CN103699436A - Image coding method based on local linear constraint and global structural information - Google Patents

Abstract

The invention discloses an image coding method based on local linear constraint and global structural information. The method is used for solving the technical problem that an existing image coding method is poor in image classification precision. According to the technical scheme, the method includes: according to a hypothesis that distribution of dictionary elements and local features obeys Gaussian distribution, utilizing a Gaussian algorithm and a transitive closure method to respectively construct local similarity of the elements among dictionaries and local similarity among features of an image; using the dictionary elements for reconstructing a topological structure of the features in the image by the aid of a reconstruction error minimization method to obtain a direct-relation matrix of the local features and the dictionaries; multiplying a local similarity matrix of the elements among the dictionaries, the relation matrix of the local features and the dictionaries and a local similarity matrix among the local features to obtain final codes. By the method, the local similarity among the local features is calculated by aid of the Gaussian algorithm and the transitive closure method, image information included in the codes is completed, and image classification accuracy is improved under the condition of using a same classifier.

Description

Method for encoding images based on local linear constraint and global structure information

Technical field

The present invention relates to a kind of method for encoding images, particularly a kind of method for encoding images based on local linear constraint and global structure information.

Background technology

Image Coding is the method that the information in image is showed with less bit number, aspect Images Classification, target following, detection identification, is having very important significance.

Document " From Local Similarity to Global Coding; An Application to Image Classification, IEEE Conference on Computer Vision and Pattern Recognition, 2013, p2794-2801 " a kind of overall encryption algorithm based on local similarity is disclosed, and be applied in Images Classification.The method is set about from local similarity, utilizes the similarity between element in Gaussian Computation method Dictionary of Computing, calculates the global information of local feature and dictionary encode with conditional probability function.But the Image Coding part described in literary composition has only been considered the global information between local feature and dictionary, does not consider the structural information between local feature, the information of token image is comprehensive not.

Summary of the invention

In order to overcome the deficiency of conventional images coding method Images Classification low precision, the invention provides a kind of method for encoding images based on local linear constraint and global structure information.The method, first according to the hypothesis of the equal Gaussian distributed of distribution of dictionary element and local feature, utilizes Gauss algorithm and transitive closure method to build respectively the local similarity of element between dictionary and the local similarity between each feature of image; Secondly, utilize the method that minimizes reconstruction error with dictionary unit, usually to rebuild the topological structure of feature in image, obtain the direct relation matrix of local feature and dictionary; Last coding generation is to be multiplied each other and obtained by the relational matrix of element local similarity matrix, local feature and dictionary between dictionary and the local similarity matrix between local feature, and this encoded packets has contained the topological structure relation between local feature.The inventive method adopts Gauss algorithm and transitive closure method to calculate the local similarity between local feature, structural information between feature is added in coding, the image information comprising in perfect coding can improve Images Classification precision in the situation that using same category device.

The technical solution adopted for the present invention to solve the technical problems is: a kind of method for encoding images based on local linear constraint and global structure information, is characterized in comprising the following steps:

Step 1, suppose that in dictionary, the distribution of each element is Gaussian distributed, utilize the local similarity of element between Gaussian Computation method Dictionary of Computing:

$W(i,j)=\left\{\begin{array}{c}\exp (-\frac{\left|\right|b_i-b_j\left|\right|}{\mathrm{\σ}}),\mathrm{if}(b_j\∈k-\mathrm{NN}\left(b_i\right))\\ 0,\mathrm{otherwise}\end{array}\right.---\left(1\right)$

In formula, b _i(b _i∈ R ^d) be an element in dictionary, and dimension is d, dictionary is B _{d * c}=(b ₁, b ₂..., b _c), c is the number of all elements in dictionary, and W (i, j) is the matrix of local similarity between i element and j element in dictionary, and k-NN wherein gets k neighbour element.After W has calculated, define its normalization matrix P as follows:

P＝D ^-1W (2)

In formula, D is a diagonal matrix, and

p _ij=p (b _j| b _i) represent in dictionary that j element belongs to the posterior probability of i element arest neighbors set.

Utilize condition probability formula to obtain:

$p^{\left(t\right)}\left(b_k\right|b_i)=\underset{l=1}{\overset{c}{\mathrm{\Σ}}}p\left(b_k\right|b_l)p^{(t-1)}\left(b_l\right|b_i)---\left(3\right)$

In formula, P ^twhen being illustrated in conditional transfer step and being set to t, in dictionary there is not direct neighbor relation in k element and i element, but walked with the interior condition probability formula of utilizing and obtained their indirect neighbor's relation by t.

The weight matrix S of local similarity between each element in definition measurement dictionary:

$S=\frac{1}{t}\underset{m=0}{\overset{t-1}{\mathrm{\Σ}}}{P}^m---\left(4\right)$

Step 2, use dictionary element are rebuild the topological structure of characteristics of image, formula (5) are optimized, and obtain reconstructed coefficients in the situation that of reconstruction error minimum.

In optimizing process, meet following constraint:

||b _k||≤1,k＝1,2,...,c

1 ^Tu _i＝1

In formula, the dot product of ⊙ representing matrix element, x _i(x _i∈ R ^d) be i local feature in image, u _i(u _i∈ R ^m) be the coefficient vector of coding, m is the dimension of Image Coding, u _ijbe the coefficient of i local feature and j dictionary element, U is u _i, i=1,2 ..., the set of n, represents all local features.

$d_{\mathrm{ij}}=\exp \left(\frac{\mathrm{dist}(x_i,b_j)}{\mathrm{\σ}}\right)---\left(6\right)$

In formula, σ is the key element of controlling locality, dist (x _i, b _j) be the Euclidean distance of i local feature and j dictionary element, d _ijd _ij element.

The u that this step obtains _ithe follow-up exactly local feature that will use and the coding of the local similarity between dictionary.

Step 3, suppose the distribution Gaussian distributed of local feature, definition F represents the local similarity between local feature:

$F(i,j)=\left\{\begin{array}{c}\exp (-\frac{\left|\right|x_i-x_j\left|\right|}{\mathrm{\σ}}),\mathrm{if}(x_j\∈k-\mathrm{NN}\left(x_i\right))\\ 0,\mathrm{otherwise}\end{array}\right.---\left(7\right)$

In formula, F (i, j) is the similarity between i local feature and j local feature.

After F has calculated, define its normalization matrix Q as follows:

Q＝E ^-1F (8)

In formula, E is a diagonal matrix, and

q _ij=p (x _j| x _i) represent that j feature belongs to the posterior probability of i feature arest neighbors set.

Utilize conditional probability and transitive closure definition to weigh the weight matrix A of the local similarity between each feature:

$A=\frac{1}{h}\underset{m=0}{\overset{h-1}{\mathrm{\Σ}}}{Q}^m---\left(9\right)$

In formula, h is the transfer step that between local feature, similarity is calculated.

Step 4, utilize condition probability formula to represent that k dictionary element belongs to the probability of i local feature arest neighbors set:

$p\left(b_k\right|x_i)=\underset{l=1}{\overset{c}{\mathrm{\&Sigma;}}}{p}^{(<t)}\left(b_k\right|b_l)p\left(b_l\right|x_j)\underset{j=1}{\overset{a}{\mathrm{\&Sigma;}}}{p}^{(<h)}\left(x_j\right|x_i)=\underset{l=1}{\overset{c}{\mathrm{\&Sigma;}}}{S}_{\mathrm{lk}}{u}_{\mathrm{jl}}\underset{j=1}{\overset{a}{\mathrm{\&Sigma;}}}{A}_{\mathrm{ij}}---\left(10\right)$

In formula, S _lk=p ^{(< t)}(b _k| b _l) be element similarity matrix between the dictionary that obtains of the first step, u _jlbe the coding that reconstruction features topological structure obtains, A is the similarity measurement matrix between feature.

Adopt formula (11):

z _i＝S ^Tu _iA ^T (11)

Obtain final coding z _i.

The invention has the beneficial effects as follows: the method, first according to the hypothesis of the equal Gaussian distributed of distribution of dictionary element and local feature, utilizes Gauss algorithm and transitive closure method to build respectively the local similarity of element between dictionary and the local similarity between each feature of image; Secondly, utilize the method that minimizes reconstruction error with dictionary unit, usually to rebuild the topological structure of feature in image, obtain the direct relation matrix of local feature and dictionary; Last coding generation is to be multiplied each other and obtained by the relational matrix of element local similarity matrix, local feature and dictionary between dictionary and the local similarity matrix between local feature, and this encoded packets has contained the topological structure relation between local feature.The inventive method adopts Gauss algorithm and transitive closure method to calculate the local similarity between local feature, structural information between feature is added in coding, the image information comprising in perfect coding has improved Images Classification precision in the situation that using same category device.

Below in conjunction with embodiment, describe the present invention in detail.

Embodiment

1, the similarity between element in Dictionary of Computing.

First suppose that in dictionary, the distribution of each element is Gaussian distributed, utilize the local similarity of element between Gaussian Computation method Dictionary of Computing:

$W(i,j)=\left\{\begin{array}{c}\exp (-\frac{\left|\right|b_i-b_j\left|\right|}{\mathrm{\&sigma;}}),\mathrm{if}(b_j\&Element;k-\mathrm{NN}\left(b_i\right))\\ 0,\mathrm{otherwise}\end{array}\right.---\left(1\right)$

B _i(b _i∈ R ^d) be an element in dictionary, and dimension is d, dictionary is B _{d * c}=(b ₁, b ₂..., b _c), c is the number of all elements in dictionary, and W (i, j) is the matrix of local similarity between i element and j element in dictionary, and k-NN wherein gets k neighbour element.After W has calculated, define its normalization matrix P as follows:

P＝D ^-1W (2)

Wherein, D is a diagonal matrix, and

this step is in order to guarantee

be normalized.And P _ij=p (b _j| b _i) represented in dictionary that j element belongs to the posterior probability of i element arest neighbors set.

Utilize condition probability formula to obtain:

$p^{\left(t\right)}\left(b_k\right|b_i)=\underset{l=1}{\overset{c}{\mathrm{\&Sigma;}}}p\left(b_k\right|b_l)p^{(t-1)}\left(b_l\right|b_i)---\left(3\right)$

P ^twhen being illustrated in conditional transfer step and being set to t, in dictionary there is not direct neighbor relation in k element and i element, but walked with the interior condition probability formula of utilizing and obtained their indirect neighbor's relation by t.

The metric S of the local similarity between each element in dictionary is weighed in definition:

$S=\frac{1}{t}\underset{m=0}{\overset{t-1}{\mathrm{\&Sigma;}}}{P}^m---\left(4\right)$

S is the weight matrix of local similarity between each element in required dictionary.

2, with dictionary element, rebuild the topological structure of characteristics of image.

The topological structure of rebuilding characteristics of image with dictionary element, is optimized formula (5), obtains reconstructed coefficients in the situation that of reconstruction error minimum.

In optimizing process, meet following constraint:

||b _k||≤1,k＝1,2,...,c

1 ^Tu _i＝1

The dot product of ⊙ representing matrix element, x _i(x _i∈ R ^d) be i local feature in image, u _i(u _i∈ R ^m) be the coefficient vector of coding, m is the dimension of Image Coding, u _ijbe the coefficient of i local feature and j dictionary element, U is u _i, i=1,2 ..., the set of n, represents all local features.

$d_{\mathrm{ij}}=\exp \left(\frac{\mathrm{dist}(x_i,b_j)}{\mathrm{\&sigma;}}\right)---\left(6\right)$

σ is the key element of controlling locality, dist (x _i, b _j) be the Euclidean distance of i local feature and j dictionary element, d _ijd _ij element.

The u that this step obtains _ithe follow-up exactly local feature that will use and the coding of the local similarity between dictionary.

3, the local similarity between calculated characteristics.

Suppose the distribution Gaussian distributed of local feature, definition F represents the local similarity between local feature:

$F(i,j)=\left\{\begin{array}{c}\exp (-\frac{\left|\right|x_i-x_j\left|\right|}{\mathrm{\&sigma;}}),\mathrm{if}(x_j\&Element;k-\mathrm{NN}\left(x_i\right))\\ 0,\mathrm{otherwise}\end{array}\right.---\left(7\right)$

F (i, j) is the similarity between i local feature and j local feature.

After F has calculated, define its normalization matrix Q as follows:

Q＝E ^-1F (8)

Wherein, E is a diagonal matrix, and

this step is in order to guarantee

be normalized.And Q _ij=p (x _j| x _i) represented that j feature belongs to the posterior probability of i feature arest neighbors set.

Utilize conditional probability and transitive closure definition to weigh the metric A of the local similarity between each feature:

$A=\frac{1}{h}\underset{m=0}{\overset{h-1}{\mathrm{\&Sigma;}}}{Q}^m---\left(9\right)$

A is the weight matrix of local similarity between required each feature, and h is the transfer step that between local feature, similarity is calculated.

4, the generation of final image coding.

After first three step completes, utilize condition probability formula to represent that k dictionary element belongs to the probability of i local feature arest neighbors set:

$p\left(b_k\right|x_i)=\underset{l=1}{\overset{c}{\mathrm{\&Sigma;}}}{p}^{(<t)}\left(b_k\right|b_l)p\left(b_l\right|x_j)\underset{j=1}{\overset{a}{\mathrm{\&Sigma;}}}{p}^{(<h)}\left(x_j\right|x_i)=\underset{l=1}{\overset{c}{\mathrm{\&Sigma;}}}{S}_{\mathrm{lk}}{u}_{\mathrm{jl}}\underset{j=1}{\overset{a}{\mathrm{\&Sigma;}}}{A}_{\mathrm{ij}}---\left(10\right)$

S _lk=p ^{(< t)}(b _k| b _l) be element similarity matrix between the dictionary that obtains of the first step, u _jlbe the coding that reconstruction features topological structure obtains, A is the similarity measurement matrix between feature.

Final coding z _iwith formula (11), obtain:

z _i＝S ^Tu _iA ^T (11)。

Claims (1)

1. the method for encoding images based on local linear constraint and global structure information, is characterized in that comprising the following steps:

Step 1, suppose that in dictionary, the distribution of each element is Gaussian distributed, utilize the local similarity of element between Gaussian Computation method Dictionary of Computing:

$W(i,j)=\left\{\begin{array}{c}\exp (-\frac{\left|\right|b_i-b_j\left|\right|}{\mathrm{\&sigma;}}),\mathrm{if}(b_j\&Element;k-\mathrm{NN}\left(b_i\right))\\ 0,\mathrm{otherwise}\end{array}\right.---\left(1\right)$

In formula, b _i(b _i∈ R ^d) be an element in dictionary, and dimension is d, dictionary is B _{d * c}=(b ₁, b ₂..., b _c), c is the number of all elements in dictionary, and W (i, j) is the matrix of local similarity between i element and j element in dictionary, and k-NN wherein gets k neighbour element; After W has calculated, define its normalization matrix P as follows:

P＝D ^-1W (2)

In formula, D is a diagonal matrix, and

p _ij=p (b _j| b _i) represent in dictionary that j element belongs to the posterior probability of i element arest neighbors set;

Utilize condition probability formula to obtain:

$p^{\left(t\right)}\left(b_k\right|b_i)=\underset{l=1}{\overset{c}{\mathrm{\&Sigma;}}}p\left(b_k\right|b_l)p^{(t-1)}\left(b_l\right|b_i)---\left(3\right)$

In formula, P ^twhen being illustrated in conditional transfer step and being set to t, in dictionary there is not direct neighbor relation in k element and i element, but walked with the interior condition probability formula of utilizing and obtained their indirect neighbor's relation by t;

The weight matrix S of local similarity between each element in definition measurement dictionary:

$S=\frac{1}{t}\underset{m=0}{\overset{t-1}{\mathrm{\&Sigma;}}}{P}^m---\left(4\right)$

Step 2, use dictionary element are rebuild the topological structure of characteristics of image, formula (5) are optimized, and obtain reconstructed coefficients in the situation that of reconstruction error minimum;

In optimizing process, meet following constraint:

||b _k||≤1,k＝1,2,...,c

1 ^Tu _i＝1

In formula, the dot product of ⊙ representing matrix element, x _i(x _i∈ R _d) be i local feature in image, u _i(u _i∈ R ^m) be the coefficient vector of coding, m is the dimension of Image Coding, u _ijbe the coefficient of i local feature and j dictionary element, U is u _i, i=1,2 ..., the set of n, represents all local features;

$d_{\mathrm{ij}}=\exp \left(\frac{\mathrm{dist}(x_i,b_j)}{\mathrm{\&sigma;}}\right)---\left(6\right)$

In formula, σ is the key element of controlling locality, dist (x _i, b _j) be the Euclidean distance of i local feature and j dictionary element, d _ijd _ij element;

The u that this step obtains _ithe follow-up exactly local feature that will use and the coding of the local similarity between dictionary;

Step 3, suppose the distribution Gaussian distributed of local feature, definition F represents the local similarity between local feature:

$F(i,j)=\left\{\begin{array}{c}\exp (-\frac{\left|\right|x_i-x_j\left|\right|}{\mathrm{\&sigma;}}),\mathrm{if}(x_j\&Element;k-\mathrm{NN}\left(x_i\right))\\ 0,\mathrm{otherwise}\end{array}\right.---\left(7\right)$

In formula, F (i, j) is the similarity between i local feature and j local feature;

After F has calculated, define its normalization matrix Q as follows:

Q＝E ^-1F (8)

In formula, E is a diagonal matrix, and

q _ij=p (x _j| x _i) represent that j feature belongs to the posterior probability of i feature arest neighbors set;

Utilize conditional probability and transitive closure definition to weigh the weight matrix A of the local similarity between each feature:

$A=\frac{1}{h}\underset{m=0}{\overset{h-1}{\mathrm{\&Sigma;}}}{Q}^m---\left(9\right)$

In formula, h is the transfer step that between local feature, similarity is calculated;

Step 4, utilize condition probability formula to represent that k dictionary element belongs to the probability of i local feature arest neighbors set:

$p\left(b_k\right|x_i)=\underset{l=1}{\overset{c}{\mathrm{\&Sigma;}}}{p}^{(<t)}\left(b_k\right|b_l)p\left(b_l\right|x_j)\underset{j=1}{\overset{a}{\mathrm{\&Sigma;}}}{p}^{(<h)}\left(x_j\right|x_i)=\underset{l=1}{\overset{c}{\mathrm{\&Sigma;}}}{S}_{\mathrm{lk}}{u}_{\mathrm{jl}}\underset{j=1}{\overset{a}{\mathrm{\&Sigma;}}}{A}_{\mathrm{ij}}---\left(10\right)$

In formula, S _lk=p ^{(< t)}(b _k| b _l) be element similarity matrix between the dictionary that obtains of the first step, u _jlbe the coding that reconstruction features topological structure obtains, A is the similarity measurement matrix between feature;

Adopt formula (11):

z _i＝S ^Tu _iA ^T (11)

Obtain final coding z _i.