CN103258210A - High-definition image classification method based on dictionary learning - Google Patents

High-definition image classification method based on dictionary learning Download PDF

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CN103258210A
CN103258210A CN2013102027998A CN201310202799A CN103258210A CN 103258210 A CN103258210 A CN 103258210A CN 2013102027998 A CN2013102027998 A CN 2013102027998A CN 201310202799 A CN201310202799 A CN 201310202799A CN 103258210 A CN103258210 A CN 103258210A
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visual signature
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罗笑南
邓伟财
陈湘萍
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Sun Yat Sen University
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Abstract

The invention discloses a high-definition image classification method based on dictionary learning and relates to the field of digital image processing. The high-definition image classification method based on the dictionary learning comprises the following steps of extracting visual characteristics of all high-definition image samples, for the visual characteristics, conducting sparse coding on the high-definition image samples, continuously conducting dictionary learning through the iterative method until classification errors are less than a threshold, determining a classification dictionary of high-definition image classes, determining a corresponding weight based on the degree of influence of each visual characteristic on one reconstruction error, establishing an image nonlinear classifier based on the dictionary of the high-definition image classes and the corresponding weights of the visual characteristics, and determining the class of the high-definition image. Through the high-definition image classification method based on the dictionary learning, the dictionary learning through the sparse coding can be conducted, and sparse codes with a high distinction degree can be obtained. Therefore, the high-definition image classification method based on the dictionary learning has good self adaptability, to sample space distribution of a high-definition image data set, has better robustness for a complicated image, and has good generality and high practical value.

Description

A kind of high-definition image sorting technique based on dictionary study
Technical field
The present invention relates to digital image processing field, be specifically related to a kind of high-definition image sorting technique based on dictionary study.
Background technology
At present, along with development and the widespread use of computer network rapid development, digital media technology and intelligent information processing technology, extensive image resource constantly occurs.Image information facing to magnanimity, how image is classified or mark in case from mass image data, retrieve rapidly, effectively the research focus in artificial intelligence and the pattern-recognition of interested image, have a wide range of applications in fields such as scientific research, national defense and military, commercial production, Aero-Space, biomedicine, traffic monitorings.
To history decades of the research of image classification, during emerged in large numbers various sorting techniques based on different theories, still, this field never forms design and the realization that a unified theoretical system instructs new sorting technique.In recent years, the common method of image classification comprises statistical method and structural approach, but statistical method shows active in image classification field, a lot of new methods have been produced, as neural net method, support vector machine (Support Vector Machine, SVM) method and Boosting method.According to the difference of implementation method, statistical method can be divided into:
1) unsupervised classification method: claim clustering methodology again, carry out category division according to the similarity between the pattern, the mode division that similarity is strong is same classification.This method does not need that grouped data is had more deep understanding, forms categorized data set adaptively, but classifying quality is not ideal in complex data.
2) supervised classification: according to the training sample of known class in advance, obtain all kinds of distribution scales at feature space, and utilize this regularity of distribution that unknown data is carried out sorting technique.This method takes full advantage of the priori of grouped data, and can improve nicety of grading by the repeated examinations training sample, so the widespread use in the high-definition image classification of this method.
Support vector machine (SVM) is widely used in image classification field and obtains good classifying quality at present, support vector machine the earliest (SVM) method is to be proposed in " Support-Vector Networks; Machine Learning; 20,1995. " literary composition by Vapnik and Chervonenkis.Support vector machine (SVM) is novel machine learning method, has complete Statistical Learning Theory basis, it adopts the empiric risk minimization principle based on large sample in the structural risk minimization replacement traditional statistics, having overcome neural network, to be subjected to the influence of the complicated network structure and sample size big, the deficiency that occurred study or low generalization ability easily, data analysis has outstanding learning ability and popularization ability for small sample, in pattern-recognition and Function Estimation, obtained effective application, but still there is following problem in this method:
(1) the SVM algorithm is difficult to carry out extensive training sample, because SVM finds the solution support vector by quadratic programming, and find the solution the calculating (m is the number of sample) that quadratic programming will be referred to m rank matrix, the storage of this matrix and calculating will expend a large amount of machine internal memory and operation time when the m number is very big.
(2) complexity of SVM method can increase fast with the increase of feature number, is used for the sample size of training classifier and test result can be exponential relationship along with the quantity of feature and increase; If increase the not strong feature of adaptability or with existing feature the feature of strong correlation arranged, the classification capacity of sorter is descended, reduce the ability of system identification classification.
Afterwards, the France scholar thinks that at central this algorithm that proposes of I.Guyon document " Guyon I; Weston J; Barnhill; et al.Gene Selection for Cancer Classification Using Support Vector Machines.Machine Learning; 2002; 46 (1/2/3): 389-422 " using the SVM-RFE algorithm can guarantee to keep optimizes character subset when feature is sorted in the process of feature ordering, the information in the discriminant function of this method use support vector machine realizes.The SVM-RFE method is the process of a circulation, comprises following steps: 1) use the current data set training classifier, obtain the relevant information of institute's use characteristic according to the gained sorter; 2) according to the rule of formulating in advance, calculate the ranking criteria mark of all features; 3) concentrate the feature that removes corresponding to minimum ranking criteria mark in current data.This cyclic process finishes the algorithm execution result when carrying out in the feature set last variable of residue be that row are according to the feature sequence number tabulation of feature importance ranking.
The present invention program is based on the existing deficiency of above-mentioned sorting technique, non-linear sorting technique based on dictionary study has been proposed, utilize dictionary learning method adaptive training to go out the potential general character of image pattern in the classification, distinguish the characteristic of different images effectively, and can automatically give weights according to the correlativity of feature in the dictionary learning process, improve the feature of strong correlation to the influence of classification capacity, improve the efficient of classification effectively.
Summary of the invention
The objective of the invention is provides a kind of sorting technique to high-definition image, and this method can solve that the classification speed of present supervised classification method is slow, complexity increases along with the feature number and the problem of exponential increase, feature affects nicety of grading that correlativity is not strong.
The invention provides a kind of high-definition image sorting technique based on dictionary study, comprise the steps:
S1: the visual signature that extracts all high-definition image samples;
S2: for described visual signature, the high-definition image sample is carried out sparse coding, constantly carry out dictionary study by alternative manner,, determine the classifying dictionary of high-definition image classification and according to visual signature the degree of influence of reconstructed error is determined corresponding weights less than threshold value up to error in classification;
S3: set up the image non-linear sorter according to the dictionary of described high-definition image classification and the weights of visual signature correspondence, determine the classification that described high-definition image is affiliated.
Above-mentioned high-definition image sorting technique based on dictionary study, the visual signature of all high-definition image samples of the described extraction of step S1 wherein, carry out as follows:
S1.1: feature (color, texture, shape, direction gradient histogram (HOG), word bag feature (BoW), yardstick invariant features conversion (SIFT) etc.) x that extracts every image i, i=1 ..., k, k are the quantity of visual signature;
S1.2: obtaining visual feature of image according to S1.1 is X=[x 1..., x k].
Above-mentioned high-definition image sorting technique based on dictionary study, wherein step S2 is described for described visual signature, the high-definition image sample is carried out sparse coding, constantly carry out dictionary study by alternative manner, up to error in classification less than threshold value, determine the classifying dictionary of high-definition image classification and according to visual signature the degree of influence of reconstructed error determined corresponding weights, carry out as follows:
S2.1: the classifying dictionary D of initialization high-definition image all categories P, 0Weights ω with visual signature P, 0
For the high-definition image sample of each classification, the initialization dictionary is
Figure BDA00003249856900031
The weights of visual signature are
ω p , 0 = { ω i } 1 m , ω i = 1
Wherein, x iBe the proper vector of high-definition image, m is the eigenwert number.
S2.2: the high-definition image sample is carried out rarefaction representation, obtain the corresponding sparse coding of image pattern;
For each classification sample of high-definition image, its sparse coding matrix Be the sparse coding of j image pattern of p classification, C is the classification number of high-definition image sample, m pBe the sample number of p classification, t is iterations, and then the sparse coding matrix A should satisfy
min { D p , t , A p , t } p = 1 · · · C Σ p = 1 C { | | X p - D p , t · A p , t | | 2 2 + λ Σ i = 1 m p | | α i p , t | | }
Wherein, λ is balance parameters.
S2.3: the reconstructed error that calculates each classification in the high-definition image sample;
For each classification sample of high-definition image, its reconstructed error is
R p , t ( X p ) = Σ i = 1 n | x i p , t - D p , t · α i p , t |
Wherein
S2.4: utilize Nonlinear Programming Theory that the reconstructed error of all categories is optimized, determine the significance level of visual signature;
For the visual signature of high-definition image sample, its significance level matrix is The principle more important according to visual signature, that reconstructed error is more few, characteristic importance β P, tShould satisfy
Figure BDA00003249856900045
s . t . 0 &le; &beta; j p , t < 1 , &Sigma; j = 1 m &beta; j p , t = 1
Figure BDA00003249856900047
S2.5: utilize the above-mentioned characteristic importance that obtains to upgrade weights and the classifying dictionary of visual signature;
For resulting visual signature and importance degree β P, t, the weights of renewal visual signature
&omega; j p , t = &beta; j p , t , &beta; j p , t < &mu; 1 , &beta; j p , t &GreaterEqual; &mu;
ω p,tp,t-1·ω p,t
And classifying dictionary
D p,t=D p,t-1·ω p,t-1
S2.6: judge that the reconstructed error summation of all categories whether less than threshold epsilon, if be not less than threshold value, then returns step S2.2, till satisfying reconstructed error and less than threshold condition being.
Above-mentioned high-definition image sorting technique based on dictionary study, wherein the weights of the dictionary of the described high-definition image classification of the described foundation of step S3 and visual signature correspondence are set up the image non-linear sorter, determine the classification that described high-definition image is affiliated, carry out as follows:
According to the weight matrix W of described sparse coding matrix A, classifying dictionary D and visual signature, the non-linear sorter of structure high-definition image is:
c * = arg min p ( &omega; p , t * - 1 &CenterDot; &beta; p , t * ) T | y - D p , t * &CenterDot; &alpha; p , t * |
Wherein, y is the visual feature vector of high-definition image sample to be sorted, t *Be final iterations.
Technical scheme of the present invention compared with prior art has the following advantages:
(1) the present invention has taken into full account association potential between the similar image owing to used the dictionary learning method that generic image is carried out sparse coding with identical classifying dictionary, has improved the precision of classification effectively;
(2) the present invention is owing to give weights to the degree of influence of reconstructed error to each visual signature value according to visual signature, solved adaptability not strong or the feature of strong correlation is arranged to the reaction result of nicety of grading with existing feature, further improved the precision of classification;
(3) emulation experiment shows, the nicety of grading of the more existing supervised classification method of the present invention is higher and classification effectiveness is better.
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In order to be illustrated more clearly in the embodiment of the invention or technical scheme of the prior art, to do to introduce simply to the accompanying drawing of required use in embodiment or the description of the Prior Art below, apparently, accompanying drawing in describing below only is some embodiments of the present invention, for those of ordinary skills, under the prerequisite of not paying creative work, can also obtain other accompanying drawing according to these accompanying drawings.
Fig. 1 is the high-definition image sorting technique process flow diagram based on dictionary study in the embodiment of the invention;
Fig. 2 is the present invention and conventional images sorting technique NS, SVM-RFE, the LP-Boost contrast and experiment figure at the different visual signatures of standard drawing image set the 17 category Oxford Flowers data set;
Fig. 3 is the present invention and the contrast and experiment figure of existing image classification method NS, SVM-RFE, the LP-Boost different visual signatures on standard drawing image set the 102 category Oxford Flowers data set;
Fig. 4 is the present invention and the contrast and experiment figure of conventional images sorting technique NS, SVM-RFE, the LP-Boost different visual signatures on standard drawing image set the Caltech 101 dataset.
Embodiment
Below in conjunction with the accompanying drawing in the embodiment of the invention, the technical scheme in the embodiment of the invention is clearly and completely described, obviously, described embodiment only is the present invention's part embodiment, rather than whole embodiment.Based on the embodiment among the present invention, those of ordinary skills belong to the scope of protection of the invention not making all other embodiment that obtain under the creative work prerequisite.
With reference to Fig. 1, the high-definition image sorting technique based on dictionary study of the technical program comprises the steps:
Step 1: the visual signature that extracts all high-definition image samples.
(1) feature of every image of extraction (color, texture, shape, direction gradient histogram (HOG), word bag feature (BoW), yardstick invariant features conversion (SIFT) etc.) x i, i=1 ..., k, k are the quantity of visual signature;
(2) obtaining visual feature of image according to (1) is X=[x 1..., x k].
Step 2: for described visual signature, the high-definition image sample is carried out sparse coding, constantly carry out dictionary study by alternative manner,, determine the classifying dictionary of high-definition image classification and according to visual signature the degree of influence of reconstructed error is determined corresponding weights less than threshold value up to error in classification
(1) the classifying dictionary D of initialization high-definition image all categories P, 0Weights ω with visual signature P, 0
For the high-definition image sample of each classification, the initialization dictionary is
Figure BDA00003249856900061
The weights of visual signature are
&omega; p , 0 = { &omega; i } 1 m , &omega; i = 1
Wherein, x iBe the proper vector of high-definition image, m is the eigenwert number.
(2) the high-definition image sample is carried out rarefaction representation, obtain the corresponding sparse coding of image pattern;
For each classification sample of high-definition image, its sparse coding matrix Be the sparse coding of j image pattern of p classification, C is the classification number of high-definition image sample, m pBe the sample number of p classification, t is iterations, and then the sparse coding matrix A should satisfy
min { D p , t , A p , t } p = 1 &CenterDot; &CenterDot; &CenterDot; C &Sigma; p = 1 C { | | X p - D p , t &CenterDot; A p , t | | 2 2 + &lambda; &Sigma; i = 1 m p | | &alpha; i p , t | | }
Wherein, λ is balance parameters.
(3) reconstructed error of each classification in the calculating high-definition image sample;
For each classification sample of high-definition image, its reconstructed error is
R p , t ( X p ) = &Sigma; i = 1 n | x i p , t - D p , t &CenterDot; &alpha; i p , t |
Wherein
Figure BDA00003249856900073
(4) utilize Nonlinear Programming Theory that the reconstructed error of all categories is optimized, determine the significance level of visual signature;
For the visual signature of high-definition image sample, its significance level matrix is
Figure BDA00003249856900074
The principle more important according to visual signature, that reconstructed error is more few, characteristic importance β P, tShould satisfy
Figure BDA00003249856900075
s . t . 0 &le; &beta; j p , t < 1 , &Sigma; j = 1 m &beta; j p , t = 1
Figure BDA00003249856900077
(5) utilize the above-mentioned characteristic importance that obtains to upgrade weights and the classifying dictionary of visual signature;
For resulting visual signature and importance degree β P, t, the weights of renewal visual signature
&omega; j p , t = &beta; j p , t , &beta; j p , t < &mu; 1 , &beta; j p , t &GreaterEqual; &mu;
ω p,tp,t-1·ω p,t
And classifying dictionary
D p,t=D p,t-1·ω p,t-1
(6) if whether the reconstructed error summation of judging all categories be not less than threshold value, then returns step (2) less than threshold epsilon, till satisfying reconstructed error and less than threshold condition being.
Step 3: set up the image non-linear sorter according to the dictionary of described high-definition image classification and the weights of visual signature correspondence, determine the classification that described high-definition image is affiliated.
According to the weight matrix W of described sparse coding matrix A, classifying dictionary D and visual signature, the non-linear sorter of structure high-definition image is:
c * = arg min p ( &omega; p , t * - 1 &CenterDot; &beta; p , t * ) T | y - D p , t * &CenterDot; &alpha; p , t * |
Wherein, y is the visual feature vector of high-definition image sample to be sorted, t *Be final iterations.
Below validity and practicality by emulation experiment checking the inventive method.
The emulation content:
(1) employing contrast experiment's form selects two representative sorting techniques to test at same image set, to verify validity of the present invention.What specifically select is nearest subspace (NS) method that is proposed by people such as Li, concrete list of references " Li; S.Z.:Face recognition based on nearest linear combinations. In:Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition; pp.839 – 844.IEEE Computer Society; Washington; DC; USA (1998) ", by I.Guyon, the SVM-RFE method that J.Westo and Barnhill propose, concrete list of references " Guyon I; Weston J; Barnhill; et al.Gene Selection for Cancer Classification Using Support Vector Machines.Machine Learning; 2002; 46 (1/2/3): 389-422. " and the LP-Boost method that is proposed by P.Gehler and S.Nowozin, concrete list of references " P.Gehler and S.Nowozin.On feature combination for multiclass object classification.In International Conference on Computer Vision.IEEE, 2009. "
(2) use standard drawing image set the 17 category Oxford Flowers data set, the 102 category Oxford Flowers data set, the Caltech 101 dataset to carry out emulation experiment, with the classifying quality of checking the present invention to the different images collection, concrete simulated conditions sees the description of each experiment for details.
Experiment one: image set the 17 category Oxford Flowers data set are image data sets of the common flowers of Britain, it comprises 17 class flowers, each class comprises 80 width of cloth images, and this experiment is carried out the precision contrast to method of the present invention respectively on single feature situation, a plurality of feature situation.Under single feature situation, this experiment is carried out the nicety of grading contrast to NS, SVM-RFE, LP-Boost and the inventive method respectively on color (Color), direction gradient histogram (HOG), word bag feature features such as (BoW) and all features of having extracted, its classification results as shown in Figure 2, simulation result shows: the nicety of grading of the inventive method under different characteristic is all than NS, SVM-RFE, LP-Boost method height.
Experiment two: image set the 102 category Oxford Flowers data set are image data sets of the common flowers of Britain, it comprises 102 class flowers, each class comprises 40 to 258 width of cloth images, and this experiment is carried out the precision contrast to method of the present invention respectively on single feature situation, a plurality of feature situation.Under single feature situation, this experiment is carried out the nicety of grading contrast to NS, SVM-RFE, LP-Boost and the inventive method respectively on color (Color), direction gradient histogram (HOG), word bag feature features such as (BoW), its classification results as shown in Figure 3, simulation result shows: the nicety of grading of the inventive method under different characteristic is all than NS and SVM method height.
Experiment three: image set the Caltech 101 dataset are image data sets that California Institute of Technology is used to test recognizer, it comprises 101 class images, each class comprises 40 to 800 width of cloth images, the size of image approximately is 300 * 200 pixels, and this experiment is carried out the precision contrast to method of the present invention respectively on single feature situation, a plurality of feature situation.Under single feature situation, this experiment is carried out the nicety of grading contrast to NS, SVM-RFE, LP-Boost and the inventive method respectively on color (Color), direction gradient histogram (HOG), word bag feature features such as (BoW), its classification results as shown in Figure 4, simulation result shows: the nicety of grading of the inventive method under different characteristic is all than NS, SVM-RFE, LP-Boost method height.
Experimental result shows, no matter the nicety of grading of method of the present invention is all than being higher than existing supervised classification method under single feature or many features combine situation.
More than the high-definition image sorting technique based on dictionary study that the embodiment of the invention is provided, be described in detail, used specific case herein principle of the present invention and embodiment are set forth, the explanation of above embodiment just is used for helping to understand method of the present invention and core concept thereof; Simultaneously, for one of ordinary skill in the art, according to thought of the present invention, the part that all can change in specific embodiments and applications, in sum, this description should not be construed as limitation of the present invention.

Claims (10)

1. the high-definition image sorting technique based on dictionary study is characterized in that, comprises the steps:
Extract the visual signature of all high-definition image samples;
For described visual signature, the high-definition image sample is carried out sparse coding, constantly carry out dictionary study by alternative manner,, determine the classifying dictionary of high-definition image classification and according to visual signature the degree of influence of reconstructed error is determined corresponding weights less than threshold value up to error in classification;
Set up the image non-linear sorter according to the dictionary of described high-definition image classification and the weights of visual signature correspondence, determine the classification that described high-definition image is affiliated.
2. the high-definition image sorting technique based on dictionary study as claimed in claim 1 is characterized in that the visual signature that extracts all high-definition image samples comprises:
Extract the color, texture, shape, direction gradient histogram, word bag feature, yardstick invariant features converting characteristic of every image as its visual signature X=[x 1..., x k], k is the quantity of visual signature.
3. the high-definition image sorting technique based on dictionary study as claimed in claim 1 is characterized in that, the classifying dictionary of described definite high-definition image classification and the degree of influence of reconstructed error is determined that corresponding weights comprise according to visual signature:
The classifying dictionary D of initialization high-definition image all categories P, 0Weights ω with visual signature P, 0
For initialized classifying dictionary D P, 0, use process of iteration constantly classifying dictionary to be learnt, make error in classification be less than threshold epsilon, obtain final classifying dictionary and visual signature weights.
4. the high-definition image sorting technique based on dictionary study as claimed in claim 2 is characterized in that the classifying dictionary D of described initialization high-definition image all categories P, 0Weights ω with visual signature P, 0Specifically comprise:
For the high-definition image sample of each classification, the initialization dictionary is
Figure FDA00003249856800011
The weights of visual signature are
&omega; p , 0 = { &omega; i } 1 m , &omega; i = 1
Wherein, x iBe the proper vector of high-definition image, m is the eigenwert number.
5. the high-definition image sorting technique based on dictionary study as claimed in claim 2 is characterized in that, and is described for initialized classifying dictionary D P, 0, use process of iteration constantly classifying dictionary to be learnt, make error in classification be less than threshold epsilon, obtain final classifying dictionary and the visual signature weights also comprise:
The high-definition image sample is carried out rarefaction representation, obtain the corresponding sparse coding of image pattern;
Calculate the reconstructed error of each classification in the high-definition image sample;
Utilize Nonlinear Programming Theory that the reconstructed error of all categories is optimized, determine the significance level of visual signature;
Utilize the above-mentioned characteristic importance that obtains to upgrade weights and the classifying dictionary of visual signature;
Whether judge the reconstructed error summation of all categories less than threshold epsilon, if be not less than threshold value, then return step the high-definition image sample is carried out rarefaction representation, obtain the corresponding sparse coding of image pattern, till satisfying reconstructed error and less than threshold condition being.
6. the high-definition image sorting technique based on dictionary study as claimed in claim 5 is characterized in that, described the high-definition image sample is carried out rarefaction representation, obtains the corresponding sparse coding of image pattern and comprises:
For each classification sample of high-definition image, its sparse coding matrix Be the sparse coding of j image pattern of p classification, C is the classification number of high-definition image sample, m pBe the sample number of p classification, t is iterations, and then the sparse coding matrix A should satisfy
min { D p , t , A p , t } p = 1 . . . C &Sigma; p = 1 C { | | X p - D p , t &CenterDot; A p , t | | 2 2 + &lambda; &Sigma; i = 1 m p | | &alpha; i p , t | | }
Wherein, λ is balance parameters.
7. the high-definition image sorting technique based on dictionary study as claimed in claim 5 is characterized in that the reconstructed error of each classification comprises in the described calculating high-definition image sample:
For each classification sample of high-definition image, its reconstructed error is
R p , t ( X p ) = &Sigma; i = 1 n | x i p , t - D p , t &CenterDot; &alpha; i p , t |
Wherein
Figure FDA00003249856800032
8. the high-definition image sorting technique based on dictionary study as claimed in claim 5 is characterized in that the described Nonlinear Programming Theory of utilizing is optimized the reconstructed error of all categories, determines that the significance level of visual signature comprises:
For the visual signature of high-definition image sample, its significance level matrix is
Figure FDA00003249856800033
The principle more important according to visual signature, that reconstructed error is more few, characteristic importance β P, tShould satisfy
Figure FDA00003249856800034
s . t . 0 &le; &beta; j p , t < 1 , &Sigma; j = 1 m &beta; j p , t = 1
Figure FDA00003249856800036
9. the high-definition image sorting technique based on dictionary study as claimed in claim 5 is characterized in that described weights and the classifying dictionary that utilizes the above-mentioned characteristic importance that obtains to upgrade visual signature comprises:
For resulting visual signature and importance degree β P, t, the weights of renewal visual signature
&omega; j p , t = &beta; j p , t , &beta; j p , t < &mu; 1 , &beta; j p , t &GreaterEqual; &mu;
ω p,tp,t-1·ω p,t
And classifying dictionary
D p,t=D p,t-1·ω p,t-1
10. the high-definition image sorting technique based on dictionary study as claimed in claim 1, it is characterized in that, set up the image non-linear sorter according to the dictionary of described high-definition image classification and the weights of visual signature correspondence, determine the classification that described high-definition image is affiliated, also comprise:
According to the weight matrix W of described sparse coding matrix A, classifying dictionary D and visual signature, the non-linear sorter of structure high-definition image is:
c * = arg min p ( &omega; p , t * - 1 &CenterDot; &beta; p , t * ) T | y - D p , t * &CenterDot; &alpha; p , t * |
Wherein, y is the visual feature vector of high-definition image sample to be sorted, t *Be final iterations.
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