm proposed by Kim S C in 2007.
Detailed Description
Example 1: as shown in fig. 1, a method for extracting and identifying image texture features based on a multivariate logarithmic gaussian mixture model includes the following specific steps:
step1, firstly, filtering a texture image by adopting a Gaussian two-dimensional Gabor filter, and constructing a logarithmic Gaussian random vector;
the definition of the Step1.1, gaussian two-dimensional Gabor filter is as follows:
Figure BDA0001916624130000065
wherein
Figure BDA0001916624130000066
k v ＝k max /f v ，
Figure BDA0001916624130000067
k max Is the maximum frequency, typically k max ＝π/2，
Figure BDA0001916624130000071
The scale parameter v takes the value v = 0.., 4, and the direction parameter μ takes the values μ =0,1,2,3, z = (h, s) and | | z | = (h, s) 2 +s 2 ) H, s denote the coordinates of a gaussian two-dimensional Gabor filter, where i denotes the imaginary unit; the parameter sigma determines the bandwidth of a Gaussian two-dimensional Gabor filter, and the value is 2 pi;
step1.2, assuming that the texture image is represented as I (h, s), and h, s also represent the coordinates of the image, the result obtained after filtering with the gaussian two-dimensional Gabor filter is represented as a complex matrix: r is u,v (h,s)＝ψ μ,v (h, s) I (h, s); step step1.1 mentions z = (h, s), so ψ μ,v (h, s) is psi μ,v (z), I (h, s) represents an image, I (h, s) and psi μ,v (h, s) wherein h, s respectively represent the abscissa and the ordinate;
step1.3, constructing a logarithmic Gaussian random vector X;
let abs (R) u,v (h, s)) represents the resulting complex matrix R obtained after filtering u,v The norm of (h, s), i.e. the magnitude of the filtering result, vector Hist (abs (R) u,v (h, s))) represents abs (R) u,v (h, s)) histogram vector from Hist (abs (R) u,v (h, s))) to construct a logarithmic gaussian random variable X u,v The logarithmic Gaussian random vector X is composed of logarithmic Gaussian random variables X u,v Composition, thus constructing a log-gaussian random vector X containing 40 log-gaussian random variables as:
Figure BDA0001916624130000072
wherein, if histogram vector Hist (abs (R) u,v (h, s))) has a length of 128, a logarithmic gaussian random vector X formed by the Gabor filtering and histogram vector calculation of one texture image corresponds to 128 sample vectors with the length of 40; wherein, the 1 st sample of all random variables in the logarithmic Gaussian random vector X forms the 1 st sample vector, the 2 nd sample of all random variables in the logarithmic Gaussian random vector X forms the 2 nd sample vector, and so on; the 128 th sample of all random variables in the log-gaussian random vector X constitutes the 128 th sample vector. The extraction of the texture image features refers to logarithmic Gaussian random vectors obtained in the steps Step1.3 and 1.3.
Further, when the method is actually applied to texture recognition, all random variables do not need to be selected when the logarithmic gaussian random vector X is selected in step1.3, and a subset of the random vector X in the formula (2) is actually selected.
Step2, performing parameter modeling on the logarithmic Gaussian random vector X by adopting a multivariable logarithmic Gaussian probability model to obtain a logarithmic Gaussian probability function model of the parameterized logarithmic Gaussian random vector X;
suppose there is a Gaussian random vector Y: [ Y 0,0 ,Y 0,1 ,...,Y 0,4 ,Y 1,0 ,Y 1,1 ,...,Y 1,4 ,...,Y 7,0 ,Y 7,1 ,...,Y 7,4 ]The mean vector and covariance are mu and sigma respectively, and X is defined according to the logarithmic Gaussian random variable u,v ＝exp(Y u,v ) Then, the log gaussian probability function model of the log gaussian random vector X is:
Figure BDA0001916624130000081
f X (x) And can be written as: f. of X (x) = f (X | θ), where the parameter θ represents the mean vector μ and covariance matrix Σ in the log gaussian random vector X probability density function; x is a radical of a fluorine atom 1 ,x 2 ,...,x 40 Is 40 random variables of a logarithmic gaussian random vector X.
Step3, performing parameter modeling on the logarithmic Gaussian random vector X by adopting a plurality of multivariate logarithmic Gaussian probability models to obtain a parameterized multivariate logarithmic Gaussian probability mixture model, wherein the model is as follows:
Figure BDA0001916624130000082
in this model, the parameter Θ = (ω =) is present 1 ,ω 2 ,…,ω M ,θ 1 ,θ 2 ,…,θ M ) In which
Figure BDA0001916624130000083
ω i The mixing coefficient, theta, representing the ith multivariate logarithmic Gaussian probability mixture model i Representing the mean vector μ in the ith multivariate logarithmic Gaussian probability model i Sum covariance matrix Σ i ；p i (x|θ i ) The probability of the image X in the ith multivariate log-gaussian probability model, the number of M multivariate log-gaussian probability models, and p (X | Θ) also represent the multivariate log-gaussian probability mixture model of the log-gaussian random vector X.
Step4, estimating parameters theta related in the multivariate logarithmic Gaussian probability mixture model obtained by parameter modeling by adopting the expectation maximization to obtain the multivariate logarithmic Gaussian probability mixture model;
the main steps of the estimation are as follows:
step4.1, initializing theta to be theta 0 ，
Figure BDA0001916624130000084
Step4.2, let t =1, the following cycle is started:
Figure BDA0001916624130000085
Figure BDA0001916624130000091
Figure BDA0001916624130000092
Figure BDA0001916624130000093
Figure BDA0001916624130000094
t＝t+1
when the parameter theta t When the change is not large or the preset cycle step number is reached, the cycle is stopped;
in the above cycle, t is a cycle variable, x j For the jth sample vector of the logarithmic Gaussian random vector X, n sample vectors are used in the above cycle for parameter estimation; through the above circulation, the parameter Θ can be obtained, thereby obtaining the multivariate logarithmic Gaussian probability mixture model p (x | Θ) in the formula (4);
Figure BDA0001916624130000095
represents omega in the t-1 th iteration process l A value of (d);
Figure BDA0001916624130000096
represents theta in the t-1 th iteration process l A value of (d); theta t-1 Representing the value of theta in the t-1 iteration process;
Figure BDA0001916624130000097
represents μ in the t-1 th iteration l A value of (d);
Figure BDA00019166241300000911
representing Σ in the t-th iteration l A value of (d); p (l | x) j ,Θ t-1 ) An intermediate variable during the t-1 th iteration is shown.
The step Step4.1 comprises the following steps:
step4.1.1, initialize theta 0 Then, clustering a certain type of samples to be classified by adopting a fuzzy C-means clustering algorithm, taking the formed cluster number A as the number M of the models in the multivariate logarithmic Gaussian probability mixed model, and then calculating the mean vector of each cluster and initializing the expected vector corresponding to the multivariate logarithmic Gaussian probability model;
step4.1.2, assuming that a cluster contains x 1 ,x 2 ,…,x t A sample, then matrix
Figure BDA0001916624130000099
Initializing a covariance matrix corresponding to a multivariate logarithmic Gaussian probability model; mixing coefficient omega of ith multivariable logarithmic Gaussian probability mixture model i (i =1,2, \ 8230;, M) is initialized to
Figure BDA00019166241300000910
The criterion for the end of the iteration is | Θ t -Θ t-1 |/|Θ t-1 The | is less than 0.1 or the iteration number reaches 40.
And Step5, finally, calculating the probability that the texture image to be classified belongs to the multivariable logarithm Gaussian mixture model of various images, wherein the probability is the basis of classification.
Assuming that the texture images to be identified and classified have c classes, extracting a part of image from each class of texture image, and then obtaining a multivariate logarithmic Gaussian probability mixture model of each class of texture image by using the method introduced in Step4, wherein the multivariate logarithmic Gaussian probability mixture model is respectively expressed as p (x | theta) 1 ),p(x|Θ 2 ),…,p(x|Θ c ) (ii) a For a sample image x to be classified, the corresponding Gabor histogram is 128 vectors of 40 dimensions, which are expressed as x 1 ,x 2 ,…,x 128 The classification of the image x is then completed by the following method steps:
(1) And calculating
Figure BDA0001916624130000101
Wherein "c" represents the total number of categories of the image; p (theta) m ) Is the probability of class m, let p (Θ) 1 )＝p(Θ 2 )＝…＝p(Θ c )＝1/c，
Figure BDA0001916624130000102
Representing a vector x i The probability of (d); p (x) i |Θ m ) Representing a vector x i Probability of belonging to class m;
(2) If p (theta) m I x) is p (Θ) 1 |x),p(Θ 2 |x),…,p(Θ c | x), the class of image x is class m, where p (Θ) m | x) represents the probability that the image x belongs to the mth multivariate logarithmic gaussian mixture probability model.
This example further makes statistics that the method is performed in the USPTex texture database [ backs, a.r.; casanova, d.; bruno, O.M. color texture analysis based on detailed descriptors Pattern Recognition,45 (5): 1984-1992,2012.]And drawing a corresponding recognition performance curve according to the relation between the medium recognition rate and the number of the training samples. The texture picture set used in this embodiment has 191 types of texture images, each type of texture has 12 different texture pictures, and total 2292 pictures have a picture size of 64x64. Fig. 2 (b) is a representative 4 sample pictures of 4 types of textures in the database. In the experiment, 1,2,3,4,5 images of each type of texture image are respectively randomly extracted to train a multivariate logarithmic Gaussian mixture model, and the rest samples of each type of texture image are used for testing. For the test image, the category of the image is judged according to the method of the invention, and the judgment results of all the categories of the test image are counted, so that the obtained recognition rate is shown in fig. 3. Wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0001916624130000103
represents the algorithm "Steerable Sub-Gaussian Modeling" proposed by G Tzagkarakis et al 2008;
Figure BDA0001916624130000104
represents the algorithm "Multivariate Generalized Gaussian Mixture Model" proposed by KN Kumar in 2015;
Figure BDA0001916624130000105
representing the multi-variable logarithm Gaussian mixed probability model algorithm provided by the invention;
Figure BDA0001916624130000106
represents the "Gaussian mixture model" algorithm proposed by Kim S C in 2007. It can be seen from fig. 3 that the recognition rate of the multivariate logarithmic gaussian mixture model provided by the invention is high in several algorithms compared.
Example 2: as shown in fig. 1, the present embodiment is the same as embodiment 1, except that:
this example further accounts for the fact that the method is performed in a Brodatz texture database [ DB/OL ]].http://multibandtexture.recherche.usherbrooke.ca/colored％20_brodatz.html]And drawing a corresponding recognition performance curve according to the relation between the medium recognition rate and the number of the training samples. The texture picture set used in this embodiment has 100 types of texture images, each type of texture has 9 different texture photos, and the total size of the photos is 900 photos, and the size of the photos is 64x64. Fig. 2 (a) is a representative 4 sample pictures of 4 types of textures in the database. In the experiment, 1,2,3,4,5 images of each type of texture image are respectively randomly extracted to train a multivariate logarithmic Gaussian mixture model, and the rest samples of each type of texture image are used for testing. For the test image, the category of the image is judged according to the method of the invention, and the judgment results of all the categories of the test image are counted, so that the obtained recognition rate is shown in fig. 4. Wherein the content of the first and second substances,
Figure BDA0001916624130000111
represents the algorithm "Steerable Sub-Gaussian Modeling" proposed by G Tzagkarakis et al 2008;
Figure BDA0001916624130000112
represents the algorithm "Multivariate Generalized Gaussian Mixture Model" proposed by KN Kumar in 2015;
Figure BDA0001916624130000113
representing the multi-variable logarithm Gaussian mixed probability model algorithm provided by the invention;
Figure BDA0001916624130000114
the "Gaussian mixture model" algorithm proposed by Kim S C in 2007 is shown. It can be seen from fig. 4 that the identification performance of the multivariate logarithmic gaussian mixture model proposed by the present invention is the highest among several algorithms compared.
While the present invention has been described in detail with reference to the embodiments shown in the drawings, the present invention is not limited to the embodiments, and various changes can be made without departing from the spirit of the present invention within the knowledge of those skilled in the art.

Claims (8)

1. An image texture feature extraction and identification method based on a multivariate logarithmic Gaussian mixture model is characterized by comprising the following steps:
step1, firstly, filtering a texture image by adopting a Gaussian two-dimensional Gabor filter, and constructing a logarithmic Gaussian random vector;
step2, performing parameter modeling on the logarithmic Gaussian random vector X by adopting a multivariate logarithmic Gaussian probability model to obtain a logarithmic Gaussian probability function model of the parameterized logarithmic Gaussian random vector X;
step3, performing parameter modeling on the logarithmic Gaussian random vector X by adopting a plurality of multivariate logarithmic Gaussian probability models to obtain a parameterized multivariate logarithmic Gaussian probability mixture model;
step4, estimating parameters theta related in the multivariate logarithmic Gaussian probability mixture model obtained by parameter modeling by adopting the expectation maximization to obtain the multivariate logarithmic Gaussian probability mixture model;
and Step5, calculating the probability of the multi-variable logarithm Gaussian mixture model of the texture image to be classified belonging to various images, wherein the probability is the basis of classification.
2. The method for extracting and identifying image texture features based on multivariate logarithmic Gaussian mixture model as claimed in claim 1, wherein: the specific steps of Step1 are as follows:
the definition of the Step1.1, gaussian two-dimensional Gabor filter is as follows:
Figure FDA0001916624120000011
wherein
Figure FDA0001916624120000012
k v ＝k max /f v ，
Figure FDA0001916624120000013
k max Is the maximum frequency, typically k max ＝π/2，
Figure FDA0001916624120000014
The scale parameter v takes the value v = 0.., 4, and the direction parameter μ takes the values μ =0,1,2,3, z = (h, s) and | | z | = (h, s) 2 +s 2 ) H, s denote the coordinates of a gaussian two-dimensional Gabor filter, where i denotes the imaginary unit; the parameter sigma determines the bandwidth of the Gauss two-dimensional Gabor filter, and the value is 2 pi;
step1.2, assuming that the texture image is represented as I (h, s), and h, s also represent the coordinates of the image, the result obtained after filtering with the gaussian two-dimensional Gabor filter is represented as a complex matrix: r u,v (h,s)＝ψ μ,v (h, s) I (h, s); step step1.1 mentions z = (h, s), so ψ μ,v (h, s) is psi μ,v (z), I (h, s) represents an image, I (h, s) and psi μ,v (h, s) wherein h, s respectively represent the abscissa and the ordinate;
step1.3, constructing a logarithmic Gaussian random vector X;
let abs (R) u,v (h, s)) represents the resulting complex matrix R obtained after filtering u,v The norm of (h, s), i.e. the magnitude of the filtering result, vector Hist (abs (R) u,v (h, s))) represents abs (R) u,v (h, s)) histogram vector from Hist (abs (R) u,v (h, s))) to construct a logarithmic gaussian random variable X u,v The logarithmic Gaussian random vector X is composed of logarithmic Gaussian random variables X u,v Are composed so as to construct a single unit containing 40 pairsThe logarithmic gaussian random vector X of the gaussian random variables is:
Figure FDA0001916624120000021
wherein, if histogram vector Hist (abs (R)) u,v (h, s))) is 128, a log gaussian random vector X formed by the texture image after Gabor filtering and histogram vector calculation corresponds to 128 sample vectors with the length of 40; wherein, the 1 st sample of all random variables in the logarithmic Gaussian random vector X forms the 1 st sample vector, the 2 nd sample of all random variables in the logarithmic Gaussian random vector X forms the 2 nd sample vector, and so on; the 128 th sample of all random variables in the log-gaussian random vector X constitutes the 128 th sample vector.
3. The multivariate logarithm Gaussian mixture model-based image texture feature extraction and identification method as claimed in claim 1, wherein: in Step 2:
suppose there is a Gaussian random vector Y: [ Y 0,0 ,Y 0,1 ,...,Y 0,4 ,Y 1,0 ,Y 1,1 ,...,Y 1,4 ,...,Y 7,0 ,Y 7,1 ,...,Y 7,4 ]The mean vector and covariance are mu and sigma respectively, and X is defined according to the logarithmic Gaussian random variable u,v ＝exp(Y u,v ) Then, the log gaussian probability function model of the log gaussian random vector X is:
Figure FDA0001916624120000022
f X (x) And can be written as: f. of X (x) = f (X | θ), where the parameter θ represents the mean vector μ and covariance matrix Σ in the logarithmic gaussian random vector X probability density function; x is a radical of a fluorine atom 1 ,x 2 ,...,x 40 Is 40 random variables of a logarithmic gaussian random vector X.
4. The method for extracting and identifying image texture features based on multivariate logarithmic Gaussian mixture model as claimed in claim 1, wherein: in Step 3: performing parameter modeling on a logarithmic Gaussian random vector X by adopting a plurality of multivariate logarithmic Gaussian probability models to obtain a parameterized multivariate logarithmic Gaussian probability mixture model, wherein the model is as follows:
Figure FDA0001916624120000031
in this model, the parameter Θ = (ω =) exists 1 ,ω 2 ,…,ω M ,θ 1 ,θ 2 ,…,θ M ) Wherein
Figure FDA0001916624120000032
ω i Representing the mixing coefficient, theta, of the ith multivariate logarithmic Gaussian probability mixture model i Representing the mean vector μ in the ith multivariate logarithmic Gaussian probability model i Sum covariance matrix Σ i ；p i (x|θ i ) The probability of the image X in the ith multivariate log-gaussian probability model, the number of M multivariate log-gaussian probability models, and p (X | Θ) also represent the multivariate log-gaussian probability mixture model of the log-gaussian random vector X.
5. The multivariate logarithm Gaussian mixture model-based image texture feature extraction and identification method as claimed in claim 1, wherein: in Step4, the main steps of estimation are as follows:
step4.1, initializing theta to be theta 0 ，
Figure FDA0001916624120000033
Step4.2, let t =1, the following cycle is started:
Figure FDA0001916624120000034
Figure FDA0001916624120000035
Figure FDA0001916624120000036
Figure FDA0001916624120000037
Figure FDA0001916624120000038
t＝t+1
when the parameter theta t When the change is not large or the preset cycle step number is reached, the cycle is stopped;
in the above cycle, t is a cycle variable, x j For the jth sample vector of the logarithmic Gaussian random vector X, n sample vectors are used in the above cycle for parameter estimation; through the above circulation, the parameter Θ can be obtained, thereby obtaining the multivariate logarithmic Gaussian probability mixture model p (x | Θ) in the formula (4);
Figure FDA0001916624120000041
represents omega in the process of t-1 iteration l A value of (d);
Figure FDA0001916624120000042
represents theta in the process of the t-1 iteration l A value of (d); theta t-1 Representing the value of theta in the process of t-1 iteration;
Figure FDA0001916624120000043
represents μ in the t-1 th iteration l A value of (d);
Figure FDA0001916624120000044
representing Σ in the t-th iteration l A value of (d); p (l | x) j ,Θ t-1 ) An intermediate variable during the t-1 th iteration is shown.
6. The method for extracting and identifying image texture features based on multivariate logarithmic Gaussian mixture model as claimed in claim 1, wherein: in the Step 5:
assuming that the texture images to be identified and classified have c classes, extracting a part of image from each class of texture image, and then obtaining a multivariate logarithmic Gaussian probability mixture model of each class of texture image by using the method introduced in Step4, wherein the multivariate logarithmic Gaussian probability mixture model is respectively expressed as p (x | theta) 1 ),p(x|Θ 2 ),…,p(x|Θ c ) (ii) a For a sample image x to be classified, the corresponding Gabor histogram is 128 vectors of 40 dimensions, which are expressed as x 1 ,x 2 ,…,x 128 The classification of the image x is then completed by the following method steps:
(1) And calculating
Figure FDA0001916624120000045
Wherein "c" represents the total number of categories of the image; p (theta) m ) Is the probability of class m, let p (Θ) 1 )＝p(Θ 2 )＝…＝p(Θ c )＝1/c，
Figure FDA0001916624120000046
Representing a vector x i The probability of (d); p (x) i |Θ m ) Representing a vector x i Probability of belonging to class m;
(2) If p (theta) m I x) is p (Θ) 1 |x),p(Θ 2 |x),…,p(Θ c | x), the class of image x is class m, where p (Θ) m | x) represents the probability that the image x belongs to the mth multivariate logarithmic gaussian mixture probability model.
7. The method for extracting and identifying image texture features based on multivariate logarithmic Gaussian mixture model as claimed in claim 2, wherein: when the method is actually used for texture recognition, all random variables do not need to be selected when the logarithmic Gaussian random vector X in the step Step1.3 is selected, and a subset of the random vector X in the formula (2) is actually selected.
8. The multivariate logarithm Gaussian mixture model-based image texture feature extraction and identification method as claimed in claim 5, wherein: the step Step4.1 comprises the following steps:
step4.1.1, initialize theta 0 Then, clustering a certain type of samples to be classified by adopting a fuzzy C-means clustering algorithm, taking the formed cluster number A as the number M of the models in the multivariate logarithmic Gaussian probability mixed model, and then calculating the mean vector of each cluster and initializing the expected vector corresponding to the multivariate logarithmic Gaussian probability model;
step4.1.2, assuming that a cluster contains x 1 ,x 2 ,…,x t A sample, then matrix
Figure FDA0001916624120000047
Initializing a covariance matrix corresponding to a multivariate logarithmic Gaussian probability model; mixing coefficient omega of ith multivariate logarithmic Gaussian probability mixture model i (i =1,2, \ 8230;, M) is initialized to
Figure FDA0001916624120000051
The criterion for the end of the iteration is | Θ t -Θ t-1 |/|Θ t-1 The | is less than 0.1 or the iteration number reaches 40.
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