CN102122353A - Method for segmenting images by using increment dictionary learning and sparse representation - Google Patents

Abstract

The invention discloses a method for segmenting images by using increment dictionary learning and sparse representation, which mainly solves the problem that the accuracy rate of the sparse representation segmentation result is reduced quickly when the similarity among the categories is increased in the prior art. The method comprises the following steps of: obtaining clustering results of to-be-segmented image categories K by a K mean algorithm; training a part of results of each category serving as a training sample set to obtain K dictionaries; performing sparse representation on characteristic points of each unknown tag by using the dictionaries to obtain K sparse representation errors; performing classification by using the magnitude of the sparse representation errors, selecting a training sample set for increment learning based on the classification result, and retraining the training sample set to obtain K dictionaries; performing sparse representation on input signals by using the dictionaries to obtain K sparse representation errors; and performing final segmentation of the images by using the errors. Compared with the prior art, the method remarkably improves the segmentation performance of the images, and can be used for target detection and background separation.

Description

Utilize study of increment dictionary and rarefaction representation to carry out the method for image segmentation

Technical field

The invention belongs to technical field of image processing, relate to a kind of dividing method of image, can be used for texture image is cut apart.

Background technology

Image segmentation is one of technology basic and crucial in Flame Image Process and the computer vision, its objective is target and background is separated.Image segmentation just is meant image is divided into the zone of each tool characteristic and extracts the technology and the process of interesting target, for follow-up classification, identification and retrieval provide foundation.Here characteristic can be gray scale, color, texture of pixel etc., and Dui Ying target can corresponding single zone in advance, also can corresponding a plurality of zones.The application of image segmentation is very extensive, almost appears at all spectra of relevant Flame Image Process, for example medical image analysis, and the military field engineering field, the remote sensing meteorological field, traffic image analysis etc., image partition method also becomes the focus of people's research.The method of image segmentation has a variety of, rarefaction representation sorter for example, K mean algorithm etc.

The rarefaction representation sorter that people such as Wright propose is to use training data as base, utilizes the error of rarefaction representation to come image is classified.The weak point of this method is the selection that accuracy relatively depends on base, and when having selected reasonable sample as base, this method can obtain reasonable segmentation effect.

And K mean algorithm velocity ratio is very fast, though can obtain better segmentation effect, not enough place is because the selection of initial point is at random, so segmentation result and unstable.

Summary of the invention

The objective of the invention is to overcome the shortcoming of above-mentioned prior art, a kind of method of utilizing study of increment dictionary and rarefaction representation to carry out image segmentation has been proposed, with the rarefaction representation of realization, thereby improve effect of cutting apart and the stability that increases segmentation result to each width of cloth image.

For achieving the above object, at first obtain the cluster result of image K class to be split by the K mean algorithm, then with the part among every class result as training sample set, training obtains K dictionary, utilize dictionary that the unique point of each Unknown Label is done rarefaction representation again, obtain K rarefaction representation error, utilize the size of rarefaction representation error to classify, on the basis of this classification results, select to carry out the training sample set of incremental learning, again training obtains K dictionary, utilize dictionary that each input signal is done rarefaction representation again, obtain K rarefaction representation error, utilize error to carry out finally cutting apart of image.Concrete steps comprise:

(1) image to be split of input one width of cloth N * N, this image to be split is carried out three layers of wavelet transformation successively, extracts the wavelet character of image to be split and calculates gray level co-occurrence matrixes, and from gray level co-occurrence matrixes, extract gray scale symbiosis feature, obtain the wavelet character vector of 10 * 1 corresponding dimensions of each point and the gray scale symbiosis feature of 12 * 1 dimensions, the total dimension of composition characteristic vector is 22 * 1, and size is 22 * N ²The eigenmatrix M of dimension,

Described gray scale symbiosis feature is included in 0 °, and 45 °, 90 °, the angle second moment f on 135 ° of four directions ₁, homogeneity district f ₂With contrast f ₃Three statistics are calculated these statistics respectively on 4 directions, obtain characteristic v=(f ₁,, f ₂..., f ₁₂);

(2) utilize eigenmatrix M, treat split image with the K mean algorithm and carry out cluster, be divided into the K class, and put from this K class and to choose 50% proper vector K training sample set Y=Y the pairing proper vector respectively as correspondence ₁, Y ₂... Y _K, Y _iBe 50% the proper vector of from i category feature vector, choosing, i=1,2, L, K;

(3) utilize the KSVD algorithm to separate formula:

Obtain target training dictionary D=[D ₁, D ₂... D _K], D _iBe i class training sample set Y _iThe dictionary that training obtains, i=1,2, L, K

In the formula, X is sparse matrix of coefficients, and min|||| represents to allow the value of bracket the inside reach minimum, and Subject to represents constraint condition,

Be any i row, X _iBe the i row of sparse matrix of coefficients, || || ₀Be 0 norm of vector,

For 2 norms of matrix square, T ₀Be the degree of rarefication control coefrficient;

(4) utilize the BP algorithm to separate formula: min||X _i|| Subject to M _j=D _iX _i, i=1,2, L, K upgrades K sparse matrix of coefficients X=[X ₁, X ₂... X _K], X _iBe the sparse matrix of coefficients of i category dictionary correspondence, i=1,2, L, K,

In the formula, M _jJ column vector for M in the eigenmatrix is proper vector, j=1,2, L, N ², N ²Dimension for image to be split;

(5) utilize identify (M _j)=min{M _j-D _iX _i, i=1,2, L, K is the calculated characteristics vector M respectively _jRarefaction representation error under the K category dictionary is with proper vector M _jCorresponding point is assigned in pairing that class of the dictionary that makes rarefaction representation error amount minimum and is gone, in the formula, and identify (M _j) be proper vector M _jAffiliated classification;

(6) repeating step (5) all points in image are all classified and are finished, and according to the classification under the pixel, image are cut apart, and obtain K class initial segmentation result;

(7) in K class initial segmentation result, according to existing label, the correct point of classification in the segmentation result is elected, in the correct point of these classification, when this point is consistent with some classification in its neighborhood window, select the training sample of this characteristic of correspondence vector as such, with each class choose total sample number 50% as training sample, obtain K class training sample set Y ' ₁, Y ' ₂... Y ' _K

(8) repeating step (3) obtains the final segmentation result of image, and with different colors different classes of pixel is showed to step (6).

The present invention has the following advantages compared with prior art:

(1) the present invention makes that the segmentation result of this method is more stable owing to utilize KSVD algorithm training dictionary;

(2) the present invention makes that the segmentation result of this method is more accurate owing to taked the method for incremental learning.

Description of drawings

Fig. 1 is realization flow figure of the present invention;

Fig. 2 is the present invention and existing K mean algorithm, the KNSC algorithm segmentation result comparison diagram to two class texture image test1;

Fig. 3 is the present invention and existing K mean algorithm, the KNSC algorithm segmentation result comparison diagram to three class texture image test2;

Fig. 4 is the present invention and existing K mean algorithm, the KNSC algorithm segmentation result comparison diagram to four class texture image test3;

Fig. 5 is the present invention and existing K mean algorithm, the KNSC algorithm segmentation result comparison diagram to four class texture image test4;

Fig. 6 is the present invention and existing K mean algorithm, the KNSC algorithm segmentation result comparison diagram to four class texture image test5.

Specific implementation method

With reference to accompanying drawing 1, concrete steps of the present invention comprise:

Step 1. input size is the image to be split of N * N, extracts the eigenmatrix M of image to be split

The textural characteristics that the present invention treats the split image extraction comprises gray scale symbiosis feature and wavelet character:

1a) use gray level co-occurrence matrixes to treat split image and carry out feature extraction

Image to be split is generated gray level co-occurrence matrixes p _Ij(s, θ), wherein s is pixel x _iAnd x _jBetween distance, the value of θ is 4 discrete directions: 0 °, 45 °, 90 °, 135 °, get three statistics on each direction: the angle second moment, the homogeneity district, contrast, each statistic is calculated according to following formula:

The angle second moment: $f_1=\underset{i=0}{\overset{N^2-1}{\mathrm{\Σ}}}\underset{j=0}{\overset{N^2-1}{\mathrm{\Σ}}}{p}^2(i,j)$

The homogeneity district: $f_2=\underset{i=0}{\overset{N^2-1}{\mathrm{\Σ}}}\underset{j=0}{\overset{N^2-1}{\mathrm{\Σ}}}p(i,j)/{[1+{(i-j)}^2]}^2$

Contrast: $f_3=\underset{i=0}{\overset{N^2-1}{\mathrm{\Σ}}}\underset{j=0}{\overset{N^2-1}{\mathrm{\Σ}}}|i-j|p(i,j)$

Wherein, N ²Be total sample number, (i j) is gray level co-occurrence matrixes p to p _Ij(s, θ) element of the capable j row of i calculates above-mentioned statistic respectively on 4 directions, obtains characteristic v=(f ₁,, f ₂..., f ₁₂);

1b) wavelet character extracts

Treat that the pixel with feature to be extracted is the center in the split image, image subblock in the characteristic window of setting carries out one-dimensional filtering respectively along x direction and y direction, again each yardstick is resolved into four subband LL, HL, LH and HH, with the details on the low-frequency information of token image respectively and level, the vertical and tilted direction, the LL subband of ground floor is decomposed, obtain four subband LL, HL, LH and HH of the second layer, LL subband to the second layer decomposes again, obtain the 3rd layer four subband LL, HL, LH and HH, three layers obtain 10 subbands altogether;

By formula

Obtain the L of each subband respectively ₁Norm, in the formula, W represents the L of subband ₁Norm, A is the line number of sub-band coefficients, B is the columns of sub-band coefficients, A * B is the subband size, and a represents the index of row coefficient in the subband, and b represents the index of row coefficient in the subband, (a is the coefficient value of the capable b row of a in this subband b) to coef, thereby obtains the proper vector (W of one 10 dimension ₀, W ₁..., W ₉).

Step 2. utilizes the K mean algorithm that this eigenmatrix M is carried out cluster

2a) from the N of eigenmatrix M ²Picked at random K is listed as K initial cluster center in the row, is designated as C=[C ₁, C ₂, L, C _K], each column vector C _iAll be 22 * 1 dimensions, i=1,2, L, K;

2b) to the proper vector among the eigenmatrix M

I=1,2, L, N ², utilize formula

K=1,2, L, K is the calculated characteristics vector M respectively _iWith K initial cluster center C=[C ₁, C ₂, L, C _K] Euclidean distance, obtain K Euclidean distance (O ₁, O ₂, L, O _K), from these Euclidean distances, take out minimum Euclidean distance O _j, j ∈ 1,2, L, K is with M _iCorresponding pixel is divided into C _jGo in that corresponding class;

2c) in eigenmatrix M, to K initial cluster center C=[C ₁, C ₂, L, C _K] in addition the multiple step 2b of each column weight), obtain K cluster result;

2d) in K cluster result of gained, with all proper vector additions of each class,, obtain such new cluster centre: C '=[C respectively again divided by the number of the proper vector that such comprised ₁', C ₂', L, C _K'], repeating step 2b) to 2c) the renewal cluster result;

2e) repeating step 2b) to 2d) reach its set iterations up to the K mean algorithm, obtain K cluster result at last, and it is made as the initial clustering result of image, number of iterations is relevant with different classes of texture similarity, for example to the image to be split among the accompanying drawing figure of the present invention (3a), number of times chooses 1000 just can obtain result preferably.

Step 3. is extracted K training sample set Y=Y from the initial clustering result ₁, Y ₂, L, Y _K

3a) to being divided into any one point in the k class, k=1,2, L, K judges whether point in this vertex neighborhood window and its are same class, if 22 * 1 dimensional feature vectors of its correspondence are made as a training sample that collects in the k class training sample;

3b) training sample of choosing the k class reaches the ratio of setting up to number of samples, then forwarding to and utilize step 3a in other class) the selected characteristic vector comes the composing training sample, this ratio is relevant with different classes of texture similarity, for example, under 50% ratio, just can obtain result preferably to the image to be split among the accompanying drawing figure of the present invention (3a).

Step 4. utilizes the KSVD algorithm to K class training sample set Y=Y ₁, Y ₂, L, Y _KTrain, obtain K target training dictionary D ₁, D ₂... D _k

4a) from the KSVD algorithm, provide total optimization formula

Wherein, D=[D ₁, D ₂... D _k] being initialized as dictionary at random, X is sparse matrix of coefficients, and min|||| represents to allow the value of bracket the inside reach minimum, and Subject to represents constraint condition,

Be any i row, X _iBe the i row of sparse matrix of coefficients, || || ₀Be 0 norm of vector, For 2 norms of matrix square, T ₀Be the degree of rarefication control coefrficient;

4b) in total optimization formula

Be out of shape and obtain:

${\left|\right|Y-\mathrm{DX}\left|\right|}_2^2={\left|\right|Y-\underset{j=1}{\overset{L}{\mathrm{\Σ}}}{d}_j{x}_j^T\left|\right|}_2^2={\left|\right|(Y-\underset{j\≠z}{\overset{L}{\mathrm{\Σ}}}{d}_j{x}_j^T)-d_z{x}_z^T\left|\right|}_2^2={\left|\right|E_z{-d}_z{x}_z^T\left|\right|}_2^2$

In the formula, d _jBe the j row atom of D,

For the j of X is capable, L is total columns of D, d _zBe the z row atom of D,

For the z of X is capable, E _zFor not using the z row atom d of D _zCarry out the error matrix that Sparse Decomposition produced;

4c) to being out of shape the formula of back gained

Multiply by matrix Ω _z, obtain the target decomposition formula ${\left|\right|E_z{\mathrm{\Ω}}_z-d_z{x}_z^T{\mathrm{\Ω}}_z\left|\right|}_2^2={\left|\right|E_z^R-d_z{x}_z^R\left|\right|}_2^2,$

Distortion inaccuracy matrix in the formula

Be error matrix E _zDistortion,

Ω _zSize be P * | ω _z|, P is the columns of training sample set Y,

| ω _z| be ω _zThe mould value, and Ω _zAt (ω _z(j), j) locating is 1, and other place is 0 entirely, wherein 1≤j≤| ω _z|, ω _z(j) be ω _zThe j number;

4d) to gained target decomposition formula

In the distortion inaccuracy matrix

Carrying out the SVD decomposition obtains

Wherein U is a left singular matrix, V ^TBe right singular matrix, Δ is a singular value matrix;

4e) first row with gained left singular matrix U remove the more z row atom d of fresh target train word allusion quotation D _z

4f) repeating step 4c) to step 4e) all atoms among the D are upgraded processing, obtain K new dictionary D ' ₁, D ' ₂... D ' _K

Step 5. couple gained eigenmatrix M is at K dictionary D ' ₁, D ' ₂... D ' _KOn utilize the BP algorithm to carry out Sparse Decomposition, obtain the sparse matrix of coefficients corresponding, and obtain the error of the rarefaction representation of each category dictionary with the K category dictionary, utilize the gained error that image is carried out cluster

5a) to a column vector M among the gained eigenmatrix M _i, utilize the BP algorithm to separate following formula:

Obtain and the corresponding K of K category dictionary sparse matrix of coefficients X _j, j=1,2, L, K, wherein, M _iBe i proper vector in the eigenmatrix, D _jBe the dictionary of j class data correspondence, X _jBe the sparse matrix of coefficients corresponding with it;

5b) utilize formula R _j=M _i-D _jX _j, j=1,2, L, K calculate the error of each category dictionary, obtain the error amount R of a minimum _Min, min ∈ 1,2, and L, k} is with this feature M _iPairing point is poly-again in the min class, just allows the label of this point be made as min;

5c) to each column vector of gained eigenmatrix M, repeating step 5a) and 5b), finish up to have a few all again cluster.

The cluster label that step 6. obtains according to step 5 is treated split image and is carried out initial segmentation, and the pixel that is about to identical cluster label is grouped in the same classification, obtains initial segmentation result.

Step 7. is extracted the K class sample set Y ' that carries out incremental learning according to initial segmentation result ₁, Y ' ₂, L, Y ' _K

7a), will cut apart correct clicking and take out by given correct label;

7b) cut apart correct point in the k class and judge being divided into, k=1,2, L, K, if the point in this neighborhood of a point window all belongs to a class together with this point, then the proper vector that will put is grouped in such training sample set;

7c) point in the same classification is judged successively, reach a set ratio up to the training sample number, then such training sample extracts and finishes, and forward to utilize step 7b in other classifications) the selected characteristic vector comes the composing training sample set, this ratio is relevant with different classes of texture similarity, for example, under 50% ratio, just can obtain result preferably to the image to be split among the accompanying drawing figure of the present invention (3a).

Step 8. repeating step 4 obtains final segmentation result to step 6

Utilize K class training sample set Y ' ₁, Y ' ₂, L, Y ' _KRepeating step 4 obtains final segmentation result to step 6 and also with different colors different classes of pixel is showed.

Effect of the present invention can further specify by following experiment:

1) experiment condition

The experiment simulation environment is: MATLAB 7.1.0.246 (R14) Service Pack 3,

4CPU 2.4GHz, Window XP Professional; Experimental image is: two class texture image test1, and three class texture image test2, three four class texture image: test3, test4, test5, five width of cloth texture image sizes are 256 * 256; The test feature parameter is: gray scale symbiosis feature and wavelet character, proper vector dimension are 22 * 1, and gray scale symbiosis characteristic window size is 17 * 17, and the wavelet character window is 16 * 16.

2) experiment content

2.1) with the present invention and K-means and three kinds of methods of KNSC texture image test1 is experimentized, three kinds of dividing method results as shown in Figure 2, wherein figure (2a) is the original image of test1; Figure (2b) is the template of cutting apart of figure (2a); Figure (2c) is the segmentation result of existing K-means algorithm to figure (2a); Figure (2d) is the segmentation result of existing KNSC algorithm to figure (2a); Figure (2e) is the segmentation result of algorithm of the present invention to figure (2a);

2.2) with the present invention and K-means and three kinds of methods of KNSC texture image test2 is experimentized, three kinds of dividing method results as shown in Figure 3, wherein figure (3a) is the original image of test2; Figure (3b) is the template of cutting apart of figure (3a); Figure (3c) is the segmentation result of existing K-means algorithm to figure (3a); Figure (3d) is the segmentation result of existing KNSC algorithm to figure (3a); Figure (3e) is the segmentation result of algorithm of the present invention to figure (3a);

2.3) with the present invention and K-means and three kinds of methods of KNSC texture image test3 is experimentized, three kinds of dividing method results as shown in Figure 4, wherein figure (4a) is the original image of test3; Figure (4b) is the template of cutting apart of figure (4a); Figure (4c) is the segmentation result of existing K-means algorithm to figure (4a); Figure (4d) is the segmentation result of existing KNSC algorithm to figure (4a); Figure (4e) is the segmentation result of algorithm of the present invention to figure (4a);

2.4) with the present invention and K-means and three kinds of methods of KNSC texture image test4 is experimentized, three kinds of dividing method results as shown in Figure 5, wherein figure (5a) is the original image of test4; Figure (5b) is the template of cutting apart of figure (5a); Figure (5c) is the segmentation result of existing K-means algorithm to figure (5a); Figure (5d) is the segmentation result of existing KNSC algorithm to figure (5a); Figure (5e) is the segmentation result of algorithm of the present invention to figure (5a);

2.5) with the present invention and K-means and three kinds of methods of KNSC texture image test5 is experimentized, three kinds of dividing method results as shown in Figure 6, wherein figure (6a) is the original image of test5; Figure (6b) is the template of cutting apart of figure (6a); Figure (6c) is the segmentation result of existing K-means algorithm to figure (6a); Figure (6d) is the segmentation result of existing KNSC algorithm to figure (6a); Figure (6e) is the segmentation result of algorithm of the present invention to figure (6a).

3) interpretation

From Fig. 2, Fig. 3, Fig. 4, Fig. 5, Fig. 6 can see that K average and the segmentation effect of KNSC algorithm on the edge are not fine, and the result that result of the present invention obtains on the edge is relatively good.In addition, preceding two kinds of methods keep to such an extent that be not fine on regional consistance mutually for purposes of the invention.

Table 1 has provided algorithms of different to test1, test2, test3, test4, test5 segmentation result, the number percent of correct classified pixels point number of data representation and total number of image pixels in the table 1, correct classified pixels number/total number of image pixels * 100%.

Table 1. texture image mistake divides rate relatively

As can be known from Table 1, segmentation result of the present invention is compared with other two kinds of algorithm segmentation results, and accuracy obviously improves.

Claims (6)

1. method of utilizing increment dictionary study and rarefaction representation to carry out image segmentation comprises following steps:

(1) image to be split of input one width of cloth N * N, this image to be split is carried out three layers of wavelet transformation successively, extracts the wavelet character of image to be split and calculates gray level co-occurrence matrixes, and from gray level co-occurrence matrixes, extract gray scale symbiosis feature, obtain the wavelet character vector of 10 * 1 corresponding dimensions of each point and the gray scale symbiosis feature of 12 * 1 dimensions, the total dimension of composition characteristic vector is 22 * 1, and size is 22 * N ²The eigenmatrix M of dimension,

Described gray scale symbiosis feature is included in 0 °, and 45 °, 90 °, the angle second moment f on 135 ° of four directions ₁, homogeneity district f ₂With contrast f ₃Three statistics are calculated these statistics respectively on 4 directions, obtain characteristic v=(f ₁,, f ₂..., f ₁₂);

(2) utilize eigenmatrix M, treat split image with the K mean algorithm and carry out cluster, be divided into the K class, and put from this K class and to choose 50% proper vector K training sample set Y=Y the pairing proper vector respectively as correspondence ₁, Y ₂... Y _K, Y _iBe 50% the proper vector of from i category feature vector, choosing, i=1,2, L, K;

(3) utilize the KSVD algorithm to separate formula:

Obtain target training dictionary D=[D ₁, D ₂... D _K], D _iBe i class training sample set Y _iThe dictionary that training obtains, i=1,2, L, K

In the formula, X is sparse matrix of coefficients, and min|||| represents to allow the value of bracket the inside reach minimum, and Subject to represents constraint condition,

Be any i row, X _iBe the i row of sparse matrix of coefficients, || || ₀Be 0 norm of vector,

For 2 norms of matrix square, T ₀Be the degree of rarefication control coefrficient;

(4) utilize the BP algorithm to separate formula: min||X _i|| Subject to M _j=D _iX _i, i=1,2, L, K upgrades K sparse matrix of coefficients X=[X ₁, X ₂... X _K], X _iBe the sparse matrix of coefficients of i category dictionary correspondence, i=1,2, L, K,

In the formula, M _jJ column vector for M in the eigenmatrix is proper vector, j=1,2, L, N ², N ²Dimension for image to be split;

(5) utilize identify (M _j)=min{M _j-D _iX _i, i=1,2, L, K is the calculated characteristics vector M respectively _jRarefaction representation error under the K category dictionary is with proper vector M _jCorresponding point is assigned in pairing that class of the dictionary that makes rarefaction representation error amount minimum and is gone, in the formula, and identify (M _j) be proper vector M _jAffiliated classification;

(6) repeating step (5) all points in image are all classified and are finished, and according to the classification under the pixel, image are cut apart, and obtain K class initial segmentation result;

(7) in K class initial segmentation result, according to existing label, the correct point of classification in the segmentation result is elected, in the correct point of these classification, when this point is consistent with some classification in its neighborhood window, select the training sample of this characteristic of correspondence vector as such, with each class choose total sample number 50% as training sample, obtain K class training sample set Y ' ₁, Y ' ₂... Y ' _K

(8) repeating step (3) obtains the final segmentation result of image, and with different colors different classes of pixel is showed to step (6).

2. according to claims 1 described image partition method, wherein step (1) is described treats the wavelet character that split image carries out three layers of wavelet transformation successively, extracts image to be split, carries out according to following steps:

2a) treat that the pixel with feature to be extracted is the center in the split image, image subblock in the characteristic window of setting carries out one-dimensional filtering respectively along x direction and y direction, again each yardstick is resolved into four subband LL, HL, LH and HH, the details on the low-frequency information of token image and level, the vertical and tilted direction respectively, the LL subband of ground floor is decomposed, obtain four subband LL, HL, LH and HH of the second layer, LL subband to the second layer decomposes again, obtain the 3rd layer four subband LL, HL, LH and HH, three layers obtain 10 subbands altogether;

2b) by formula

Obtain the L of each subband respectively ₁Norm, in the formula, W represents the L of subband ₁Norm, A is the line number of sub-band coefficients, B is the columns of sub-band coefficients, A * B is the subband size, and a represents the index of row coefficient in the subband, and b represents the index of row coefficient in the subband, (a is the coefficient value of the capable b row of a in this subband b) to coef, thereby obtains the proper vector (W of one 10 dimension ₀, W ₁..., W ₉).

3. according to claims 1 described image partition method, step (1) described angle second moment f wherein ₁, be calculated as follows:

$f_1=\underset{i=0}{\overset{N^2-1}{\mathrm{\Σ}}}\underset{j=0}{\overset{N^2-1}{\mathrm{\Σ}}}{p}^2(i,j)$

Wherein, N ²Be the dimension of image to be split, (i j) is the gray level co-occurrence matrixes p of image to be split to p _Ij(s is pixel x for s, the θ) element of the capable j row of i _iAnd x _jBetween distance, the value of θ is 4 discrete directions: 0 °, 45 °, 90 °, 135 °.

4. according to claims 1 described image partition method, the described homogeneity of step (1) district f wherein ₂, be calculated as follows:

$f_2=\underset{i=0}{\overset{N^2-1}{\mathrm{\Σ}}}\underset{j=0}{\overset{N^2-1}{\mathrm{\Σ}}}p(i,j)/{[1+{(i-j)}^2]}^2.$

5. according to claims 1 described image partition method, the described contrast f of step (1) wherein ₃, be calculated as follows:

$f_3=\underset{i=0}{\overset{N^2-1}{\mathrm{\Σ}}}\underset{j=0}{\overset{N^2-1}{\mathrm{\Σ}}}|i-j|p(i,j).$

6. according to claims 1 described image partition method method, wherein the described KSVD of the utilization algorithm of step (3) is separated formula:

Carry out according to following steps:

6a) in total optimization formula Be out of shape and obtain:

${\left|\right|Y-\mathrm{DX}\left|\right|}_2^2={\left|\right|Y-\underset{j=1}{\overset{L}{\mathrm{\Σ}}}{d}_j{x}_j^T\left|\right|}_2^2={\left|\right|(Y-\underset{j\≠z}{\overset{L}{\mathrm{\Σ}}}{d}_j{x}_j^T)-d_z{x}_z^T\left|\right|}_2^2={\left|\right|E_z{-d}_z{x}_z^T\left|\right|}_2^2$

In the formula, Y=Y ₁, Y ₂... Y _KBe training sample set, D=[D ₁, D ₂... D _k] being initialized as dictionary at random, X is sparse matrix of coefficients,

For 2 norms of matrix square, T ₀Be degree of rarefication control coefrficient, d _jBe the j row atom of D,

For the j of X is capable, L is total columns of D, d _zBe the z row atom of D,

For the z of X is capable, E _zFor not using the z row atom d of D _zCarry out the error matrix that Sparse Decomposition produced;

6b) to being out of shape the formula of back gained

Multiply by matrix Ω _z, obtain the target decomposition formula ${\left|\right|E_z{\mathrm{\Ω}}_z-d_z{x}_z^T{\mathrm{\Ω}}_z\left|\right|}_2^2={\left|\right|E_z^R-d_z{x}_z^R\left|\right|}_2^2,$

Distortion inaccuracy matrix in the formula

Be error matrix E _zDistortion,

Ω _zSize be P * | ω _z|, P is the columns of training sample set Y,

| ω _z| be ω _zThe mould value, and Ω _zAt (ω _z(j), j) locating is 1, and other place is 0 entirely, wherein 1≤j≤| ω _z|, ω _z(j) be ω _zThe j number;

6c) to gained target decomposition formula

In the distortion inaccuracy matrix

Carrying out the SVD decomposition obtains

Wherein U is a left singular matrix, V ^TBe right singular matrix, Δ is a singular value matrix;

6d) first row with gained left singular matrix U remove the more z row atom d of fresh target train word allusion quotation D _z

6e) repeating step 6b) to step 6d) all atoms among the D are upgraded processing, obtain K new dictionary D ' ₁, D ' ₂... D ' _K

Images