CN103324923A - Handwritten character recognition method based on sparse representation - Google Patents

Handwritten character recognition method based on sparse representation Download PDF

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CN103324923A
CN103324923A CN201310291044XA CN201310291044A CN103324923A CN 103324923 A CN103324923 A CN 103324923A CN 201310291044X A CN201310291044X A CN 201310291044XA CN 201310291044 A CN201310291044 A CN 201310291044A CN 103324923 A CN103324923 A CN 103324923A
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sparse
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image
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傅迎华
王崇阳
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University of Shanghai for Science and Technology
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Abstract

The invention relates to a handwritten character recognition method based on sparse representation. The handwritten character recognition method based on sparse representation comprises the following steps of: pretreating images; representing to-be-recognized characters as sparse representation based on a training set through a training sample dictionary according to the coefficient resolution obtained through convex optimization; finding out the maximal L1/2 norm numerical value according to the obtained sparse coefficient resolution, wherein the type corresponding to the maximal L1/2 norm numerical value is a recognition result. The method can prevent influences of character extraction and a classifier on a classification result in the target recognition problem. Through a great amount of experiments, as long as the obtained sparsity is sparse enough, the classification based on L1/2 norm can obtain a good recognition rate; also the algorithm running time is reduced; testing images can be recognized accurately.

Description

Hand-written character recognition method based on rarefaction representation
Technical field
The present invention relates to a kind of mode identification technology, particularly a kind of hand-written character recognition method based on rarefaction representation.
Background technology
Handwritten Digits Recognition is abbreviated as HCR(Handwritten Character Recognition usually).In area of pattern recognition, HCR is most important and challenging research always.It helps greatly to improve automation process, strengthens the various interactive application between the human and computer.New technology and method are absorbed in some research work always, with the processing time that reduces, provide simultaneously higher identification accurate.
At present, widely used hand-written recognition method accuracy rate is not high enough, and noise resisting ability a little less than.And need to extract the feature of character picture, carry out characteristic matching again, this has increased the work complexity, has reduced work efficiency.Existing main recognition methods is as follows:
(1) hand-written character recognition method of geometric properties:
Geometric properties can be the shape of eye, nose, mouth etc. and the geometric relationship between them, such as distance each other.
Advantage: these algorithm identified speed are fast, and the internal memory that needs is little.
Shortcoming: discrimination is lower.
(2) based on the hand-written character recognition method of eigenface (PCA):
The eigenface method is based on the hand-written character recognition method of KL conversion, and the KL conversion is a kind of optimum orthogonal transformation of compression of images.Obtain one group of new orthogonal basis after the image space process KL conversion of higher-dimension, keep wherein important orthogonal basis, can open into the low-dimensional linear space by these bases.Have separability if suppose hand-written character in the projection of these low-dimensional linear space, just can be with the eigenvector of these projections as identification, the basic thought of eigenface method that Here it is.
Shortcoming: these methods need more training sample, and are based on the statistical property of gradation of image fully.
(3) hand-written character recognition method of neural network:
The input of neural network can be the hand-written character image that reduces resolution, the autocorrelation function of regional area, the second moment of local grain etc.
Shortcoming: these class methods need more sample training equally, and in many application, sample size is very limited.
(4) hand-written character recognition method of line segment Hausdorff distance (LHD):
Psychologic studies show that, human at contour identification figure (such as caricature) speed and accuracy at all poor unlike the identification gray-scale map.LHD is based on the line chart that extracts from the hand-written character gray level image, what its defined is two distances between the line-segment sets, distinguished is that LHD does not set up the one-to-one relationship of line segment between the different line-segment sets, so it more can adapt to the subtle change between the line chart.Advantage: experimental result shows, LHD has very outstanding performance under different illumination conditions with in the different attitude situations,
Shortcoming: but it is in the situation that large expression recognition effect is bad.
(5) hand-written character recognition method of support vector machine (SVM): in recent years, support vector machine is a new focus in statistical model identification field, it is attempted so that learning machine reaches a kind of compromise at empiric risk and generalization ability, thereby improves the performance of learning machine.What support vector machine mainly solved is 2 classification problems, and its basic thought is the problem of attempting the problem of the linearly inseparable of a low-dimensional is changed into the linear separability of a higher-dimension.
Advantage: common experimental result shows that SVM has preferably discrimination.
Shortcoming: it needs a large amount of training samples (300 of every classes), and this is unpractical often in actual applications.And the support vector machine training time is long, and method realizes complicated, and following the example of of this function do not have unified theory.
Summary of the invention
The present invention be directed to existing Handwritten Digits Recognition accuracy rate not high enough, noise resisting ability hangs down and ineffective problem, proposes a kind of hand-written character recognition method based on rarefaction representation, overcomes the problem that prior art exists.With respect to traditional extraction characteristics of image, the method that the sorter that designs is again identified,, and rarefaction representation only need to pass through the training sample dictionary, the coefficient solution of trying to achieve according to protruding optimization, exactly Recognition test image.
Technical scheme of the present invention is: a kind of hand-written character recognition method based on rarefaction representation specifically comprises the steps:
1) image pre-service: obtain the character grey image, the character picture to be identified that obtains is carried out binaryzation, do inversion operation again, obtain at last pretreated image, each character picture resolution sizes is
Figure 201310291044X100002DEST_PATH_IMAGE001
, each image is as M(
Figure 514393DEST_PATH_IMAGE002
) vector of dimension space;
2) character to be identified is expressed as the rarefaction representation of gathering based on training:
A: defining i class character has n i Individual samples pictures, the test pattern vector v I, 1 , v I, 2 ..., v I, ni , vector consists of the linear space of i character type, inputs i(i ∈ [1, k]) and class testing image y,
Figure 148636DEST_PATH_IMAGE004
, y is expressed as in such linear space:
Figure 201310291044X100002DEST_PATH_IMAGE005
Wherein
Figure 777064DEST_PATH_IMAGE006
It is real scalar;
B: each hand-written character class of obtaining has n iIndividual sample is with the sample of all kinds of characters classes
Figure DEST_PATH_IMAGE007
Addition gets
Figure 78732DEST_PATH_IMAGE008
Namely the sum of all character samples is trained as crossing complete dictionary vector A, and each sample is as the row of A, and n is listed as altogether, (M＜n):
Figure DEST_PATH_IMAGE009
C: the sample dictionary that obtains training, utilize protruding optimization to find character to be identified based on the rarefaction representation of dictionary, sparse coefficient solution solution formula is as follows:
Figure 767202DEST_PATH_IMAGE010
Wherein
Figure DEST_PATH_IMAGE011
The L1 norm of x,
Figure 888742DEST_PATH_IMAGE012
It is the noise threshold of setting;
3) the coefficient solution is classified: according to step 2) in ask the sparse coefficient solution that obtains
Figure DEST_PATH_IMAGE013
, calculate i
Figure 320861DEST_PATH_IMAGE014
Then the L1/2 norm of class finds maximum L1/2 norm value, and its corresponding class is recognition result.
Beneficial effect of the present invention is: the present invention is based on the hand-written character recognition method of rarefaction representation, can avoid the impact that feature extraction and sorter produce classification results in the target identification problem.By great many of experiments, draw as long as gained is sparse enough sparse, can obtain better discrimination based on the classification of L1/2 norm, and reduce Riming time of algorithm, and Recognition test image exactly.
Description of drawings
Fig. 1 is the method formula geometric meaning figure of the sparse regularization constraint of L2 norm of the present invention;
Fig. 2 is the method formula geometric meaning figure of the sparse regularization constraint of L1 norm of the present invention;
Fig. 3 is the hand-written character recognition method process flow diagram that the present invention is based on rarefaction representation;
Fig. 4 is the embodiment of the invention one test hand-written character " 6 " schematic diagram;
Fig. 5 is the embodiment of the invention one " 6 " sparse coefficient solution schematic diagram;
Fig. 6 is the L1/2 norm schematic diagram of the embodiment of the invention one 0-9 class;
Fig. 7 is the embodiment of the invention two test noise character " 2 " schematic diagram;
Fig. 8 obtains figure to be identified after the embodiment of the invention two pre-service;
Fig. 9 is the embodiment of the invention two " 2 " sparse coefficient solution schematic diagram;
Figure 10 is the L1/2 norm schematic diagram of the embodiment of the invention two 0-9 classes.
Embodiment
Character Recognition scheme based on rarefaction representation:
(1) rarefaction representation of hand-written character:
Hand-written character HC(handwritten character) rarefaction representation, the complete dictionary of mistake by abundant sample HC trains approaches HC to be identified with minimum dictionary atom most by linear combination.This process can use formula (1) to describe
Figure DEST_PATH_IMAGE015
?（1）
Wherein A was complete dictionary, xIt is linear equation
Figure 477035DEST_PATH_IMAGE016
The coefficient solution, y is HC to be identified,
Figure DEST_PATH_IMAGE017
Sparse solution the most,
Figure 834942DEST_PATH_IMAGE018
It is the L0 norm of x.
Each HC image resolution ratio size is
Figure 443778DEST_PATH_IMAGE001
, can regard a vector of M dimension space as,
Figure DEST_PATH_IMAGE019
We define iClass HC character has NiIndividual samples pictures, vector v I, 1 , v I, 2 ..., v I, ni
Figure 351691DEST_PATH_IMAGE020
, consisted of the linear space of i character type by these vectors.Input i(i ∈ [1, k]) class testing image y,
Figure 362373DEST_PATH_IMAGE004
, y has following expression in such linear space:
Figure DEST_PATH_IMAGE021
Wherein
Figure 392645DEST_PATH_IMAGE022
It is real scalar.
Each HC class has n i Individual sample is with the sample of all different HC classes
Figure 488777DEST_PATH_IMAGE007
Addition gets
Figure DEST_PATH_IMAGE023
Namely the sum of all character samples is trained as crossing complete dictionary vector A, and each sample is listed as the n of A, (M＜n):
Figure 262698DEST_PATH_IMAGE024
Hypothesis testing sample y can use complete dictionary A linear expression to be fully:
Figure DEST_PATH_IMAGE025
At this moment
Figure 127886DEST_PATH_IMAGE026
Figure DEST_PATH_IMAGE027
Have the non-zero element of only a few relevant with the i class, other all are 0.Known by formula (4): an effective test pattern can illustrate with the linear list of crossing complete dictionary A.If number of samples is rationally large, coefficient x 0 Naturally be sparse.
(2) ask sparse coefficient solution based on the L1 norm regularization.
Our target is for solution formula (1), seeks a coefficient solution the most sparse based on the L0 Norm minimum
Figure 329060DEST_PATH_IMAGE017
, unfortunately finding the solution such alignment equation of owing is NP-hard.
If dictionary A be owe fixed (under-determined) (
Figure 912489DEST_PATH_IMAGE028
And
Figure DEST_PATH_IMAGE029
), its solution is not unique, and existing common solution is selected by least square method, that is:
Figure 427783DEST_PATH_IMAGE030
We know that the coefficient solution of trying to achieve is more sparse, with regard to easier test pattern are carried out discriminator.Yet this method formula (5) by the sparse regularization constraint of L2 norm can not obtain sparse solution.
As long as the theoretical latest developments of compressed sensing have disclosed the coefficient solution x 0 Enough sparse, formula (1) is equivalent to
Figure DEST_PATH_IMAGE031
The sparse regularization constraint problem of norm:
Figure 711260DEST_PATH_IMAGE032
Fig. 1 is formula (5) geometric meaning figure, Fig. 2 is formula (6) geometric meaning figure, and alignment equation y=Ax is owed in the oblique line representative, enlarges the norm ball and seeks the point tangent with oblique line, this point is exactly under the sparse regularization constraint of norm, the most sparse underdetermined equation solution that obtains.We for example, then derive and arrive higher dimensional space in two-dimensional space.
Above two figure of contrast, can learn that the L1 norm is more more sparse than the solution that L2 norm obtains according to oblique line and norm ball points of tangency position.
Yet the image of test is generally all noisy, can think the stack with ideal image, and formula (7) is supposed the finite energy of this noise z, namely
Figure DEST_PATH_IMAGE033
,
Figure 21018DEST_PATH_IMAGE034
Figure DEST_PATH_IMAGE035
We still can find the solution the coefficient solution based on the L1 norm regularization by the following method:
Figure 154059DEST_PATH_IMAGE036
Wherein
Figure DEST_PATH_IMAGE037
Be the picture noise energy, AxBe the image that reconstructs, Y-AxBe the poor of former figure and restructuring graph, this difference is thought noise.
(3) test pattern classification
Above algorithm is in order to find the solution the coefficient solution based on sparse regularization, and then we utilize the sparse solution of trying to achieve to classify.In order to improve algorithm process efficient, as long as the coefficient solution is enough sparse, we can directly find the solution respectively the L1/2 norm to every class, classify according to its maximal value.By a large amount of experiments, compare the method for mentioning in the background technology, there is good raising discrimination and times two aspect.
As shown in Figure 3 recognition methods flow process is as follows:
1. input: the tested image array A of k target,, A
Figure 207466DEST_PATH_IMAGE038
, test pattern
Figure DEST_PATH_IMAGE039
2. standardization
Figure 109563DEST_PATH_IMAGE040
With
Figure DEST_PATH_IMAGE041
Row make its long measure;
3. find the solution the convex optimization problem, formula (8);
4. calculate i The L1/2 norm of class, r-- i=|| || 1/2
Wherein
Figure DEST_PATH_IMAGE043
To select the only coefficient solution relevant with the i class;
5. output recognition result: Identity(y-)=
Figure 802078DEST_PATH_IMAGE044
Find the solution based on the L1 norm regularization in the 1-3 step and to find the solution the coefficient solution.In order to improve algorithm process efficient, as long as the coefficient solution is enough sparse, we find the solution respectively the L1/2 norm to every class in the 4th, 5 step, classify according to its maximal value.By a large amount of experiments, compare with additive method, there is good raising discrimination and times two aspect.Different sorting technique fiducial value as shown in table 1.
Table 1
Figure DEST_PATH_IMAGE045
The below is explanation the inventive method as an example of hand-written character " 6 " and noise character " 2 " example.
Step 1, image is carried out pre-service:
Obtain the character grey image, such as Fig. 4 and hand-written character shown in Figure 7 " 6 " and noise character " 2 " figure, at first unified image resolution ratio size M=N*N, because character picture generally all is white gravoply, with black engraved characters, we adopt the numerical data base MNIST of existing standard, it is the black matrix wrongly written or mispronounced character, for unification, we carry out binaryzation to the character picture to be identified that obtains, do again an inversion operation, on the one hand can remove some noises, can reduce memory data output on the one hand, for the algorithm of back calculate improve convenient.Design sketch obtains figure to be identified after noise character " 2 " pre-service as shown in Figure 8.
Step 2 is expressed as character to be identified the rarefaction representation of gathering based on training.
Each hand-written character image resolution ratio size is M=N*N, can regard a vector of M dimension space as.We define i class character has
Figure 496365DEST_PATH_IMAGE046
Individual samples pictures, the test pattern vector v I, 1 , v I, 2 ..., v I, ni
Figure DEST_PATH_IMAGE047
, consisted of the linear space of i character type by these vectors.Input i(i ∈ [1, k]) class testing image y,
Figure 974357DEST_PATH_IMAGE048
, y has following expression in such linear space:
Figure DEST_PATH_IMAGE049
Wherein
Figure 754094DEST_PATH_IMAGE050
It is real scalar.
Each hand-written character class has n iIndividual sample is with the sample of all kinds of characters classes
Figure 211621DEST_PATH_IMAGE007
Addition gets
Figure DEST_PATH_IMAGE051
Namely the sum of all character samples is trained as crossing complete dictionary vector A, and each sample is as the row of A, and n is listed as altogether, (M＜n):
Figure 25993DEST_PATH_IMAGE052
The above sample dictionary that we obtain training, next we utilize protruding optimization to find character to be identified based on the rarefaction representation of dictionary, and sparse coefficient solution is found the solution following formula:
Wherein || x|| 1The L1 norm of x,
Figure 910772DEST_PATH_IMAGE012
It is the noise threshold of setting.Be respectively hand-written character " 6 " and the sparse coefficient solution of noise character " 2 " such as Fig. 5 and Fig. 9.
Step 3 is classified according to the coefficient solution.
According to asking the sparse coefficient solution that obtains in the step 2
Figure 177805DEST_PATH_IMAGE013
, the coefficient solution of the correspondence of every class is asked the L1/2 norm, then find maximum L1/2 norm value, its corresponding class is recognition result.For example in our experiment, as Fig. 6 and Figure 10 be hand-written character " 6 " and noise character " 2 " 0-9 class the L1/2 norm value, according to the maximal value of L1/2 norm, can identify accurately hand-written character " 6 ", and noisy hand-written character " 2 ".

Claims (1)

1. the hand-written character recognition method based on rarefaction representation is characterized in that, specifically comprises the steps:
1) image pre-service: obtain the character grey image, the character picture to be identified that obtains is carried out binaryzation, do inversion operation again, obtain at last pretreated image, each character picture resolution sizes is
Figure 933954DEST_PATH_IMAGE002
, each image is as M(
Figure 449249DEST_PATH_IMAGE004
) vector of dimension space;
2) character to be identified is expressed as the rarefaction representation of gathering based on training:
A: defining i class character has n i Individual samples pictures, the test pattern vector v I, 1 , v I, 2 ..., v I, ni
Figure 434522DEST_PATH_IMAGE006
, vector consists of the linear space of i character type, inputs i(i ∈ [1, k]) and class testing image y,
Figure 806598DEST_PATH_IMAGE008
, y is expressed as in such linear space:
Figure 611743DEST_PATH_IMAGE010
Wherein
Figure 665149DEST_PATH_IMAGE012
It is real scalar;
B: each hand-written character class of obtaining has n iIndividual sample is with the sample of all kinds of characters classes
Figure 504929DEST_PATH_IMAGE014
Addition gets Namely the sum of all character samples is trained as crossing complete dictionary vector A, and each sample is as the row of A, and n is listed as altogether, (M＜n):
Figure 605927DEST_PATH_IMAGE018
C: the sample dictionary that obtains training, utilize protruding optimization to find character to be identified based on the rarefaction representation of dictionary, sparse coefficient solution solution formula is as follows:
Wherein || x|| 1The L1 norm,
Figure 157311DEST_PATH_IMAGE022
It is the noise threshold of setting;
3) the coefficient solution is classified: according to step 2) in ask the sparse coefficient solution that obtains
Figure 808872DEST_PATH_IMAGE024
, calculate i
Figure 152391DEST_PATH_IMAGE026
Then the L1/2 norm of class finds maximum L1/2 norm value, and its corresponding class is recognition result.
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CN103679209A (en) * 2013-11-29 2014-03-26 广东领域安防有限公司 Sparse theory based character recognition method
CN103903630A (en) * 2014-03-18 2014-07-02 北京捷通华声语音技术有限公司 Method and device used for eliminating sparse noise
CN104848883A (en) * 2015-03-27 2015-08-19 重庆大学 Sensor noise and fault judging method based on sparse representation
CN105139036A (en) * 2015-06-19 2015-12-09 四川大学 Handwritten figure identification method based on sparse coding
CN106650820A (en) * 2016-12-30 2017-05-10 山东大学 Matching recognition method of handwritten electrical component symbols and standard electrical component symbols

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Cited By (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103679209A (en) * 2013-11-29 2014-03-26 广东领域安防有限公司 Sparse theory based character recognition method
CN103679209B (en) * 2013-11-29 2017-03-29 广东领域安防有限公司 Character identifying method based on sparse theory
CN103903630A (en) * 2014-03-18 2014-07-02 北京捷通华声语音技术有限公司 Method and device used for eliminating sparse noise
CN104848883A (en) * 2015-03-27 2015-08-19 重庆大学 Sensor noise and fault judging method based on sparse representation
CN105139036A (en) * 2015-06-19 2015-12-09 四川大学 Handwritten figure identification method based on sparse coding
CN105139036B (en) * 2015-06-19 2018-10-19 四川大学 A kind of Handwritten Numeral Recognition Method based on sparse coding
CN106650820A (en) * 2016-12-30 2017-05-10 山东大学 Matching recognition method of handwritten electrical component symbols and standard electrical component symbols
CN106650820B (en) * 2016-12-30 2020-04-24 山东大学 Matching and recognizing method for handwritten electric component symbol and standard electric component symbol

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Application publication date: 20130925