CN101620638A - Image retrieval method based on gauss mixture models - Google Patents

Abstract

The invention discloses an image retrieval method based on gauss mixture models, belonging to the field of image retrieval, overcoming the defect of inadequate accuracy of the prior distance measurement method of gauss mixture models, further enhancing the distance measurement accuracy of the gauss mixture models on human perception, and consequently enhancing the image retrieval performance. The image retrieval method based on gauss mixture models comprises the following steps: firstly, picking up the gauss mixture models which correspond to all images in an image storeroom; secondly, picking up a gauss mixture model of an image to be retrieved; thirdly, computing the distances between the gauss mixture model of the image to be retrieved and the gauss mixture models of all the images in the image storeroom; and fourthly, sequencing the distances and returning to a retrieval result. The invention enhances the distance measurement accuracy of the gauss mixture models and consequently enhances the image retrieval performance.

Description

A kind of image search method based on gauss hybrid models

Technical field

The invention belongs to field of image search, be specifically related to a kind of image search method based on gauss hybrid models.

Background technology

Existing image search method based on gauss hybrid models generally includes: extract gauss hybrid models, the distance metric between gauss hybrid models and the distance ordering of image correspondence and return step such as result for retrieval.Wherein, the distance metric of gauss hybrid models is the core technology of image retrieval, and the distance metric reliability between gauss hybrid models is a key issue.

At present, the K-L dispersion between the widely-used gauss hybrid models of multimedia technology field (Kullback-Lieblerdivergence is called for short KLD) is as the similarity measurement of image.Though when using discrete histogram to express characteristics of image, can be according to the KLD between the direct computed image of the definition of KLD; But do not have closed expression formula, so need by Monte Carlo algorithm approximate solution for the KLD between gauss hybrid models; But use the Monte Carlo algorithm to sample in a large number at high-dimensional feature space, therefore the KLD time complexity that utilizes the Monte Carlo algorithm to find the solution between gauss hybrid models is very high, does not satisfy the time requirement of multimedia retrieval usually.

For solving the distance metric time efficiency problem of gauss hybrid models, Jacob Goldberger has proposed in " An EfficientImage Similarity Measure Based on Approximations of KL-Divergence Between TwoGaussian Mixtures " (IEEE International Conference on Computer Vision, 2003) literary composition based on the KLD algorithm of coupling with based on two kinds of improved KLD approximate solution methods of KLD algorithm of no mark conversion.Experiment is proof relatively, and these the two kinds of relative Monte Carlo of algorithm method of approximation time efficiencies all increase, but the relative Monte Carlo of accuracy method of approximation descends to some extent.

Yossi Rubner is at " The Earth Mover ' s Distance as a Metric for Image Retrival " (International Journal of Computer Vision, 2000) will move in the literary composition distance (Earth Mover ' s Distance, abbreviation EMD) distance metric that distributes as multidimensional, its basic thought is tolerance is deformed to the required cost of another probability distribution from a probability distribution a minimum cost, experimental results show that with respect to KLD, EMD is a kind of distance metric that meets human perception, therefore obtains multimedia retrieval, being extensive use of of fields such as target following.But EMD only was used to signature (a kind of method of approximate representation probability density function in the past, it is two a tuples set in form, the corresponding cluster of each two tuple, the element number that comprises of this cluster of vector sum by the expression cluster centre is formed) between distance metric, but represent that with signature the distribution form precision of probability density function is nothing like gauss hybrid models.Therefore, the present invention at first measures geodesic line distance between affine transformation matrix as the distance between Gauss model in the Lie group tangent space; Again in conjunction with the thought of EMD (Earth Mover ' s Distance), the distance metric problem of gauss hybrid models is converted into linear programming problem, thereby improves the accuracy of gauss hybrid models distance metric effectively.

Summary of the invention

The invention provides a kind of image search method based on gauss hybrid models, overcome the existing not enough problem of gauss hybrid models distance metric method accuracy, further improve the accuracy of gauss hybrid models distance metric in human perception, thereby improve the image retrieval performance.

A kind of image search method based on gauss hybrid models of the present invention comprises:

Step 1. extract the gauss hybrid models of all images correspondence in the image library, comprise following substep:

(1.1) for each pixel in the image, calculate a d dimensional feature vector, d 〉=1, proper vector comprise colouring information, the positional information of pixel, gradient information, the texture information of corresponding pixel points, and the proper vector of these all pixels of image constitutes the proper vector set of this image;

(1.2) determine the number m of the Gauss model that the gauss hybrid models of this image correspondence comprises, use the maximum likelihood parameter of the corresponding gauss hybrid models of the proper vector set of expectation-maximization algorithm estimated image: mean vector and the covariance matrix of forming each Gauss model of gauss hybrid models;

Wherein the gauss hybrid models of piece image correspondence is Q={ (μ _Q1, ∑ _Q1, β ₁) ..., (μ _Qm, ∑ _Qm, β _m), include m Gauss model, μ _QjAnd ∑ _QjMean vector and the covariance matrix of representing j Gauss model respectively, β _jBe j Gauss model shared weight in whole gauss hybrid models Q, 0≤β _j≤ 1,1≤j≤m, m 〉=1;

Step 2. extract the gauss hybrid models of image to be retrieved: according to substep (1.1) and (1.2) of step 1, extract the gauss hybrid models of image to be retrieved, the gauss hybrid models of image to be retrieved is P={ (μ _P1, ∑ _P1, α ₁) ..., (μ _Pn, ∑ _Pn, α _n), include n Gauss model, wherein μ _PiAnd ∑ _PiMean vector and the covariance matrix of representing i Gauss model respectively, α _iBe i Gauss model shared weight in whole gauss hybrid models P, 0≤α _i≤ 1,1≤i≤n;

Step 3. calculate the distance between the gauss hybrid models of all images in the gauss hybrid models P of image to be retrieved and the image library, comprise following substep:

(3.1) each Gauss model that will form the gauss hybrid models Q of piece image correspondence in gauss hybrid models P and the image library is mapped as a unique affine transformation matrix:

To forming each Gauss model N (μ, ∑) of each gauss hybrid models, decompose unique ∑=CC that obtains by Cholesky ^T, this Gauss model is with its pairing affine transformation matrix $\left(\begin{array}{cc}C& \mathrm{\μ}\\ 0& 1\end{array}\right)$ Unique expression; μ is the mean vector of Gauss model, and ∑ is the covariance matrix of Gauss model, and C is for being decomposed the lower triangular matrix that obtains by ∑;

(3.2) calculate the distance between each Gauss model in gauss hybrid models P and the Q, make up ground distance matrix D=[d _Ij]:

Calculate geodesic line between each affine transformation matrix apart from d according to following formula _Ij:

$d_{\mathrm{ij}}=\left|\right|\log \left(M_{\mathrm{pi}}^{-1}{M}_{\mathrm{qj}}\right)\left|\right|,$

M wherein _PiBe the affine transformation matrix of i Gauss model correspondence among the gauss hybrid models P, M _QjAffine transformation matrix for j Gauss model correspondence among the gauss hybrid models Q; Logm is asked in log (.) expression earlier, again matrix is converted into vector; ‖-‖ represents that vector asks modular arithmetic; With the geodesic line between each affine transformation matrix apart from d _IjAs the distance between each Gauss model; Obtain ground distance matrix D between P and Q:

(3.3) distance between two gauss hybrid models of calculating:

Find the solution distance between gauss hybrid models P and gauss hybrid models Q with linear programming method:

$\mathrm{EMD}(P,Q)=\underset{F}{\arg \min }\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{d}_{\mathrm{ij}}{f}_{\mathrm{ij}},$

The constraint condition of following formula:

(3.3.1)f _ij≥0，1≤i≤n，1≤j≤m，

(3.3.2) $\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{f}_{\mathrm{ij}}={\mathrm{\α}}_i,1\≤i\≤n,$

(3.3.3) $\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{f}_{\mathrm{ij}}={\mathrm{\β}}_j,1\≤j\≤m,$

(3.3.4) $\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{f}_{\mathrm{ij}}=1;$

Step 4. result for retrieval is also returned in distance ordering: with the distance between the gauss hybrid models of all images in the gauss hybrid models of image to be retrieved and the image library by sorting from small to large, the preceding t that returns in the image library with image distance minimum to be retrieved opens image, result for retrieval as image to be retrieved, t 〉=1 is specified by the user.

Described image search method, it is characterized in that: in the substep of described step 1 (1.2), the number m of the Gauss model that the corresponding gauss hybrid models of each image comprises is obtained or manual the appointment by minimum description length criterion (Minimum Description Length is called for short MDL);

The minimum description length criterion is meant selects m to make:

$m=\underset{m\∈H}{\arg \max }L\left(Q\right|x_1,...,x_k)-\frac{I_m}{2}\log k,$

In the formula, the likelihood score of gauss hybrid models $L\left(Q\right|x_1,...,x_k)=\underset{i=1}{\overset{k}{\mathrm{\Σ}}}\log p\left(x_i\right|Q),$ The quantity of the free parameter of gauss hybrid models $I_m=(m-1)+\mathrm{md}+m\left(\frac{d(d+1)}{2}\right);$ K is the number of proper vector, and Q represents the gauss hybrid models of this image correspondence, { x ₁..., x _kThe proper vector set of presentation video, and the dimension of d representation feature vector, the span H of m is [1,6].

L (Q|x ₁..., x _k) expression gauss hybrid models likelihood score,

The complexity of expression gauss hybrid models, the likelihood score and the complexity of model all increase along with the increase of m, and the minimum description length criterion is exactly to select m to make that the likelihood score of model is big as far as possible in the span H of m and complexity is as far as possible little.

In the substep (3.1) of step 3 of the present invention,, obtain ∑=CC by the Cholesky decomposition to forming any one Gauss model N (μ, ∑) of gauss hybrid models ^T(C is a lower triangular matrix), because ∑ is a symmetric positive definite, then this decomposition is unique, so the unique correspondence of any one Gauss model a lower triangular matrix; Make X ₀All represent n dimension random vector with X, and X ₀Obey standardized normal distribution, it is that μ, covariance matrix are the Gaussian distribution of ∑ that X obeys average, decomposes by Cholesky uniquely to obtain ∑=CC ^T, X=CX then ₀+ μ, that is:

$\left(\begin{array}{c}\mathrm{<figure-callout\; id="1"\; label="X"\; filenames="A2009103053240015H1.png"\; state="\{\{state\}\}">X</figure-callout>}\\ 1\end{array}\right)=\left(\begin{array}{cc}C& \mathrm{\&mu;}\\ 0& 1\end{array}\right)\left(\begin{array}{c}{X}_0\\ 1\end{array}\right),$

So any one Gauss model can obtain through above-mentioned affined transformation from standardized normal distribution, and the sealing of this transfer pair matrix multiplication, matrix inversion, thereby this Gauss model can be with its pairing affine transformation matrix $\left(\begin{array}{cc}C& \mathrm{\&mu;}\\ 0& 1\end{array}\right)$ Unique expression.

In the substep of step 3 (3.2), the affine transformation matrix of any one Gauss model correspondence seals matrix multiplication, matrix inversion, can prove that all affine transformation matrixs with dimension constitute a Lie group, therefore can be theoretical with asking the method for 2 distances on the solve manifold to obtain two distances between affine transformation matrix based on Lie group.If two affine transformation matrixs are respectively M _Pi, M _Qj, then the distance between them is their geodesic line length d of 2 on stream shape _Ij: $d_{\mathrm{ij}}=\left|\right|\log \left(M_{\mathrm{pi}}^{-1}{M}_{\mathrm{qj}}\right)\left|\right|.$

In the substep of step 3 (3.3), each Gauss model among gauss hybrid models P and the gauss hybrid models Q is regarded as mound set and the heatable adobe sleeping platform set that is scattered in the feature space respectively, distance between gauss hybrid models P and gauss hybrid models Q is meant the minimum cost that is deformed to the required cost of probability density function Q from probability density function P, promptly fill the minimum workload of all heatable adobe sleeping platforms, so the problems referred to above are converted into how to carry out the linear programming problem that mound moves with all soil.Wherein the soil of working unit amount respective transfer unit volume multiply by the unit ground distance of transport point process to heatable adobe sleeping platform; Ground distance is meant the distance between mound and heatable adobe sleeping platform, i.e. distance between each self-corresponding Gauss model of mound and heatable adobe sleeping platform; Wherein, the capacity of the volume of mound, heatable adobe sleeping platform is represented with each self-corresponding Gauss model shared weight in whole gauss hybrid models respectively.

Gauss hybrid models P={ (the μ of image to be retrieved _P1, ∑ _P1, α ₁) ..., (μ _Pn, ∑ _Pn, α _n) in, the corresponding mound of each Gauss model, i Gauss model shared weight in whole gauss hybrid models P _i, represent the volume of its corresponding mound;

Gauss hybrid models Q={ (the μ of image in the image library _Q1, ∑ _Q1, β ₁) ..., (μ _Qm, ∑ _Qm, β _m) in, the corresponding heatable adobe sleeping platform of each Gauss model, j Gauss model shared weight beta in whole gauss hybrid models Q _j, represent the capacity of its corresponding heatable adobe sleeping platform;

D=[d _Ij] expression ground distance matrix, wherein d _IjBe the distance between j Gauss model among i Gauss model among the gauss hybrid models P and the gauss hybrid models Q; F=[f _Ij] for moving a cubic metre of earth case, f _IjExpression moves to i mound among the gauss hybrid models P volume of the soil of j heatable adobe sleeping platform among the gauss hybrid models Q;

Expression moves on to the mobile cost of heatable adobe sleeping platform to all mounds, obtains distance between P and Q by minimizing mobile cost;

Constraint condition (3.3.1) restriction moving direction can only be from P to Q and can not be from Q to P; Constraint condition (3.3.2) limits the soil amount that shifts out from i the mound of P can not surpass total amount native i the mound; The soil amount of j heatable adobe sleeping platform reception can not surpass the capacity of j heatable adobe sleeping platform among constraint condition (3.3.3) the restriction Q; Constraint condition (3.3.4) is forced all mounds among the mobile P;

The present invention utilizes the accurately distance between the tolerance Gauss model of geodesic line distance by single Gauss model being mapped as the element in the Lie group space, thus the accuracy that improves the Gauss model distance metric; And the thought of EMD algorithm is applied to the gauss hybrid models distance metric, and be translated into linear programming problem, further optimize the accuracy of distance tolerance in human perception between gauss hybrid models, thereby improved image retrieval performance.

Description of drawings

Fig. 1 is a schematic flow sheet of the present invention;

Fig. 2 is the process flow diagram of step 3 of the present invention;

Fig. 3 carries out the retrieval precision contrast synoptic diagram of image retrieval for using the present invention and the gauss hybrid models measure based on KLD;

Fig. 4 is for using the present invention and the retrieval precision of carrying out image retrieval based on the gauss hybrid models measure of KLD-recall rate contrast synoptic diagram.

Embodiment

The present invention is further described below in conjunction with embodiment.

With the CBIR is example, and emulation platform is Matlab 7.0.Selected 377 pictures as the test pattern image set from the COREL image library, whole data set is divided into 7 classes, comprises horse, seabeach, building, American Indian, dinosaur, flower and automobile, and each class image has similar color space and distributes.By result for retrieval is retrieved and added up to image in the image set, the present invention and performance have been compared based on the gauss hybrid models distance metric method of KLD.

All images in the image set is zoomed to appointment size 230 * 154, distribute because each class image has similar color space, therefore utilize the positional information of the colouring information of pixel and pixel to extract the gauss hybrid models of each image correspondence as characteristic set.Corresponding to above-mentioned CBIR, embodiments of the invention as shown in Figure 1, wherein the flow process of step 3 is as shown in Figure 2; Specific as follows:

Step 1. extract the gauss hybrid models of all images correspondence in the image library; Comprise following substep:

(1.1) for each pixel in the image, calculate one five dimensional feature vector (R, G, B, x, y), wherein, R, G, B be the chromatic value of three colors of the corresponding red, green, blue of presentation video pixel respectively, and x, y be level, the vertical direction positional information of remarked pixel point respectively, and R, G, B, x, each component of y are carried out normalized; The proper vector of these all pixels of image constitutes the proper vector set of this image;

(1.2) by manual setting, the gauss hybrid models of all images correspondence constitutes by 3 Gauss models; Use expectation-maximization algorithm to estimate the maximum likelihood parameter of the gauss hybrid models of each image correspondence, comprise the mean vector and the covariance matrix of each Gauss model of forming gauss hybrid models;

Wherein the gauss hybrid models of piece image correspondence is Q={ (μ _Q1, ∑ _Q1, β ₁) ..., (μ _Q3, ∑ _Q3, β ₃), include 3 Gauss models, μ _QjAnd ∑ _QjMean vector and the covariance matrix of representing j Gauss model respectively, β _jBe j Gauss model shared weight in whole gauss hybrid models Q, 0≤β _j≤ 1,1≤j≤3;

Step 2. extract the gauss hybrid models of image to be retrieved at color space; The gauss hybrid models that extracts image to be retrieved is P={ (μ _P1, ∑ _P1, α ₁) ..., (μ _P3, ∑ _P3, α ₃), include 3 Gauss models, wherein μ _PiAnd ∑ _PiMean vector and the covariance matrix of representing i Gauss model respectively, α _iBe i Gauss model shared weight in whole gauss hybrid models P, 0≤α _i≤ 1,1≤i≤3;

Step 3. calculate the distance between the gauss hybrid models of all images in the gauss hybrid models P of image to be retrieved and the image library; Comprise following substep:

(3.1) each Gauss model that will form the gauss hybrid models Q of piece image correspondence in gauss hybrid models P and the image library is mapped as a unique affine transformation matrix:

To forming each Gauss model N (μ, ∑) of each gauss hybrid models, decompose unique ∑=CC that obtains by Cholesky ^T, this Gauss model is with its pairing affine transformation matrix $\left(\begin{array}{cc}C& \mathrm{\&mu;}\\ 0& 1\end{array}\right)$ Unique expression; μ is the mean vector of Gauss model, and ∑ is the covariance matrix of Gauss model, and C is for being decomposed the lower triangular matrix that obtains by ∑;

(3.2) calculate the distance between each Gauss model in gauss hybrid models P and the Q, make up ground distance matrix D=[d _Ij]:

Calculate geodesic line between each affine transformation matrix apart from d according to following formula _Ij:

$d_{\mathrm{ij}}=\left|\right|\log \left(M_{\mathrm{pi}}^{-1}{M}_{\mathrm{qj}}\right)\left|\right|,$

With the geodesic line between each affine transformation matrix apart from d _IjAs the distance between each Gauss model; Obtain ground distance matrix D between P and Q:

$D=\left(\begin{array}{ccc}{d}_{11}& d_{12}& d_{13}\\ d_{21}& d_{22}& d_{23}\\ d_{31}& d_{32}& d_{33}\end{array}\right);$

(3.3) distance between two gauss hybrid models of calculating: according to the shared weight { α of each Gauss model among the ground distance matrix D between gauss hybrid models P that tries to achieve and Q and gauss hybrid models P and the Q ₁..., α ₃And { β ₁..., β ₃, use the EMD algorithm to calculate distance between gauss hybrid models P and Q with linear programming method:

$\mathrm{EMD}(P,Q)=\underset{F}{\arg \min }\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{3}{\mathrm{\&Sigma;}}}{d}_{\mathrm{ij}}{f}_{\mathrm{ij}},$

The constraint condition of following formula:

(3.3.1)f _ij≥0，1≤i≤3，1≤j≤3，

(3.3.2) $\underset{j=1}{\overset{3}{\mathrm{\&Sigma;}}}{f}_{\mathrm{ij}}={\mathrm{\&alpha;}}_i,1\&le;i\&le;3,$

(3.3.3) $\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{f}_{\mathrm{ij}}={\mathrm{\&beta;}}_j,1\&le;j\&le;3,$

(3.3.4) $\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{3}{\mathrm{\&Sigma;}}}{f}_{\mathrm{ij}}=1;$

Step 4. with the distance between the gauss hybrid models of all images in the gauss hybrid models of image to be retrieved and the image library by ordering from small to large, the preceding t that returns in the image library with image distance minimum to be retrieved opens image, as the result for retrieval of image to be retrieved, t=1～100.

Use the present invention respectively and carry out image retrieval based on the gauss hybrid models distance metric method of KLD, and statistics retrieval performance, step is as follows: successively each width of cloth image in the image set is retrieved as image to be retrieved, sort according to the similarity degree between image in the image set and image to be retrieved, and the total number of images h similar with image to be retrieved in the picture number s similar with image to be retrieved, the image library in the statistics return results, calculate retrieval precision p and recall rate r.Wherein, retrieval precision p=s/t, recall rate r=s/h.The calculating of similarity degree can realize by the tolerance of distance between the gauss hybrid models of image between above-mentioned image, and distance is more little similar more, and the big more image difference of distance is big more.The tolerance of distance can be used method that the present invention proposes or based on the gauss hybrid models distance metric method of KLD between gauss hybrid models.Gauss hybrid models distance metric based on KLD uses the method for Monte Carlo sampling to realize, uses 10000 sampled points altogether.

Fig. 3, Fig. 4 have compared gauss hybrid models distance metric method that the present invention proposes and have been applied to image retrieval performance based on the gauss hybrid models distance metric method of KLD.Fig. 3 is the retrieval precision curve of two kinds of methods, and transverse axis represents that result for retrieval returns the picture sum, and the longitudinal axis is represented retrieval precision; Fig. 4 is the retrieval precision-recall rate curve of two kinds of methods, and transverse axis is represented recall rate, and the longitudinal axis is represented retrieval precision; The gauss hybrid models distance metric method that the corresponding the present invention of solid line proposes among the figure, the dotted line correspondence is based on the gauss hybrid models distance metric method of KLD.The gauss hybrid models distance metric method that experimental result explanation the present invention proposes is better than original gauss hybrid models distance metric method based on KLD on retrieval performance.

Claims (2)

1. image search method based on gauss hybrid models comprises:

Step 1. extract the gauss hybrid models of all images correspondence in the image library, comprise following substep:

(1.1) for each pixel in the image, calculate a d dimensional feature vector, d 〉=1, proper vector comprise colouring information, the positional information of pixel, gradient information, the texture information of corresponding pixel points, and the proper vector of these all pixels of image constitutes the proper vector set of this image;

(1.2) determine the number m of the Gauss model that the gauss hybrid models of this image correspondence comprises, use the maximum likelihood parameter of the corresponding gauss hybrid models of the proper vector set of expectation-maximization algorithm estimated image: mean vector and the covariance matrix of forming each Gauss model of gauss hybrid models;

Wherein the gauss hybrid models of piece image correspondence is Q={ (μ _Q1: ∑ _Q1: β ₁): ...: (μ _Qm: ∑ _Qm: β _m), include m Gauss model, μ _QjAnd ∑ _QjMean vector and the covariance matrix of representing j Gauss model respectively, β _jBe j Gauss model shared weight in whole gauss hybrid models Q, 0≤β _j≤ 1,1≤j≤m, m 〉=1;

Step 2. extract the gauss hybrid models of image to be retrieved: according to substep (1.1) and (1.2) of step 1, extract the gauss hybrid models of image to be retrieved, the gauss hybrid models of image to be retrieved is P={ (μ _P1: ∑ _P1: α ₁): ...: (μ _Pn: ∑ _Pn: α _n), include n Gauss model, wherein μ _PiAnd ∑ _PiMean vector and the covariance matrix of representing i Gauss model respectively, α _iBe i Gauss model shared weight in whole gauss hybrid models P, 0≤α _i≤ 1,1≤i≤n;

Step 3. calculate the distance between the gauss hybrid models of all images in the gauss hybrid models P of image to be retrieved and the image library, comprise following substep:

(3.1) each Gauss model that will form the gauss hybrid models Q of piece image correspondence in gauss hybrid models P and the image library is mapped as a unique affine transformation matrix:

To forming each Gauss model N (μ, ∑) of each gauss hybrid models, decompose unique ∑=CC that obtains by Cholesky ^T, this Gauss model is with its pairing affine transformation matrix $\left(\begin{array}{cc}C& \mathrm{\&mu;}\\ 0& 1\end{array}\right)$ Unique expression; μ is the mean vector of Gauss model, and ∑ is the covariance matrix of Gauss model, and C is for being decomposed the lower triangular matrix that obtains by ∑;

(3.2) calculate the distance between each Gauss model in gauss hybrid models P and the Q, make up ground distance matrix D=[dij]: calculate geodesic line between each affine transformation matrix apart from dij according to following formula:

$d_{\mathrm{ij}}=\left|\right|\log \left(M_{\mathrm{pi}}^{-1}{M}_{\mathrm{qj}}\right)\left|\right|,$

Wherein Mpi is the affine transformation matrix of i Gauss model correspondence among the gauss hybrid models P, and Mqj is the affine transformation matrix of j Gauss model correspondence among the gauss hybrid models Q; Logm is asked in log (.) expression earlier, again matrix is converted into vector; ‖. ‖ represents that vector asks modular arithmetic; With the geodesic line between each affine transformation matrix apart from dij as the distance between each Gauss model; Obtain ground distance matrix D between P and Q:

(3.3) distance between two gauss hybrid models of calculating:

Find the solution distance between gauss hybrid models P and gauss hybrid models Q with linear programming method:

$\mathrm{EMD}(P,Q)=\underset{F}{\arg \min }\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{d}_{\mathrm{ij}}{f}_{\mathrm{ij}},$

The constraint condition of following formula:

(3.3.1)f _ij≥0，1≤i≤n，1≤j≤m，

$\left(\mathrm{3.3.2}\right),\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{f}_{\mathrm{ij}}={\mathrm{\&alpha;}}_i,1\&le;i\&le;n,$

$\left(\mathrm{3.3.3}\right),\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{f}_{\mathrm{ij}}={\mathrm{\&beta;}}_j,1\&le;j\&le;m,$

$\left(\mathrm{3.3.4}\right),\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{f}_{\mathrm{ij}}=1;$

Step 4. result for retrieval is also returned in distance ordering: with the distance between the gauss hybrid models of all images in the gauss hybrid models of image to be retrieved and the image library by sorting from small to large, the preceding t that returns in the image library with image distance minimum to be retrieved opens image, result for retrieval as image to be retrieved, t 〉=1 is specified by the user.

2. image search method as claimed in claim 1 is characterized in that: in the substep of described step 1 (1.2), the number m of the Gauss model that the corresponding gauss hybrid models of each image comprises is obtained by the minimum description length criterion or manual the appointment;

The minimum description length criterion is meant selects m to make:

$m=\underset{m\&Element;H}{\arg \max }L\left(Q\right|x_1,...,x_k)-\frac{I_m}{2}\log k,$

In the formula, the likelihood score of gauss hybrid models $L\left(Q\right|x_1,...,x_k)=\underset{i=1}{\overset{k}{\mathrm{\&Sigma;}}}\log p\left(x_i\right|Q),$ The quantity of the free parameter of gauss hybrid models $I_m=(m-1)+\mathrm{md}+m\left(\frac{d(d+1)}{2}\right);$ K is the number of proper vector, and Q represents the gauss hybrid models of this image correspondence, { x ₁: ...: x _kThe proper vector set of presentation video, and the dimension of d representation feature vector, the span H of m is [1,6].

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