CN103440332B - A kind of image search method strengthening expression based on relational matrix regularization - Google Patents

Abstract

The invention discloses a kind of method retrieving image from image instance storehouse based on relational matrix regularization Enhancement Method, comprise the steps of: step 1, input image to be retrieved；Step 2, extracts the feature of image in image to be retrieved and image instance storehouse；Step 3, chooses P image class from image instance feature database, chooses n width image construction sample data X from each image class；Step 4, manifold learning arithmetic based on spectral graph theory, sample data X is built three matrixes；Step 5, preliminary foundation strengthens relational matrix W '；Step 6, calculates regularization and strengthens relational matrix W^*；Step 7, calculates generalized characteristic matrix A；Step 8, calculates final graphical representation；Step 9, calculates the graphical representation of image to be retrieved；Step 10, uses Euclidean distance to calculate image to be retrieved and the similarity of all images in image instance storehouse, according to image most like with image to be retrieved in similarity descending output image instance storehouse.

Description

A kind of image search method strengthening expression based on relational matrix regularization

Technical field

The invention belongs to field of image search, a kind of image retrieval based on relational matrix regularization Enhancement Method Method.

Background technology

In today that Science and Technology Day reaches increasingly, along with the fast development of image acquisition process equipment and Internet technology is with universal Application, the generation information resource with image as representative has become as has the war of status of equal importance with material, the energy Slightly resource, its data volume has reached magnanimity scale the most, becomes current information and processes and the main body of construction of information resources.By There is in image advantages such as containing much information, abundant in content, expressive force is strong, therefore the image of magnanimity scale is carried out effectively Information processing and application, it has also become the key problem of numerous practical application area.

Due to current image date in magnanimity scale, and constantly increasing, traditional technological means cannot be fitted Should this demand, this to the tissue of image, analyze, retrieve and the technology such as management is proposed brand-new challenge.Although The image retrieval research being currently based on content has been achieved for the biggest progress, effectively overcomes literary composition based on manual mark This information carries out the limitation of image retrieval, but also has a certain distance from the real practical stage, especially to image High-level semantic understanding aspect.Major part method also only reside within the low-level image feature around image carry out semantic description and Learn this level, relative to the mankind it will be appreciated that and use colourful semantic concept, bottom data feature Ability to express still has the biggest limitation, therefore there is bigger gap, the most so-called " language between low-level image feature and high-level semantic Justice wide gap " (semantic gap), thus cause in the accuracy rate and efficiency of image retrieval, do not reach the most far away actual answering Needs, especially the multiple abundant semanteme of image is understood and retrieval aspect accurately and effectively.Even to this day, " semantic gap " problem in image retrieval is not the most well solved, and remains the key of puzzlement researcher One of property difficult problem.In the middle of the numerous technology solving this difficult problem, image retrieval technologies based on relevant feedback provides A kind of feasible solution.Relevance Feedback in early days focuses primarily upon information based on relevant feedback, and correction is looked into Ask vector i.e. characteristics of image, the such as every one dimensional numerical to query vector and redistribute weights, adjust the position of query vector Put.In recent years, due to the rise of manifold learning, many researchers are diverted through manifold learning technology, by higher-dimension Image data space dimensionality reduction seeks the immanent structure of image feature space, and its main theory hypothesis is to be regarded as by image A kind of manifold, target be exactly find in it structural information.Find the lower-dimensional subspace being embedded in high dimensional data Being the important means of the potential manifold of learning data, the learning method of manifold learning sub-spaces is all based on partial analysis. Learnt the semantic subspace of its corresponding low-dimensional by the method for manifold learning, this assumes whole data with manifold learning Collection only meets Euclidean distance in local and matches, and therefore by analyzing the local message of view data, excavates the language of local Justice manifold structure is more meaningful for image retrieval.

Summary of the invention

Goal of the invention: the present invention is to solve the problems of the prior art, it is proposed that a kind of based on relational matrix regularization Strengthen the image search method represented, efficiently solve under large-scale data, the quick and precisely search problem of image.

Summary of the invention: the invention discloses a kind of image search method based on relational matrix regularization Enhancement Method, should Method retrieves image from image instance storehouse, comprises the steps of:

Step 1, inputs image to be retrieved；

Step 2, extracts the feature of image in image to be retrieved and image instance storehouse, by N-dimensional vector description each image, N=112, obtains image instance feature database U=(u₁,…,u_M), u_iFor the feature of image instance storehouse the i-th width image, I=1 ... M, M are the picture number included in image instance storehouse, and feature v of image to be retrieved, and described image is real Example storehouse includes the image class of more than 50, and each image class represents that a semantic category, each image class include 600 width Above image；

Step 3, chooses P image class from image instance feature database, and P span 20～50, from each image Class chooses n width image, n span 100～500, and P image class has n × P and open image construction sample data X； Such as in the embodiment invented, therefrom choosing 30 image classes, each class illustrates different semantic categories, each Class has 100 width images, has 3000 image construction sample datas X, X=(x₁,…,x_q), q=n × P, x_iFor The feature of the i-th width image in sample data, q is sample data size, and X is the matrix of 112 × q dimension；

Step 4, manifold learning arithmetic based on spectral graph theory, sample data X is built and strengthens relational matrix W, positive example Relational matrix W^PWith counter-example relational matrix W^N；

Step 5, strengthens the relational matrix W built, and preliminary foundation strengthens relational matrix W '；

Step 6, strengthens relational matrix W ' by probability transfer matrix regularization and obtains regularization enhancing relational matrix W^*；

Step 7, strengthens relational matrix W according to regularization^*Build target equation, calculate generalized characteristic matrix A；

Step 8, utilizes generalized characteristic matrix A all images in image instance feature database to be carried out dimensionality reduction, i.e. AU=A* (u₁,…,u_M)=(A*u₁,…,A*u_M), remember y_i=A*x_i, i=1 ... M, obtain final figure As representing Y=(y₁,…,y_M), y_iFor the feature after the i-th width characteristics of image dimensionality reduction of image instance storehouse；

Step 9, utilizes generalized characteristic matrix A to characteristics of image v dimensionality reduction to be retrieved, obtains the image table of image to be retrieved Show f=A*v；

Step 10, according to the final graphical representation of step 8 and the Euclidean of the graphical representation of the image to be retrieved of step 9 Distance calculates image to be retrieved and the similarity of all images in image instance storehouse, i.e. calculates image dimensionality reduction feature f to be retrieved With the Euclidean distance of feature after image instance feature database each image Feature Dimension Reduction | | f-y_i||², i=1 ... M, y_iFor image Feature after case library the i-th width characteristics of image dimensionality reduction, according in similarity descending output image instance storehouse with to be retrieved The image that image is most like.

In step 2, characteristics of image includes color moment, Tamura textural characteristics, Gabor textural characteristics, color histogram.

Step 4 specifically includes following steps: randomly select piece image in sample data X, calculates this image and sample The Euclidean distance of other images in notebook data X, utilizes relevance feedback retrieval technology, according to the similar figure returned in result Picture is corresponding with inhomogeneity image sets up positive example set and counter-example set, and uses simple k near neighbor method opening relationships square Battle array, i.e. belong to k neighbour and be same image class two images between weights be 1, be otherwise 0.

Step 4 use imbeding relation based on feedback technique widen the manifold learning calculation as spectral graph theory of the ARE method Method, comprises the following steps:

(1) first sample data X is built relational matrix W, from sample data X, randomly draw piece image I, image I Feature be x_i, use k near neighbor method to calculate x_iWith the Euclidean distance of other characteristics of image in sample data X, obtain with K width image most like for image I, wherein k span 5～10；

Arbitrarily taking out piece image T from k width image to belong to, the feature of image T is x_t, then between image I and image T Weights W_itBeing 1, the weights between image beyond image I and k width image are 0；I.e. x_i∈N^k(x_t) or x_t∈ N^k(x_i), W_it=1, wherein N^k(x_i) represent image x_iK neighbour set, N^k(x_t) represent image x_tK neighbour set； The value obtaining relational matrix W, relational matrix W the i-th row t row is W_it；

Formula is:

The image belonging to same image class in k width image with image I is designated as positive example set Pos, the figure of different images class As being designated as counter-example set Neg,；

(2) positive example relational matrix W is built^PIf image R and image I belongs to same image class and broadly falls into k width figure Picture, and the feature of image R is x_r, then the weights between image I and image R are 1, the figure beyond image I and k width image Weights between Xiang are 0；That is,For the weights between image I and image R, x_i,x_r∈Pos For representing feature x_i,x_rBelong to positive example set Pos, positive example relational matrix W^PI-th row r row value bePublic Formula is:

(3) counter-example relational matrix W is built^NIf image H and image I belongs to different images class and broadly falls into k width figure Picture, the feature of image H is x_h, then the weights between image I and image H are 1, the image beyond image I and k width image Between weights be 0；I.e. x_i∈ Pos and x_h∈ Neg or x_h∈ Pos andTable Show feature x_iBelong to positive example set Pos, x_h∈ Neg represents feature x_hBelong to counter-example set Neg, x_h∈ Pos represents feature x_hBelong to positive example set Pos, x_i∈ Neg represents feature x_iBelong to counter-example set Neg,For between image I and image H Weights, counter-example relational matrix W^NThe i-th h be classified asFormula is:

Finally build and obtain three relational matrix W, W^PAnd W^N, it neutralizes the relation used for calculating generalized characteristic matrix to need Matrix.

Step 5 specifically includes following steps: from relational matrix W, if image z is neighbour's image of image i, And image z is also neighbour's image of image j, then following formula is used to calculate the weights W ' strengthened between image i and image j_ij: W′_ij=Σ_zW_izW_jz

Wherein W_izFor the weights of image i Yu image z, W_jzFor the weights of image j Yu image z, W '_ijIt is enhancing relation The i row jth train value of matrix W '.

Step 6 specifically includes following steps:

The neighbor relationships repeatedly propagated between image obtains new enhancing relational matrix W ", formula is W "=W ' * W '；

The transfer relationship between image, corresponding transfer matrix are P=[P to utilize transition probability matrix to represent_ij]_n×n, P_ij=p (j | i) it is that in sample data X, any image i, to the transition probability of any image j, selects and figure according to Euclidean distance As the n width image that i is most like, the feature of image j is x_j, the computing formula of transition probability P (j | i) is:

Wherein d_ij=| | x_i-x_j||², represent the Euclidean distance of image i and image j feature.

Use the model W that following formula calculated relationship matrix regularization strengthens^R:

W^R=η P+ (1-η) ge^T

Wherein, η is the probability that image i transfers to that this event of image j occurs, and (1-η) is the probability that image i redirects at random, G=(1/n) e, wherein g is a uniformly random distribution vector, and e is that n ties up unit column vector, n the most each image class Picture number, e=(1,1 ...)^T, the i-th row jth of matrix P is classified as P (j | i)；

New relation weights between image i and image jComputing formula is:

$w_{\mathrm{ij}}^{*}=w_{\mathrm{ij}}^{\″}\·w_{\mathrm{ij}}^R$

w″_ijFor the weights of image i Yu image j, w "_ijFor W " i-th row jth row value,Figure is jumped to for image i As the probability weights of j,For W^RI-th row jth row value；

Finally give regularization and strengthen relational matrix W^*, W^*The i-th row jth be classified as

Step 7 comprises the steps:

First from sample data X, choose feature x of any two width images_iAnd x_j, the relation weights of two width images are W_ij, The positive example relation weights of two width images areThe counter-example relation weights of two width images areAccording to following target equation It is calculated generalized characteristic matrix A:

X(L^N-γL^P)X^TA=λXLX^TA,

L is the Laplacian Matrix of relational matrix W, L^NFor counter-example relational matrix W^NLaplacian Matrix, L^PFor just Example relational matrix W^PLaplacian Matrix, γ is that the ratio to counter-example image number and positive example image number is directly proportional Constant, X^TRepresenting the transposed matrix of sample data X, λ represents the characteristic value of equation solution.

In the present invention, ARE is for widening relation embedding grammar (Augmented Relation Embedding), and one widens pass The manifold learning dimension-reduction algorithm that system's figure embeds, ARE mainly utilizes positive example relational matrix to embed the overall situation with counter-example relational matrix In relational matrix, find projection matrix, i.e. generalized characteristic matrix, thus realize the dimensionality reduction to data characteristics.

The principle of the invention is, sample data X=(x₁,…,x_N),x_i∈R^m, relational matrix W ∈ R between data point^N×N Representing, entry of a matrix element has weighed the similarity between every pair of data point.Diagonal matrix D and corresponding Laplacian Matrix L by Following formula defines:

$D_{\mathrm{ii}}={\mathrm{\Σ}}_j{W}_{\mathrm{ij}},\∀i,$

L=D-W

D_iiThe i-th row i-th for diagonal matrix D arranges, it is assumed that generalized characteristic matrix is A, completes original data space by projection Low-dimensional embed, A can be minimized by following formula and try to achieve:

$\underset{\mathrm{ij}}{\mathrm{\Σ}}{(A^T{x}_i-A^T{x}_j)}^2{W}_{\mathrm{ij}}$

Each column a of matrix A_jIndependent role, therefore above formula can be write as argmin_aΣ_ij(a^Tx_i-a^Tx_j)²W_ij, wherein a is to be asked Characteristic vector.Make y_i=a^Tx_i, then have:

$\underset{\mathrm{ij}}{\mathrm{\Σ}}{(y_i-y_j)}^2{w}_{\mathrm{ij}}=\underset{\mathrm{ij}}{\mathrm{\Σ}}{y}_i^2{w}_{\mathrm{ij}}-2\underset{\mathrm{ij}}{\mathrm{\Σ}}{y}_i{y}_j{w}_{\mathrm{ij}}+\underset{\mathrm{ij}}{\mathrm{\Σ}}{y}_j^2{W}_{\mathrm{ij}}$

$=2{\mathrm{\Σ}}_i{y}_i^2{D}_{\mathrm{ii}}-2{\mathrm{\Σ}}_{\mathrm{ij}}{y}_i{y}_j{W}_{\mathrm{ij}}$

$={2y}^T(D-W)y={2y}^T\mathrm{Ly}$

Wherein, y represents the projection on this projection vector of a of all data, and y=a^TX.Coordinate after conversion is limited, D_iiRepresent the number being connected with i-th point, illustrate this importance degree in a way, and then can increase about Bundle makes y^TDy=1.After this constraint can make the some conversion that importance is high, its coordinate value is more nearly territory initial point, allows Close quarters is positioned at initial point, and the object function equation finally solved becomes:

$a^{*}=\arg \underset{a}{\min }{a}^T{\mathrm{XLX}}^{T}a,s.t.a^T{\mathrm{XDX}}^{T}a=1$

From the point of view of derivation, relational matrix W plays leading role in whole process, and data point y after projection also has with W Close relationship, such as, work as W_ijTime bigger, represent x_iAnd x_jSimilarity is relatively big, y after dimensionality reduction_iAnd y_jBetween distance also should The smaller the better;If W_ijLess, represent x_iAnd x_jSimilarity is less, y after dimensionality reduction_iAnd y_jBetween distance also should be the bigger the better. Here similarity relation can represent whether belong to same classification between data, the similarity between homogeneous data is the most very High；For not having the data of classification information, the similarity between data is just weighed by neighbor relationships, between neighbour's data point Similarity should be higher；For neither homogeneous data, the most not there is the similarity meeting between the data point of neighbor relationships Ratio is relatively low, typically makes W_ij=0.

Beneficial effect: the present invention utilizes relational matrix regularization enhancing expression that image instance feature is carried out dimensionality reduction, the party Method can effectively strengthen the relation between similar image, has merged the classification information of data during building relational matrix, Make it expand to easily in the framework of semi-supervised learning, thus make full use of flag data and Unlabeled data, have Improving the stability of algorithm and reducing computation complexity of effect, makes image querying have higher accuracy rate simultaneously, because of This relational matrix regularization strengthens the image search method represented and has higher use value.

Accompanying drawing explanation

Fig. 1 is the flow chart of the present invention.

Fig. 2 bit image case library Feature Dimension Reduction flow chart.

Fig. 3 is characteristics of image dimensionality reduction flow chart to be retrieved.

Fig. 4 is that images relations strengthens schematic diagram.

Fig. 5 is image random walk model schematic.

The regularization of Fig. 6 position strengthens relation schematic diagram.

Fig. 7 is image searching result schematic diagram.

Detailed description of the invention

As it is shown in figure 1, the invention discloses a kind of image search method represented based on regularization enhancing relational matrix； Comprise the steps of:

Step 1: input image to be retrieved；

As shown in figures 2-3, build image regulation enhancing relational matrix mainly to be carried out, to image by step 2～step 6 Example aspects storehouse dimensionality reduction is carried out by step 8, step 9 carry out characteristics of image dimensionality reduction to be retrieved:

Step 2, extracts image to be retrieved and the characteristics of image of image instance storehouse image, feature includes color moment, Tamura Textural characteristics, Gabor textural characteristics and color histogram, describe each image, N=112 with the vector of N-dimensional, treat Retrieval image is v, and image instance feature database is U=(u₁,…,u_M), M is image instance storehouse total number of images, and U is N × M Dimension matrix；

Step 3, the character representation each image after extraction, from image instance storehouse, choose 30 image classes, each class Representing a semantic category, each class has 100 width images, has 3000 images, and as sample data X, X=(x₁,…,x₃₀₀₀), matrix X is 112 × 3000 dimensions；

Step 4, manifold learning arithmetic based on spectral graph theory, sample data X is built and strengthens relational matrix W, positive example Relational matrix W^PWith counter-example relational matrix W^N；

Step 5, strengthens relational matrix W, and preliminary foundation strengthens relational matrix W '；

Step 6, strengthens relational matrix W ' by probability transfer matrix regularization and obtains regularization enhancing relational matrix W^*；

Step 7, strengthens relational matrix W according to regularization^*With positive example relational matrix W^PWith counter-example relational matrix W^NBuild Object function, solves generalized characteristic matrix A；

Step 8, utilizes generalized characteristic matrix A that images all in image instance storehouse are carried out dimensionality reduction, i.e. AU=A* (u₁,…,u_M)=(A*u₁..., A*u_M), remember y_i=A*x_i, i=1 ... M, obtain final graphical representation Y=(y₁,…,y_M)；

Step 9, as it is shown on figure 3, utilize generalized characteristic matrix A that characteristics of image v to be retrieved is carried out dimensionality reduction, is treated The graphical representation f=A*v of retrieval image；

Step 10, uses Euclidean distance to calculate image to be retrieved and the similitude of all images in image instance storehouse, i.e. counts Calculate | | f-y_i||², i=1 ... M, according to most like with image to be retrieved in similarity descending output image instance storehouse Image.

Step 2 specifically includes following steps:

Extraction each image feature, i.e. iamge description aspect is by color moment (RGB color): 9 dimensions；Color moment (LUV Color space): 9 dimensions；Tamura textural characteristics: 6 dimensions；Gabor textural characteristics: 24 dimensions；Color histogram (HSV Color space): 64 dimension compositions.

Step 4 specifically includes following steps: randomly select piece image in sample data X, calculates this image and sample The Euclidean distance of other images in notebook data X, utilizes relevance feedback retrieval technology, according to the similar figure returned in result Picture is corresponding with inhomogeneity image sets up positive example set and counter-example set, and uses simple k near neighbor method opening relationships square Battle array, i.e. belong to k neighbour and be same image class two images between weights be 1, be otherwise 0.

Step 4 use imbeding relation based on feedback technique widen the manifold learning calculation as spectral graph theory of the ARE method Method, comprises the following steps:

(1) first sample data X is built relational matrix W, from sample data X, randomly draw piece image I, image I Feature be x_i, use k near neighbor method to calculate x_iWith the Euclidean distance of other characteristics of image in sample data X, obtain with K width image most like for image I, wherein k span 5～10；

Arbitrarily taking out piece image T from k width image to belong to, the feature of image T is x_t, then between image I and image T Weights W_itBeing 1, the weights between image beyond image I and k width image are 0；I.e. x_i∈N^k(x_t) or x_t∈ N^k(x_i), W_it=1, wherein N^k(x_i) represent image x_iK neighbour set, N^k(x_t) represent image x_tK neighbour set； The value obtaining relational matrix W, relational matrix W the i-th row t row is W_it；

Formula is:

The image belonging to same image class in k width image with image I is designated as positive example set Pos, the figure of different images class As being designated as counter-example set Neg,；

(2) positive example relational matrix W is built^PIf image R and image I belongs to same image class and broadly falls into k width figure Picture, and the feature of image R is x_r, then the weights between image I and image R are 1, the figure beyond image I and k width image Weights between Xiang are 0；That is,For the weights between image I and image R, x_i,x_r∈Pos For representing feature x_i,x_rBelong to positive example set Pos, positive example relational matrix W^PI-th row r row value bePublic Formula is:

(3) counter-example relational matrix W is built^NIf image H and image I belongs to different images class and broadly falls into k width figure Picture, the feature of image H is x_h, then the weights between image I and image H are 1, the image beyond image I and k width image Between weights be 0；I.e. x_i∈ Pos and x_h∈ Neg or x_h∈ Pos andx_i∈ Pos table Show feature x_iBelong to positive example set Pos, x_h∈ Neg represents feature x_hBelong to counter-example set Neg, x_h∈ Pos represents feature x_hBelong to positive example set Pos, x_i∈ Neg represents feature x_iBelong to counter-example set Neg,For between image I and image H Weights, counter-example relational matrix W^NThe i-th h be classified asFormula is:

Finally build and obtain three relational matrix W, W^PAnd W^N, it neutralizes the relation used for calculating generalized characteristic matrix to need Matrix.

Step 5 specifically includes following steps: from relational matrix W, if image z is neighbour's image of image i, And image z is also neighbour's image of image j, then following formula is used to calculate the weights W ' strengthened between image i and image j_ij:

W′_ij=∑_zW_izW_jz

Wherein W_izFor the weights of image i Yu image z, W_jzFor the weights of image j Yu image z, W '_ijIt is enhancing relation The i row jth train value of matrix W '.

Step 6 specifically includes following steps:

The neighbor relationships repeatedly propagated between image obtains new enhancing relational matrix W ", formula is W "=W ' * W '；

The transfer relationship between image, corresponding transfer matrix are P=[P to utilize transition probability matrix to represent_ij]_n×n, P_ij=p (j | i) it is that in sample data X, any image i, to the transition probability of any image j, selects and figure according to Euclidean distance As the n width image that i is most like, the feature of image j is x_j, the computing formula of transition probability P (j | i) is:

Wherein d_ij=| | x_i-x_j||², represent the Euclidean distance of image i and image j feature.

Use the model W that following formula calculated relationship matrix regularization strengthens^R:

W^R=η P+ (1-η) ge^T Wherein, η is the probability that image i transfers to that this event of image j occurs, and (1-η) is the probability that image i redirects at random, G=(1/n) e, wherein g is a uniformly random distribution vector, and e is that n ties up unit column vector, n the most each image class Picture number, e=(1,1 ...)^T, the i-th row jth of matrix P is classified as P (j | i)；

New relation weights between image i and image jComputing formula is:

$w_{\mathrm{ij}}^{*}=w_{\mathrm{ij}}^{\″}\·w_{\mathrm{ij}}^R$

w″_ijFor the weights of image i Yu image j, w "_ijFor W " i-th row jth row value,Figure is jumped to for image i As the probability weights of j,For W^RI-th row jth row value； Finally give regularization and strengthen relational matrix W^*, W^*The i-th row jth be classified as Step 7 comprises the steps: First from sample data X, choose feature x of any two width images_iAnd x_j, the relation weights of two width images are W_ij, The positive example relation weights of two width images areThe counter-example relation weights of two width images areAccording to following target equation It is calculated generalized characteristic matrix A: X(L^N-γL^P)X^TA=λXLX^TA,

L is the Laplacian Matrix of relational matrix W, L^NFor counter-example relational matrix W^NLaplacian Matrix, L^PFor just Example relational matrix W^PLaplacian Matrix, γ is that the ratio to counter-example image number and positive example image number is directly proportional Constant, X^TRepresenting the transposed matrix of sample data X, λ represents the characteristic value of equation solution.

Embodiment 1

The present embodiment includes with lower part:

1. one image I to be retrieved of input；

2. the dimension of abstract image case library and the characteristics of image of image to be retrieved, each feature and its correspondence is as follows:

Color moment (RGB color): 9 dimensions；Color moment (LUV color space): 9 dimensions；Tamura textural characteristics: 6 dimensions；Gabor textural characteristics: 24 dimensions；Color histogram (hsv color space): 64 dimensions.So each image will Describing with the vector of 112 dimensions, image to be retrieved is v, and image instance feature database is U=(u₁,…,u_M), M is image Case library total number of images, U is that N × M ties up matrix；

3. choosing training sample data from the U of characteristics of image storehouse, each image extraction feature represents, and therefrom chooses 30 Individual image class, each class represents a semantic category, and each class has 100 width images, has 3000 images, and by it As sample data X, X=(x₁,…,x₃₀₀₀), matrix X is 112 × 3000 dimensions；.

4. in sample data X, randomly select piece image, calculate this image and the Europe of other images in sample data X Formula distance, utilizes relevance feedback retrieval technology, sets up according to the similar image returned in result is corresponding with inhomogeneity image Positive example set and counter-example set, and use simple k near neighbor method opening relationships matrix, i.e. belong to k neighbour and be Weights between two images of same image class are 1, are otherwise 0.

Step 4 use imbeding relation based on feedback technique widen the manifold learning calculation as spectral graph theory of the ARE method Method, comprises the following steps:

(1) first sample data X is built relational matrix W, from sample data X, randomly draw piece image I, image I Feature be x_i, use k near neighbor method to calculate x_iWith the Euclidean distance of other characteristics of image in sample data X, obtain with K width image most like for image I, wherein k value 5；

Arbitrarily taking out piece image T from k width image to belong to, the feature of image T is x_t, then between image I and image T Weights W_itBeing 1, the weights between image beyond image I and k width image are 0；I.e. x_i∈N^k(x_t) or x_t∈ N^k(x_i), W_it=1, wherein N^k(x_i) represent image x_iK neighbour set, N^k(x_t) represent image x_tK neighbour set； The value obtaining relational matrix W, relational matrix W the i-th row t row is W_it；

Formula is:

The image belonging to same image class in k width image with image I is designated as positive example set Pos, the figure of different images class As being designated as counter-example set Neg,；

(2) positive example relational matrix W is built^PIf image R and image I belongs to same image class and broadly falls into k width figure Picture, and the feature of image R is x_r, then the weights between image I and image R are 1, the figure beyond image I and k width image Weights between Xiang are 0；That is,For the weights between image I and image R, x_i,x_r∈Pos For representing feature x_i,x_rBelong to positive example set Pos, positive example relational matrix W^PI-th row r row value bePublic Formula is:

(3) counter-example relational matrix W is built^NIf image H and image I belongs to different images class and broadly falls into k width figure Picture, the feature of image H is x_h, then the weights between image I and image H are 1, the image beyond image I and k width image Between weights be 0;I.e. x_i∈ Pos and x_h∈ Neg or x_h∈ Pos andx_i∈ pos table Show feature x_iBelong to positive example set Pos, x_h∈ Neg represents feature x_hBelong to counter-example set Neg, x_h∈ Pos represents feature x_hBelong to positive example set Pos, x_i∈ Neg represents feature x_iBelong to counter-example set Neg,For between image I and image H Weights, counter-example relational matrix W^NThe i-th h be classified asFormula is:

Finally build and obtain three relational matrix W, W^PAnd W^N, for calculating the relational matrix that generalized characteristic matrix needs are used.

5. set up initial relation and strengthen matrix W ', from relational matrix W, if image z is neighbour's figure of image i Picture, and image z is also neighbour's image of image j, then use following formula to calculate the weights W ' strengthened between image i and image j_ij:

W′_ij=Σ_zW_izW_jz

Wherein W_izFor the weights of image i Yu image z, W_jzFor the weights of image j Yu image z, W '_ijIt is enhancing relation The i row jth train value of matrix W '.As shown in Figure 4, image 3 is neighbour's image of image 1 to instantiation, image 3 Be neighbour's image of image 2, connect with the solid line having arrow between image and represent neighbor relationships, image 1 and image 2 it Between with dotted line connect, the relation between representative image 1 and image 2 need strengthen.

6. build probability transfer matrix W^RAnd carry out regularization to strengthening relational matrix W ',

The neighbor relationships repeatedly propagated between image obtains new enhancing relational matrix W ", formula is w "=w ' * w ';

The transfer relationship between image, corresponding transfer matrix are P=[P to utilize transition probability matrix to represent_ij]_n×n, P_ij=P(j | it is i) that in sample data X, any image i, to the transition probability of any image j, selects and figure according to Euclidean distance As the n width image that i is most like, the feature of image j is x_j, the computing formula of transition probability P (j | i) is:

Wherein d_ij=| | x_i-x_j||², represent the Euclidean distance of image i and image j feature.

Use the model W that following formula calculated relationship matrix regularization strengthens^R:

W^R=η P+ (1-η) ge^T

Wherein, η is the probability that image i transfers to that this event of image j occurs, and η is taken as 0.85, and (1-η) is that image i jumps at random The probability turned, g=(1/n) e, wherein g is a uniformly random distribution vector, and e is that n ties up unit column vector, and n is the most every The picture number of individual image class, e=(1,1 ...)^T, the i-th row jth of matrix P is classified as P (j | i)；

New relation weights between image i and image jComputing formula is:

$w_{\mathrm{ij}}^{*}=w_{\mathrm{ij}}^{\″}\·w_{\mathrm{ij}}^R$

w″_ijFor the weights of image i Yu image j, w "_ijFor W " i-th row jth row value,Figure is jumped to for image i As the probability weights of j,For W^RI-th row jth row value；

Finally give regularization and strengthen relational matrix W^*, W^*The i-th row jth be classified asInstantiation such as Fig. 5～6 institute Showing, the probability transfer weights relation between Fig. 5 representative image, in Fig. 6, the picture left above 1 represents the enhancing relation square between image Battle array W ", connect with solid line between two width images is neighbour's image, and dotted line connects that to represent be that enhancing between two width images is closed System, top right plot 2 represents the transition probability matrix W between image^R, with realizing connecting existence transfer between representative image between image Relation, the regularization between lower Fig. 3 representative image strengthens relational matrix W^*, by W " and W^RIt is multiplied and obtains；

7. strengthen matrix W according to the relation after regularization^*Build object function, solve generalized characteristic matrix A,

First from sample data X, choose feature x of any two width images_iAnd x_j, the relation weights of two width images are W_ij, The positive example relation weights of two width images areThe counter-example relation weights of two width images areAccording to following target equation It is calculated generalized characteristic matrix A:

X(L^N-γL^P)X^TA=λXLX^TA,

L is the Laplacian Matrix of relational matrix W, L^NFor counter-example relational matrix W^NLaplacian Matrix, L^PFor just Example relational matrix W^PLaplacian Matrix, γ is that the ratio to counter-example image number and positive example image number is directly proportional Constant, X^TRepresenting the transposed matrix of sample data X, λ represents the characteristic value of equation solution.

Mainly utilize generalized characteristic matrix A that view data in image instance feature database is carried out dimensionality reduction and obtain final figure As representing, i.e. AU=A* (u₁,…,u_M)=(A*u_i,…,A*u_M), remember y_i=A*x_i, i=1 ... M, Whole graphical representation is Y=(y₁,…,y_M)；

Mainly utilize generalized characteristic matrix A that characteristics of image v to be retrieved is carried out dimensionality reduction, obtain the image of image to be retrieved Represent f, f=A*v；

10. calculating image to be retrieved and image similarity in image instance storehouse:

Use Euclidean distance to calculate image to be retrieved and the similitude of all images in image instance storehouse, i.e. calculate ||f-y_i||², i=1 ... M, | | f-y_i||²The least similarity is the biggest, according to similarity descending output image instance storehouse In the image most like with image to be retrieved.As it is shown in fig. 7, it is real with image to calculate image to be retrieved according to Euclidean distance The similitude of all images in example storehouse, according to 4 most like images of the descending output of similarity.

Embodiment 2

Fig. 1 is embodiment 2 retrieval flow figure, and in figure, image sources is public Corel5k database.In figure, 2 is right Original image pre-processes, with color moment, Tamura textural characteristics, Gabor textural characteristics and color histogram chart Show piece image, 3 selected characteristic sample in figure, from image instance storehouse, choose 30 image classes, each class illustrates One semantic category, each class has 100 width images, has 3000 width images, in order to improve calculating speed, only uses result Concentrate front 400 width images as the overall situation data set, for opening relationships matrix W, positive example relational matrix W^P, counter-example Relational matrix W^N.Then relational matrix W is carried out enhancing and obtains W ', and utilize probability transfer matrix W^RRegularization increases Strong relational matrix, obtains W^*, then according to the enhancing relational matrix W of regularization^*Solve the generalized character square of object function Battle array A, finally utilizes generalized characteristic matrix A that characteristics of image in image instance storehouse and characteristics of image to be retrieved are carried out dimensionality reduction, Image to be retrieved is retrieved, utilizes Euclidean distance to calculate image to be retrieved and the similarity of image in image instance storehouse, According to image most like with image to be retrieved in similarity descending output image instance storehouse.

The invention provides a kind of regularization and strengthen the image search method that relational matrix represents, implement this technical side The method of case and approach are a lot, and the above is only the preferred embodiment of the present invention, it is noted that for this technology For the those of ordinary skill in field, under the premise without departing from the principles of the invention, it is also possible to make some improvement and profit Decorations, these improvements and modifications also should be regarded as protection scope of the present invention.Each part the clearest and the most definite in the present embodiment is equal Available prior art is realized.

Claims (4)

1. the image search method strengthening to represent based on relational matrix regularization, it is characterised in that the method is from figure As case library is retrieved image, comprise the steps of:

Step 1, inputs image to be retrieved；

Step 2, extracts the feature of image in image to be retrieved and image instance storehouse, by N-dimensional vector description each image, N=112, obtains image instance feature database and the feature of image to be retrieved, and described image instance storehouse includes more than 50 Image class, each image class represents a semantic category, and each image class includes the image of more than 600 width；

Step 3, chooses P image class from image instance feature database, and P span 20～50, from each image Class chooses n width image, n span 100～500, and P image class has n × P and open image construction sample data X；

Step 4, manifold learning arithmetic based on spectral graph theory, sample data X is built relational matrix W, positive example relation Matrix W^PWith counter-example relational matrix W^N；

Step 5, strengthens the relational matrix W built, and preliminary foundation strengthens relational matrix W '；

Step 6, strengthens relational matrix W by probability transfer matrix regularization^′Obtain regularization and strengthen relational matrix W^*:

Step 7, strengthens relational matrix W according to regularization^*Build target equation, calculate generalized characteristic matrix A；

Step 8, utilizes generalized characteristic matrix A that all images in image instance feature database are carried out dimensionality reduction, obtains final Graphical representation；

Step 9, utilizes generalized characteristic matrix A to image dimensionality reduction to be retrieved, obtains the graphical representation of image to be retrieved；

Step 10, according to the final graphical representation of step 8 and the Euclidean of the graphical representation of the image to be retrieved of step 9 Distance calculates image to be retrieved and the similarity of all images in image instance storehouse, according to similarity descending output figure As image most like with image to be retrieved in case library；

In step 2, characteristics of image includes color moment, Tamura textural characteristics, Gabor textural characteristics, color histogram；

Step 4 specifically includes following steps: randomly select piece image in sample data X, calculates this image and sample The Euclidean distance of other images in notebook data X, utilizes relevance feedback retrieval technology, according to the similar figure returned in result Picture is corresponding with inhomogeneity image sets up positive example set and counter-example set, and uses simple k near neighbor method opening relationships square Battle array, i.e. belong to k neighbour and be same image class two images between weights be 1, be otherwise 0；

Step 4 use imbeding relation based on feedback technique widen the manifold learning calculation as spectral graph theory of the ARE method Method, comprises the following steps:

(1) first sample data X is built relational matrix W, from sample data X, randomly draw piece image I, image I Feature be x_i, use k near neighbor method to calculate x_iWith the Euclidean distance of other characteristics of image in sample data X, obtain with K width image most like for image I, wherein k span 5～10；

Arbitrarily taking out piece image T from k width image, the feature of image T is x_t, then the power between image I and image T Value W_itBeing 1, the weights between image beyond image I and k width image are 0；I.e. x_i∈N^k(x_t)or x_t∈ N^k(x_i), W_it=1, wherein N^k(x_i) represent image x_iK neighbour set, N^k(x_t) represent image x_tK neighbour set； The value obtaining relational matrix W, relational matrix W the i-th row t row is W_it；

The image belonging to same image class in k width image with image I is designated as positive example set Pos, the figure of different images class As being designated as counter-example set Neg；

(2) positive example relational matrix W is built^PIf image R and image I belongs to same image class and broadly falls into k width figure Picture, and the feature of image R is x_r, then the weights between image I and image R are 1, the figure beyond image I and k width image Weights between Xiang are 0；That is, x_i,x_r∈Pos, For the weights between image I and image R, x_i,x_r∈ Pos is for representing feature x_i,x_rBelong to positive example set Pos, positive example relational matrix W^PThe i-th row r row value i.e. ForFormula is:

(3) counter-example relational matrix W is built^NIf image H and image I belongs to different images class and broadly falls into k width figure Picture, the feature of image H is x_h, then the weights between image I and image H are 1, the image beyond image I and k width image Between weights be 0；I.e. x_i∈Pos and x_h∈ Neg, or x_h∈Pos and x_i∈Neg,x_i∈Pos Represent feature x_iBelong to positive example set Pos, x_h∈ Neg represents feature x_hBelong to counter-example set Neg, x_h∈ Pos represents special Levy x_hBelong to positive example set Pos, x_i∈ Neg represents feature x_iBelong to counter-example set Neg,For image I and image H it Between weights, counter-example relational matrix W^NThe i-th h be classified asFormula is:

Finally build and obtain three relational matrix W, W^PAnd W^N。

A kind of image search method strengthening expression based on relational matrix regularization the most according to claim 1, its Being characterised by, step 5 specifically includes following steps: from relational matrix W, if image z is the neighbour of image i Image, and image z is also neighbour's image of image j, then use following formula to calculate the power strengthened between image i and image j Value W '_ij: W '_ij=∑_zW_izW_jz, wherein W_izFor the weights of image i Yu image z, W_jzPower for image j Yu image z Value, W '_ijIt is the i-th row jth train value strengthening relational matrix W '.

A kind of image search method strengthening expression based on relational matrix regularization the most according to claim 2, its Being characterised by, step 6 specifically includes following steps:

The neighbor relationships repeatedly propagated between image obtains new enhancing relational matrix W ", formula is W "=W ' * W '；

The transfer relationship between image, corresponding transfer matrix are P=[P to utilize transition probability matrix to represent_ij]_n×n, P_ij=p (j | i) it is that in sample data X, any image i, to the transition probability of any image j, selects and figure according to Euclidean distance As the n width image that i is most like, the feature of image j is x_j, the computing formula of transition probability P (j | i) is:

Wherein d_ij=| | x_i-x_j||², represent the Euclidean distance of image i and image j feature；

Use the model W that following formula calculated relationship matrix regularization strengthens^R:

W^R=η P+ (1-η) ge^T

Wherein, η is the probability that image i transfers to that this event of image j occurs, and (1-η) is the probability that image i redirects at random, G=(1/n) e, wherein g is a uniformly random distribution vector, and e is that n ties up unit column vector, n the most each image class Picture number, e=(1,1 ...)^T, the i-th row jth of matrix P is classified as P (j | i)；

New relation weights between image i and image jComputing formula is:

$w_{ij}^{*}=w_{ij}^{\′\′}\·w_{ij}^R$

w″_ijFor the weights of image i Yu image j, w "_ijFor W " i-th row jth row value,Figure is jumped to for image i As the probability weights of j,For W^RI-th row jth row value；

Finally give regularization and strengthen relational matrix W^*, W^*The i-th row jth be classified as

A kind of image search method strengthening expression based on relational matrix regularization the most according to claim 3, its It is characterised by, step 7 comprises the steps:

First from sample data X, choose feature x of any two width images_iAnd x_j, the relation weights of two width images are W_ij, The positive example relation weights of two width images areThe counter-example relation weights of two width images areAccording to following target equation It is calculated generalized characteristic matrix A:

X(L^N-γL^P)X^TA=λ XLX^TA

L is the Laplacian Matrix of relational matrix W, L^NFor counter-example relational matrix W^NLaplacian Matrix, L^PClose for positive example It it is matrix W^PLaplacian Matrix, γ is the constant that the ratio to counter-example image number and positive example image number is directly proportional, X^TRepresenting the transposed matrix of sample data X, λ represents the characteristic value of equation solution.