CN103886066B - A kind of image search method based on robust Non-negative Matrix Factorization - Google Patents

Abstract

The invention discloses a kind of image search method based on robust Non-negative Matrix Factorization.The method relationship expression and deficiency of both anti-noise between image for Algorithms of Non-Negative Matrix Factorization model, the visual signature collection X for being first depending on view data builds the L1 constraint diagrams of characterize data distribution relation, and sparse noise item is added, build robust Algorithms of Non-Negative Matrix Factorization model；Then in the model training stage, using iteration optimization method for solving, the feature representation V of characteristics of image basic matrix U and all images in the subspace launched by U is obtained from X；It is last that the image x of retrieval reference is transformed into into the subspace of U in image retrieval, obtain new feature expression v；According to v and the distance of view data concentration image, image is sorted, the minimum front K image of layback realizes the search function to image to user.This method has stronger anti-noise ability, and the process to new images calculates the time for linear session, can rapidly and accurately carry out image retrieval.

Description

A kind of image search method based on robust Non-negative Matrix Factorization

Technical field

The present invention relates to CBIR and non-negative matrix factorization method, more particularly to it is a kind of non-based on robust The image search method that negative matrix decomposes.

Background technology

In recent years, with internet and smart mobile phone, the popularization of digital camera, substantial amounts of image resource is by continually Generate.In order to these image resources are effectively organized and retrieved, various image retrieval technologies are also therewith It is suggested.At present, image retrieval has become computer vision, especially a study hotspot in multimedia retrieval field.

Except the earliest image retrieval technologies based on keyword, the image retrieval technologies of the current overwhelming majority are all based on The image retrieval technologies of content.CBIR technology is by characterizing various Image Visual Features from image zooming-out Visual signature, be then based on specific algorithm calculate image to be retrieved and each picture in image data base that user submits to it Between similarity, i.e. distance, so as to the size according to characteristic distance, is ranked up to image, returns to user distance value less Image, realize retrieval to image in image data base.

In CBIR algorithm, Data Dimensionality Reduction Algorithm is a kind of technology for extensively being used.The technology Core concept be to think that primitive image features space has certain deficiency, it is impossible to effectively by different types of image distinguish Come, it is desirable to searching out a suitable proper subspace, on the subspace, different types of image is separated from each other, and The image of same type is gathered each other.This kind of method includes：Principal component analysiss（Principal Component Analysis, PCA）, linear discriminant analysis（Linear Discriminant Analysis, LDA）, Non-negative Matrix Factorization（Nonnegative Matrix Factorization, NMF）With various manifold learning arithmetics, such as multi-dimension analysis（Multidimensional Scaling, MDS）, locally linear embedding（Local Linear Embedded, LLE）, locality preserving projections（Local Preserving Projection, LPP）Deng.

In these subspace methods, NMF with the addition of nonnegativity restriction to the data after dimensionality reduction, and its object function is to solve for Two nonnegative matrixes U and V so that X ≈ UV.Due to the introducing of nonnegativity restriction so that NMF can learn to obtain special with local The basic matrix U for levying, locally constitutes the overall consistent data representation side based on local in also obtain a kind of cognition with people Method.Therefore the interpretability of the method is stronger, is widely applied to image retrieval, recognition of face, numeral identification, text classification Deng application.

The initialization procedure of NMF is expanded to Liang etc. the initialization of supervision, then using NMF in implicit semantic rope In drawing, for the relation between finding from bottom visual signature to high-level semantics features.BeAbdallah et al. then adopts NMF structures The implicit expression of image is built, for improving the mark accuracy of image.Caicedo et al. generates multi-modality images table based on NMF Reach, and image, semantic information is considered when NMF object functions are built.

However, weaker the relationship expression between view data and anti-noise acoustic energy method in traditional NMF.For this two Aspect problem, this method build vision L1 constraint diagram by L1 figures in the characteristic that automatically selects of visual signature, while introducing sparse Noise item constraint, is then added to both constraintss in traditional NMF algorithm frames, obtains robust Non-negative Matrix Factorization Algorithm model.Based on the model for being proposed, the process to new images calculates the time for linear session, rapidly and accurately can carry out Image retrieval.

The content of the invention

The purpose of the present invention be overcome it is existing based on Non-negative Matrix Factorization between image in terms of relationship expression and antinoise two On deficiency, propose a kind of image search method based on robust Non-negative Matrix Factorization.

Comprised the steps based on the image search method of robust Non-negative Matrix Factorization：

1) 50 classes totally 5000 images are selected from common image data set Corel5K, extracts PHOG visual signatures [1] collection X=[x₁,...,x_n], wherein n=5000, x_iPHOG visual feature vectors corresponding to i-th image；PHOG visions is special Summits of the collection X as L1 figures to be built, the side right weight matrix W=[w of L1 figures₁,...,w_n], wherein w_iIt is calculated as follows：

Wherein, x_iFor the visual signature of the i-th width image, w_iFor matrix W i-th arranges, and ε is error coefficient, w_iiFor vectorial w_i's I-th component；

Phenogram is built as the L1 constraint diagrams of data distribution architecture relation are as follows：

Wherein, G=(I-W) is (I-W)^T, V=[v₁,...,v_n] be image set on subspace feature representation, I is unit Matrix；

2) L1 constraint diagrams and sparse noise constraints item E are added in traditional Algorithms of Non-Negative Matrix Factorization framework, are built Robust nonnegative matrix matrix decomposition algorithm model：

Wherein, λ₁, λ₂And λ₃For regularization parameter, 0.01,0.001 and 0.1, U ∈ R are respectively set in an experiment^d×rFor Keep the image basic matrix of vision and Semantic Similarity, V ∈ R^r×nMark sheet in the subspace launched by image basic matrix U Reach, E ∈ R^d×nIt is sparse noise constraints item, dimensions of the d for characteristics of image, r are the dimension of low-dimensional feature space；

3) it is trained using 3 algorithm model of view data set pair formula, is solved using iteration optimization, be calculated holding Mark sheets of the image basic matrix U and all images of vision and Semantic Similarity in the subspace launched by image basic matrix U Up to V, calculation procedure is as follows：

I) random initializtion U, V and E matrix, makes intermediate variable X_e=X-E；

Ii) fixed E, iterates to calculate U and V, and computing formula is as follows：

Wherein | G | is matrix G Middle all elements take the matrix constituted by correspondence absolute value；

Iii) fixed U and V, calculates optimal E, and computing formula is as follows：

Wherein function f is defined as：

4) when image retrieval is carried out, the image x as retrieval reference is transformed into the son sky launched by image basic matrix U Between in, obtain new feature representation v, be calculated as follows：

V=(U^TU)^-1U^TX=Mx, 8

Wherein, M=(U^TU)^-1U^T, U^TFor matrix U transposition, (U^TU)^-1For U^TThe inverse matrix of U；

5) according to step 4）The v for obtaining, calculates v and concentrates any image x with view data_iSub-space feature expression v_iIt Between apart from s_i, computing formula is as follows：

s_i=exp (- | | v-v_i||²) 9

Finally according to apart from s_iAll images are concentrated to be ranked up view data, the minimum front K figure of layback value As giving user, so as to realize image retrieval.

This method can be between phenogram picture space structure relation, with stronger noise resisting ability, obtaining image After basic matrix U, it is linear session to the calculating time of the lower-dimensional subspace feature representation of new images, compared with the conventional method can Image retrieval is carried out more rapidly and accurately.

Description of the drawings

Fig. 1 is the part sample image on Corel5K image data sets；

When Fig. 2 (a) is Saigae Tataricae image as retrieval example, algorithm retrieval sample figure；

When Fig. 2 (b) is Saigae Tataricae image as retrieval example, 10 retrieval result figures before algorithm；

When Fig. 3 (a) is fire balloon image as retrieval example, algorithm retrieval sample figure；

When Fig. 3 (b) is fire balloon image as retrieval example, 10 retrieval result figures before algorithm；

When Fig. 4 (a) is cupboard image as retrieval example, algorithm retrieval sample figure；

When Fig. 4 (b) is cupboard image as retrieval example, 10 retrieval result figures before algorithm；

When Fig. 5 (a) is buses image as retrieval example, algorithm retrieval sample figure；

When Fig. 5 (b) is buses image as retrieval example, 10 retrieval result figures before algorithm.

Specific embodiment

Comprised the steps based on the image search method of robust Non-negative Matrix Factorization：

1) 50 classes totally 5000 images are selected from common image data set Corel5K, extracts PHOG visual signatures [1] collection X=[x₁,...,x_n], wherein n=5000, x_iPHOG visual feature vectors corresponding to i-th image；PHOG visions is special Summits of the collection X as L1 figures to be built, the side right weight matrix W=[w of L1 figures₁,...,w_n], wherein w_iIt is calculated as follows：

Wherein, x_iFor the visual signature of the i-th width image, w_iFor matrix W i-th arranges, and ε is error coefficient, w_iiFor vectorial w_i's I-th component；

Phenogram is built as the L1 constraint diagrams of data distribution architecture relation are as follows：

Wherein, G=(I-W) is (I-W)^T, V=[v₁,...,v_n] be image set on subspace feature representation, I is unit Matrix；

2) L1 constraint diagrams and sparse noise constraints item E are added in traditional Algorithms of Non-Negative Matrix Factorization framework, are built Robust nonnegative matrix matrix decomposition algorithm model：

Wherein, λ₁, λ₂And λ₃For regularization parameter, 0.01,0.001 and 0.1, U ∈ R are respectively set in an experiment^d×rFor Keep the image basic matrix of vision and Semantic Similarity, V ∈ R^r×nMark sheet in the subspace launched by image basic matrix U Reach, E ∈ R^d×nIt is sparse noise constraints item, dimensions of the d for characteristics of image, r are the dimension of low-dimensional feature space；

3) it is trained using 3 algorithm model of view data set pair formula, is solved using iteration optimization, be calculated holding Mark sheets of the image basic matrix U and all images of vision and Semantic Similarity in the subspace launched by image basic matrix U Up to V, calculation procedure is as follows：

I) random initializtion U, V and E matrix, makes intermediate variable X_e=X-E；

Ii) fixed E, iterates to calculate U and V, and computing formula is as follows：

Wherein | G | is matrix G Middle all elements take the matrix constituted by correspondence absolute value；

Iii) fixed U and V, calculates optimal E, and computing formula is as follows：

Wherein function f is defined as：

4) when image retrieval is carried out, the image x as retrieval reference is transformed into the son sky launched by image basic matrix U Between in, obtain new feature representation v, be calculated as follows：

V=(U^TU)^-1U^TX=Mx, 8

Wherein, M=(U^TU)^-1U^T, U^TFor matrix U transposition, (U^TU)^-1For U^TThe inverse matrix of U；

5) according to step 4）The v for obtaining, calculates v and concentrates any image x with view data_iSub-space feature expression v_iIt Between apart from s_i, computing formula is as follows：

s_i=exp (- | | v-v_i||²) 9

Finally according to apart from s_iAll images are concentrated to be ranked up view data, the minimum front K figure of layback value As giving user, so as to realize image retrieval.

List of references

[1] PHOG feature codes are realized：http://www.robots.ox.ac.uk/～vgg/research/ caltech/phog.html。

Embodiment 1

Using Corel5K image data sets（As shown in Figure 1）Tested, Fig. 2, Fig. 3, Fig. 4, Fig. 5 shows four respectively Retrieval result.With reference to foregoing method and step, the embodiment is illustrated as follows：

1）Extract the PHOG original image visual signatures of 680 dimensions of image to the image in Corel5K respectively, as Image feature representation, obtains Image Visual Feature matrix X=[x₁,...,x_n], n=5000.

2）According to Image Visual Feature matrix X, visual similarity is modeled, with image set original visual feature X= [x₁,...,x_n] as the summit of L1 figures, the side right weight matrix W=[w of figure₁,...,w_n] in w_iIt is calculated as follows：

ε=0.001 is set, tool kit is solved using L1_LS solution is optimized to object above function 1, be calculated W Matrix, so as to obtain such as next vision L1 constraint diagram：

Wherein, G=(I-W) is (I-W)^T, V=[v₁,...,v_n] be image set on subspace feature representation, I is unit Matrix.

3) L1 constraint diagrams and sparse noise constraints item E are added in traditional Algorithms of Non-Negative Matrix Factorization framework, are built Robust nonnegative matrix matrix decomposition algorithm model：

Wherein, λ₁, λ₂And λ₃For regularization parameter, 1.6,0.1 and 0.01, U ∈ R are respectively set to^d×rFor keep vision and The image basic matrix of Semantic Similarity, V ∈ R^r×nFeature representation in the subspace launched by image basic matrix U, E ∈ R^d×n It is sparse noise constraints item, dimensions of the d for characteristics of image, i.e., 680 dimensions, r are the dimension of low-dimensional feature space, are set to 150 dimensions；

4) it is trained using 3 algorithm model of view data set pair formula, is solved using iteration optimization, be calculated holding Mark sheets of the image basic matrix U and all images of vision and Semantic Similarity in the subspace launched by image basic matrix U Up to V, calculation procedure is as follows：

I) random initializtion U, V and E matrix, makes intermediate variable X_e=X-E；

Ii) fixed E, iterates to calculate U and V, and computing formula is as follows：

Wherein | G | is matrix G Middle all elements take the matrix constituted by correspondence absolute value；

Iii) fixed U and V, calculates optimal E, and computing formula is as follows：

Wherein function f is defined as：

5) when image retrieval is carried out, the image x as retrieval reference is transformed into the son sky launched by image basic matrix U Between in, obtain new feature representation v, be calculated as follows：

V=(U^TU)^-1U^TX=Mx, 8

Wherein, M=(U^TU)^-1U^T, U^TFor matrix U transposition, (U^TU)^-1For U^TThe inverse matrix of U；

6) according to step 5）The v for obtaining, calculates v and concentrates any image x with view data_iSub-space feature expression v_iIt Between apart from s_i, computing formula is as follows：

s_i=exp (- | | v-v_i||²) 9

Finally according to apart from s_iAll images are concentrated to be ranked up Corel5K view data, layback value minimum Front 10 images to user, so as to realize image retrieval.

Claims (1)

1. a kind of image search method based on robust Non-negative Matrix Factorization, it is characterised in that comprise the steps：

1) 50 classes totally 5000 images are selected from common image data set Corel5K, extracts PHOG visual signature collection X= [x₁,...,x_n], wherein n=5000, x_iPHOG visual feature vectors corresponding to i-th image；By PHOG visual signature collection Summits of the X as L1 figures to be built, the side right weight matrix W=[w of L1 figures₁,...,w_n], wherein w_iIt is calculated as follows：

$\begin{array}{cc}\min & \left|\right|w_i|{|}_1\\ s.t.& \left|\right|x_i-{\mathrm{Xw}}_i\left|\right|\≤\mathrm{\ϵ},w_{ii}=0,\∀i\end{array}---1$

Wherein, x_iFor the visual signature of the i-th width image, w_iFor matrix W i-th arranges, and ε is error coefficient, w_iiFor vectorial w_iI-th Individual component；

Phenogram is built as the L1 constraint diagrams of data distribution architecture relation are as follows：

$\begin{array}{c}\min R_g={\Σ}_{i=1}^n\left|\right|v_i-{\mathrm{Vw}}_i|{|}^2=||V-VW|{|}_F^2\\ =tr\left(V\right(I-W\left){\left(I-W\right)}^T{V}^T\right)=tr\left({\mathrm{VGV}}^T\right)\end{array}---2$

Wherein, G=(I-W) is (I-W)^T, V=[v₁,...,v_n] be image set on subspace feature representation, I is unit square Battle array；

2) L1 constraint diagrams and sparse noise constraints item E are added in traditional Algorithms of Non-Negative Matrix Factorization framework, build robust Nonnegative matrix matrix decomposition algorithm model：

$\underset{U,V\≥0,E}{min}\left|\right|X-UV-E|{|}_F^2+{\mathrm{\λ}}_1\·|\left|E\right||+{\mathrm{\λ}}_2\·|\left|U\right|{|}_F^2+{\mathrm{\λ}}_3\·tr\left({\mathrm{VGV}}^T\right)---3$

Wherein, λ₁, λ₂And λ₃For regularization parameter, 0.01,0.001 and 0.1, U ∈ R are respectively set in an experiment^d×rTo keep The image basic matrix of vision and Semantic Similarity, V ∈ R^r×nFeature representation in the subspace launched by image basic matrix U, E ∈R^d×nIt is sparse noise constraints item, dimensions of the d for characteristics of image, r are the dimension of low-dimensional feature space；

3) it is trained using 3 algorithm model of view data set pair formula, is solved using iteration optimization, be calculated holding vision Feature representation V with the image basic matrix U and all images of Semantic Similarity in the subspace launched by image basic matrix U, Calculation procedure is as follows：

I) random initializtion U, V and E matrix, makes intermediate variable X_e=X-E；

Ii) fixed E, iterates to calculate U and V, and computing formula is as follows：

$U_{ij}\←U_{ij}\frac{{\left({\tilde{X}}_e{\tilde{V}}^T\right)}_{ij}}{{\left(U\tilde{V}{\tilde{V}}^T\right)}_{ij}}---4$

$V_{ij}\←V_{ij}\sqrt{\frac{{(U^T{X}_e+{\mathrm{\λ}}_3{\mathrm{VG}}^{-})}_{ij}}{{(U^{T}UV+{\mathrm{\λ}}_3{\mathrm{VG}}^{+})}_{ij}}}---5$

Wherein| G | is institute in matrix G There is element to take the matrix constituted by correspondence absolute value；

Iii) fixed U and V, calculates optimal E, and computing formula is as follows：

$E=f_{\frac{{\mathrm{\λ}}_1}{2}}(X-UV)---6$

Wherein function f is defined as：

4) when image retrieval is carried out, the image x as retrieval reference is transformed into into the subspace launched by image basic matrix U In, new feature representation v is obtained, is calculated as follows：

V=(U^TU)^-1U^TX=Mx, 8

Wherein, M=(U^TU)^-1U^T, U^TFor matrix U transposition, (U^TU)^-1For U^TThe inverse matrix of U；

5) according to step 4) v that obtains, calculate v any image x is concentrated with view data_iSub-space feature expression v_iBetween Apart from s_i, computing formula is as follows：

s_i=exp (- | | v-v_i||²) 9

Finally according to apart from s_iAll images are concentrated to be ranked up view data, the minimum front K image of layback value is to use Family, so as to realize image retrieval.