CN103761538A - Traffic sign recognition method based on shape feature invariant subspace - Google Patents

Abstract

The invention relates to a traffic sign recognition method based on shape feature invariant subspace. A binary image of a traffic sign is used as a feature extraction object, the principal component analysis method and the linear discriminant analysis method are combined, and firstly the principal component analysis method is used for conducting feature extraction on the image of the traffic sign so as to obtain a feature matrix with the optimal description effect; then, the linear discriminant analysis method is used for conducting secondary feature extraction on the matrix so as to obtain a feature matrix with the optimal classification effect, and therefore features extracted in the traffic sign recognition method have the optimal description performance and the optimal discrimination performance; finally, the minimum distance classification method is adopted for identifying the extracted features, and tests verify that the traffic sign can be recognized accurately.

Description

Traffic sign recognition method based on the shape facility invariant subspace

Technical field:

The present invention relates to the recognition methods of traffic sign, particularly relate to a kind of traffic sign recognition method based on the shape facility invariant subspace.

Background technology:

Intelligent transportation system is to apply to whole traffic management system by advanced infotech, mechanics of communication, sensing technology, control technology and computer technology etc. are effectively integrated, and set up a kind of on a large scale in, comprehensive play a role, comprehensive transportation and management system accurately and efficiently in real time,, it improves traffic transportation efficiency by harmony, the close fit on people, car, road, relieving traffic jam, improve road passage capability, reduce traffic hazard, reduce energy resource consumption, alleviate environmental pollution.As the important component part of intelligent transportation system, Traffic Sign Recognition System is at important roles such as enhanced machine motor-car and pedestrains safeties.

Traffic Sign Recognition System comprises detection, location, feature extraction and the identification to traffic sign, relative with Position Research ripe to the detection of traffic sign at present, and the research of feature extraction and identification aspect is less.The invention provides a kind of traffic sign recognition method based on the shape facility invariant subspace.Aspect traffic sign feature extraction.External starting early, Typical Representative has: H.Fleyeh E.Davami is the identification for traffic sign by PCA method, first utilize the colouring information of traffic sign that suspicious traffic sign is detected and separated from natural image, and carry out affine rectification to there is the traffic sign of deformation, by PCA method, respectively speed(-)limit sign and warning notice are carried out to feature extraction, then by support vector machine, extracted result is carried out to Classification and Identification; Merve CanKus has proposed the Traffic Sign Recognition of the affine unchangeability based on shif descriptor;

cyganek identifies ban traffic sign by the method for tensor analysis.Domestic Typical Representative has: Moment Feature Extraction is done to the Traffic Sign Images in road scene by Chen Zhi association, first by SVM method, by CF, classifies, then extracts 9 eigenwerts of Zernike square, then adopt simple method for mode matching check recognition result.Mao Jianxu, Liu Min have proposed a kind of based on the affine constant Zernike moment characteristics method of ICA, the method is first converted the traffic sign of affined transformation is returned on rotation and mirror transformation by ICA, and then mates by extracting the Zernike moment characteristics of region mirror image and invariable rotary the type that identifies traffic sign.

Traffic sign has color clear, the obvious feature of shape facility, under normal circumstances, the image information of traffic sign is more clearly, but the Traffic Sign Images gathering under natural conditions is easy to be subject to the impact of external condition causes gathered image to have noise, cause take colouring information as basic recognition methods inaccurate.Therefore designing the recognition methods that a noise immunity is strong has very important realistic meaning.

Summary of the invention:

Goal of the invention:

The present invention relates to a kind of traffic sign recognition method based on the shape facility invariant subspace, its objective is to design and a kind ofly can carry out feature extraction and know method for distinguishing for the traffic sign gathering under different noise effect conditions.By picture library being carried out to the feasibility of experimental verification algorithm, can carry out according to algorithm the research of embedded system, finally realize the identification to road signs, improve road traffic safety.

Technical scheme:

The present invention is achieved through the following technical solutions:

A traffic sign recognition method based on the shape facility invariant subspace, is characterized in that: step is as follows:

(1) set up Traffic Sign Images database: for traffic sign main mark, identify, set up respectively indication Traffic Sign Images database, warning Traffic Sign Images database and ban Traffic Sign Images database, be divided into the following steps:

1) download the coloured image of standard traffic sign, set up corresponding color image data storehouse;

2) utilize formula gray=0.299R+0.587G+0.114B that Traffic Sign Images is converted into gray level image, set up corresponding gray level image database;

3) image is added to noise;

4) gray level image is carried out to binaryzation, set up the shape database of traffic sign;

(2) calculate principal component analysis (PCA) (PCA) proper subspace:

Suppose that Traffic Sign Images set is: X={f ₁(x, y), f ₂(x, y) ..., f _n(x, y) }, every piece image f _i(x, y) can both become according to row sequential deployment the vector of a M dimension

m is image pixel number, and its covariance matrix is defined as: C=XX ^t=E{ (X-u) (X-u) ^t, u=E{X} wherein;

C is carried out to svd:

Matrix U column vector u ₁, u ₂..., u _mbe unit quadrature, form the base in major component space, they are referred to as major component; KL has converted covariance matrix diagonalization, by KL, converts, and has eliminated former directed quantity

each component between correlativity, thereby reach the object that reduces feature space dimension;

If image vector

in major component space, coordinate is a _i=[a _1i, a _2i..., a _mi] ^t∈ R ^m, have

${\stackrel{\&OverBar;}{x}}_i={\mathrm{Ua}}_i=[u_1,{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="140110160519.png,140110160522.png"\; state="\{\{state\}\}">u</figure-callout>}}_2,...,u_M]\&CenterDot;\left[{[a_{1i},a_{2i},...,a_{\mathrm{Mi}}]}^T\right]=\underset{k=1}{\overset{M}{\mathrm{\&Sigma;}}}{a}_{\mathrm{ki}}\&CenterDot;u_k,---\left(2\right)$

Because U is unit orthogonal matrix, UU ^t=U ^tu=E,

${[a_{1i},a_{2i},...,a_{\mathrm{Mi}}]}^T={[u_1,u_2,...,u_M]}^T{\stackrel{\&OverBar;}{x}}_i=[u_1^T{\stackrel{\&OverBar;}{x}}_i,u_2^T{\stackrel{\&OverBar;}{x}}_i,...,u_M^T{\stackrel{\&OverBar;}{x}}_i],---\left(3\right)$

$a_{\mathrm{ki}}=u_k^T{\stackrel{\&OverBar;}{x}}_i,---\left(4\right)$

Substitution above formula obtains: ${\stackrel{\&OverBar;}{x}}_i=\underset{k=1}{\overset{M}{\mathrm{\&Sigma;}}}\left\{u_k^T{\stackrel{\&OverBar;}{x}}_i{u}_k\right\}---\left(5\right)$

Its physical significance is expressed as: with the weighted accumulation of major component vector with carry out matching input picture

Suppose only with a front d finite term, to estimate

${\hat{x}}_i=\underset{k=1}{\overset{d}{\mathrm{\&Sigma;}}}{u}_k^T{\stackrel{\&OverBar;}{x}}_i{u}_k---\left(6\right)$

So just completed the dimensionality reduction to original image, due to the good characteristic that KL conversion has, thought that feature space after dimensionality reduction is enough to represent the essential characteristic of original image; Get the corresponding proper vector of a front d eigenwert as the base of PCA proper subspace, all Traffic Sign Images, to this subspace projection, have just been obtained representing the proper subspace of original image collection;

(3) calculate linear discriminant analysis (LDA) proper subspace:

What in classical linear discriminant analysis, use is Fisher criterion function, the Fisher linear discriminant analysis so linear judgment analysis is otherwise known as (Fisher Linear Discriminant Analysis/FLDA); Fisher criterion function is definition like this:

$J\left(w\right)=\arg \underset{w}{\max }\frac{\left|w^T{S}_{B}w\right|}{\left|w^T{S}_{w}w\right|}---\left(7\right)$

Wherein, dispersion S between class _bwith dispersion S in class _wbe defined as:

$S_B=\frac{1}{C(C-1)}\underset{i=1}{\overset{C}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{C}{\mathrm{\&Sigma;}}}(u_i-u_j){(u_i-u_j)}^T---\left(8\right)$

$S_B=\frac{1}{C}\underset{i=1}{\overset{C}{\mathrm{\&Sigma;}}}\frac{1}{N}\underset{j=1}{\overset{N_i}{\mathrm{\&Sigma;}}}(x_j^i-u_i){(x_j^i-u_i)}^T---\left(9\right)$

C is total class number, N _ithe sample number that represents i class,

be j sample in i class,

it is the sample average in i class;

On mathematics, the optimum solution that solves Fisher criterion function just equals to solve

eigenvalue problem; Ask and make

eigenwert while obtaining maximal value, corresponding proper vector is exactly the base of LDA subspace; Feature set in PCA proper subspace, to LDA subspace projection, is just obtained to the final PLA feature space that represents former Traffic Sign Images;

(4) adopt the recognition effect of minimum distance classification checking institute feature extraction feature.

Advantage and effect:

The difficult problem that the present invention brings Traffic Sign Recognition System for solving Complex Noise, a kind of traffic sign recognition method based on the shape facility invariant subspace has been proposed, it is feature extraction object that the bianry image of traffic sign is take in the present invention, principal component analytical method and linear discriminant analysis method are combined, first utilize principal component analytical method to carry out feature extraction to Traffic Sign Images, obtain having the best eigenmatrix of describing effect; On this matrix, by linear discriminant analysis method, carry out quadratic character extraction again, obtain having the eigenmatrix of optimal classification effect, so the feature that this method is extracted had both had the best descriptive best property distinguished that also has; Finally adopt minimum distance classification to identify extracted feature, checking can identify traffic sign accurately by experiment.

The method contrast additive method is short if having time, and the advantage that accuracy rate is high particularly can accurately be identified traffic sign in noisy situation, has strengthened the real-time of system, can develop embedded system, realizes the ONLINE RECOGNITION of road signs.

Four, accompanying drawing explanation:

Fig. 1 is the recognition time of PCA method to prohibitory sign gray level image and bianry image;

Fig. 2 is the recognition time of PCA method to Warning Mark gray level image and bianry image;

Fig. 3 is the recognition time of PCA method to warning notice gray level image and bianry image;

Fig. 4 is the recognition time of PLA method to prohibitory sign gray level image and bianry image;

Fig. 5 is the recognition time of PLA method to Warning Mark gray level image and bianry image;

Fig. 6 is the recognition time of PLA method to warning notice gray level image and bianry image;

Table 1 is the recognition efficiency of different characteristic extracting method to traffic sign gray level image;

Table 2 is the recognition efficiency of different characteristic extracting method to traffic sign bianry image;

The Traffic Sign Images storehouse that reference paper 1 adopts for this patent (comprise traffic sign coloured image, add traffic sign gray-scale map after noise, add the traffic sign binary map after noise).

Embodiment:

Below in conjunction with accompanying drawing and concrete embodiment, the present invention is described further:

China's road signs are divided into main mark and derivative sign two large classes, and totally 116 kinds of main marks have redness, yellow, blueness and white four large classes by color classification, by Shape Classification, have triangle, circle and rectangle three major types.According to the comparatively single feature of China's road signs CF, the recognition methods of traffic sign is mainly divided into recognition methods and the recognition methods based on shape based on color.

Subspace pattern recognition can be take gradation of image information as basis, reduces the impact of aberration, has increased the stability of identification, can reduce in a large number the redundant information of sign image simultaneously, improves recognition speed, increases the real-time of Traffic Sign Recognition System.Because principal component analytical method is rebuild and reverted to basis and carry out feature extraction with the optimum of all samples, the feature of extracting is but optimal classification feature not necessarily of best Expressive Features, and linear discriminant method can make the minimum between class distance simultaneously of sample inter-object distance maximum, be more suitable for for pattern recognition problem, if but do not have enough training samples to guarantee that within class scatter matrix is nonsingular, just can not directly apply, the inventive method combines principal component analytical method and linear discriminant analysis method, not only guaranteed extracted being characterized as best Expressive Features but also having guaranteed that the otherness between different traffic signs is maximum.

The present invention relates to a kind of traffic sign recognition method based on the shape facility invariant subspace, its objective is to design and a kind ofly can carry out feature extraction and know method for distinguishing for the traffic sign gathering under different noise effect conditions.By Traffic Sign Images storehouse is tested, prove the feasible of the method, there is discrimination high, the feature that recognition speed is fast, also can carry out according to algorithm the research of embedded system, finally realizes the identification to road signs, improves road traffic safety.

A kind of traffic sign recognition method based on the shape facility invariant subspace, it is characterized in that: subspace pattern recognition can be take gradation of image information as basis, reduce the impact of aberration, increased the stability of identification, can reduce in a large number the redundant information of sign image simultaneously, improve recognition speed, increase the real-time of Traffic Sign Recognition System.The present invention takes the method that principal component analysis (PCA) combines with linear discriminant analysis on the bianry image of traffic sign, to do feature extraction and identification, and the feature of extracting not only has descriptive strong feature but also has the advantages that classification is good.Specific implementation method is as follows: Criterion Traffic Sign Images storehouse; By coloured image gray processing, and parts of images is done to histogram equalization and process; Image is added to noise, and by Binary Sketch of Grey Scale Image, set up traffic sign bianry image storehouse; Bianry image is done to feature extraction; With minimum distance classification, identify.

Invariant subspace recognition methods based on traffic sign shape, performing step is as follows:

(1) set up Traffic Sign Images database: the inventive method is identified for traffic sign main mark, comprise altogether 29 kinds of Warning Marks, 49 kinds of warning notices, 38 kinds of prohibitory signs, totally 116 kinds; Set up respectively indication Traffic Sign Images database, warning Traffic Sign Images database and ban Traffic Sign Images database, be mainly divided into the following steps:

1) download the coloured image of standard traffic sign, set up corresponding color image data storehouse;

2) utilize formula gray=0.299R+0.587G+0.114B to carry out gray count to Traffic Sign Images, set up corresponding gray level image database;

3) with Matlab software, add respectively white Gaussian noise, poisson noise, salt-pepper noise and speckle noise, the symbiosis of every kind of sign becomes four kinds of images that add noise, sets up totally 116 kinds of signs, the traffic sign storehouse of every kind of sign 5 width images;

4) gray level image is carried out to binaryzation, set up the shape database of traffic sign.In binaryzation process, because in prohibitory sign, no parking and traffic prohibited sign large area region is red, in gray level image, just showing as large area is darker regions, after binaryzation, large area is the figure in black almost illegible sign, this method has been done histogram equalization processing before to its binaryzation, and the image identification degree after its binaryzation is increased.

(2) calculate principal component analysis (PCA) (PCA) proper subspace:

Suppose that Traffic Sign Images set is: X={f ₁(x, y), f ₂(x, y) ..., f _n(x, y) }, every piece image f _i(x, y) can become according to row sequential deployment the vector of a M dimension

m is image pixel number, and its covariance matrix is defined as: C=XX ^t=E{ (X-u) (X-u) ^t, u=E{X} wherein.

C is carried out to svd:

Matrix U column vector u ₁, u ₂..., u _mbe unit quadrature, form the base in major component space, they are referred to as major component.Obviously, KL has converted covariance matrix diagonalization, by KL, converts, and has eliminated former directed quantity

each component between correlativity, thereby likely remove those coordinate axis with less information to reach the object that reduces feature space dimension.

If image vector

in major component space, coordinate is a _i=[a _1i, a _2i..., a _mi] ^t∈ R ^m, have

${\stackrel{\&OverBar;}{x}}_i={\mathrm{Ua}}_i=[{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="140110160519.png,140110160522.png"\; state="\{\{state\}\}">u</figure-callout>}}_1,{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="140110160519.png,140110160522.png"\; state="\{\{state\}\}">u</figure-callout>}}_2,...,u_M]\&CenterDot;\left[{[a_{1i},a_{2i},...,a_{\mathrm{Mi}}]}^T\right]=\underset{k=1}{\overset{M}{\mathrm{\&Sigma;}}}{a}_{\mathrm{ki}}\&CenterDot;u_k,---\left(2\right)$

Because U is unit orthogonal matrix, UU ^t=U ^tu=E,

${[a_{1i},a_{2i},...,a_{\mathrm{Mi}}]}^T={[{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="140110160519.png,140110160522.png"\; state="\{\{state\}\}">u</figure-callout>}}_1,{\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="140110160519.png,140110160522.png"\; state="\{\{state\}\}">u</figure-callout>}}_2,...,u_M]}^T{\stackrel{\&OverBar;}{x}}_i=[u_1^T{\stackrel{\&OverBar;}{x}}_i,u_2^T{\stackrel{\&OverBar;}{x}}_i,...,u_M^T{\stackrel{\&OverBar;}{x}}_i],---\left(3\right)$

$a_{\mathrm{ki}}=u_k^T{\stackrel{\&OverBar;}{x}}_i,---\left(4\right)$

Substitution above formula (2) obtains: ${\stackrel{\&OverBar;}{x}}_i=\underset{k=1}{\overset{M}{\mathrm{\&Sigma;}}}\left\{u_k^T{\stackrel{\&OverBar;}{x}}_i{u}_k\right\}---\left(5\right)$

Its physical significance is expressed as: with the weighted accumulation of major component vector with carry out matching input picture

Suppose only with a front d finite term, to estimate

${\hat{x}}_i=\underset{k=1}{\overset{d}{\mathrm{\&Sigma;}}}{u}_k^T{\stackrel{\&OverBar;}{x}}_i{u}_k---\left(6\right)$

So just completed the dimensionality reduction to original image, due to the good characteristic that KL conversion has, can think that feature space after dimensionality reduction is enough to represent the essential characteristic of original image; In experiment, choose respectively 2～4 groups of images as training sample, residual image is as test sample book, the method of taking to retain the energy of original image 90% retains the corresponding proper vector of maximum eigenwert as the base of PCA proper subspace, Traffic Sign Images, to this subspace projection, is obtained representing the eigenmatrix collection of original image collection;

(3) calculate linear discriminant analysis (LDA) proper subspace:

On the feature space basis of extracting in PCA method, carry out LDA feature extraction, what in classical linear discriminant analysis, use is Fisher criterion function, the Fisher linear discriminant analysis so linear judgment analysis is otherwise known as (Fisher Linear Discriminant Analysis/FLDA); Fisher criterion function is definition like this:

$J\left(w\right)=\arg \underset{w}{\max }\frac{\left|w^T{S}_{B}w\right|}{\left|w^T{S}_{w}w\right|}---\left(7\right)$

Wherein, dispersion S between class _bwith dispersion S in class _wcan be defined as:

$S_B=\frac{1}{C(C-1)}\underset{i=1}{\overset{C}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{C}{\mathrm{\&Sigma;}}}(u_i-u_j){(u_i-u_j)}^T---\left(8\right)$

$S_B=\frac{1}{C}\underset{i=1}{\overset{C}{\mathrm{\&Sigma;}}}\frac{1}{N}\underset{j=1}{\overset{N_i}{\mathrm{\&Sigma;}}}(x_j^i-u_i){(x_j^i-u_i)}^T---\left(9\right)$

C is total class number, N _ithe sample number that represents i class,

be j sample in i class,

it is the sample average in i class.

On mathematics, the optimum solution that solves Fisher criterion function just equals to solve

eigenvalue problem.Ask and make

eigenwert while obtaining maximal value, corresponding proper vector is exactly the base of LDA subspace.Eigenmatrix collection in PCA proper subspace, to LDA subspace projection, just can be obtained to the final PLA feature space that represents former Traffic Sign Images;

(4) adopt the recognition effect of minimum distance classification checking institute feature extraction feature.Traffic indication map image set is divided into training plan image set and test pattern image set.First by training image set pair program, do simulation training, obtain representing the test feature matrix stack of training plan image set; With test pattern image set, test again, obtain representing the test feature matrix stack of test pattern image set, and test feature matrix and training characteristics matrix are compared one by one, find and the immediate training image matrix of test pattern matrix, if belong on the same group, be considered as identification correct, if do not belong on the same group, be considered as identification error.In gray level image storehouse, PCA method, when training sample is 1 width image, is 95.92% to the discrimination of warning notice, and other situations are 100%; PLA method is 100% to the discrimination of all signs in all cases.In bianry image storehouse, PCA method, when training sample is 1 width image, is 97.37% to the discrimination of prohibitory sign, and other situations are 100%; PLA method is 100% to the discrimination of all signs in all cases.。

Below by specific embodiment, and by reference to the accompanying drawings, technical scheme of the present invention is described in further detail.

Embodiment: with reference to file 1～file 3, Fig. 1～Fig. 6, table 1, table 2, a kind of invariant subspace recognition methods based on traffic sign shape facility, step is as follows:

(1) download standard Traffic Sign Images, set up respectively the color image data storehouse of Warning Mark, warning notice, prohibitory sign, as shown in file 1.

(2) coloured image of file 1 is normalized to 75*67 size, and is converted into gray level image, add respectively white Gaussian noise, poisson noise, salt-pepper noise and speckle noise, set up the gray level image database of traffic sign, as shown in file 2.

(3) part Traffic Sign Images is done to equalization processing, then by all image binaryzations, set up the bianry image storehouse of traffic sign, as shown in file 3.

(4) use respectively the method for principal component analysis (PCA) (PCA), major component linear discriminant analysis (PLA) to do feature extraction and identification to traffic sign gray level image storehouse and traffic sign bianry image storehouse, recognition efficiency is as shown in table 1～2, and recognition time is as shown in Fig. 1～6.

For totally 580 width of three kinds of Traffic Sign Images under different noise effects, training sample is got respectively 1 width to 4 width images, and the discrimination of this method all can reach 100%; Compare with gray level image, on bianry image, do feature extraction, can reduce recognition time.Prove by experiment, the inventive method can be carried out traffic sign feature extraction and identification fast and effectively, is suitable for applying.

The discrimination comparing result of table 1 different characteristic extracting method to traffic sign gray level image.

The discrimination comparing result of table 2 different characteristic extracting method to traffic sign bianry image.

Claims (1)

1. the traffic sign recognition method based on the shape facility invariant subspace, is characterized in that: step is as follows:

(1) set up Traffic Sign Images database: for traffic sign main mark, identify, set up respectively indication Traffic Sign Images database, warning Traffic Sign Images database and ban Traffic Sign Images database, be divided into the following steps:

1) download the coloured image of standard traffic sign, set up corresponding color image data storehouse;

2) utilize formula gray=0.299R+0.587G+0.114B that Traffic Sign Images is converted into gray level image, set up corresponding gray level image database;

3) image is added to noise;

4) gray level image is carried out to binaryzation, set up the shape database of traffic sign;

(2) calculate principal component analysis (PCA) (PCA) proper subspace:

Suppose that Traffic Sign Images set is: X={f ₁(x, y), f ₂(x, y) ..., f _n(x, y) }, every piece image f _i(x, y) can both become according to row sequential deployment the vector of a M dimension

m is image pixel number, and its covariance matrix is defined as: C=XX ^t=E{ (X-u) (X-u) ^t, u=E{X} wherein;

C is carried out to svd:

Matrix U column vector u ₁, u ₂..., u _mbe unit quadrature, form the base in major component space, they are referred to as major component; KL has converted covariance matrix diagonalization, by KL, converts, and has eliminated former directed quantity

each component between correlativity, thereby reach the object that reduces feature space dimension;

If image vector

in major component space, coordinate is a _i=[a _1i, a _2i..., a _mi] ^t∈ R ^m, have

${\stackrel{\&OverBar;}{x}}_i={\mathrm{Ua}}_i=[u_1,u_2,...,u_M]\&CenterDot;\left[{[a_{1i},a_{2i},...,a_{\mathrm{Mi}}]}^T\right]=\underset{k=1}{\overset{M}{\mathrm{\&Sigma;}}}{a}_{\mathrm{ki}}\&CenterDot;u_k,---\left(2\right)$

Because U is unit orthogonal matrix, UU ^t=U ^tu=E,

${[a_{1i},a_{2i},...,a_{\mathrm{Mi}}]}^T={[u_1,u_2,...,u_M]}^T{\stackrel{\&OverBar;}{x}}_i=[u_1^T{\stackrel{\&OverBar;}{x}}_i,u_2^T{\stackrel{\&OverBar;}{x}}_i,...,u_M^T{\stackrel{\&OverBar;}{x}}_i],---\left(3\right)$

$a_{\mathrm{ki}}=u_k^T{\stackrel{\&OverBar;}{x}}_i,---\left(4\right)$

Substitution above formula obtains: ${\stackrel{\&OverBar;}{x}}_i=\underset{k=1}{\overset{M}{\mathrm{\&Sigma;}}}\left\{u_k^T{\stackrel{\&OverBar;}{x}}_i{u}_k\right\}---\left(5\right)$

Its physical significance is expressed as: with the weighted accumulation of major component vector with carry out matching input picture

Suppose only with a front d finite term, to estimate

${\hat{x}}_i=\underset{k=1}{\overset{d}{\mathrm{\&Sigma;}}}{u}_k^T{\stackrel{\&OverBar;}{x}}_i{u}_k---\left(6\right)$

So just completed the dimensionality reduction to original image, due to the good characteristic that KL conversion has, thought that feature space after dimensionality reduction is enough to represent the essential characteristic of original image; Get the corresponding proper vector of a front d eigenwert as the base of PCA proper subspace, all Traffic Sign Images, to this subspace projection, have just been obtained representing the proper subspace of original image collection;

(3) calculate linear discriminant analysis (LDA) proper subspace:

What in classical linear discriminant analysis, use is Fisher criterion function, the Fisher linear discriminant analysis so linear judgment analysis is otherwise known as (Fisher Linear Discriminant Analysis/FLDA); Fisher criterion function is definition like this:

$J\left(w\right)=\arg \underset{w}{\max }\frac{\left|w^T{S}_{B}w\right|}{\left|w^T{S}_{w}w\right|}---\left(7\right)$

Wherein, dispersion S between class _bwith dispersion S in class _wbe defined as:

$S_B=\frac{1}{C(C-1)}\underset{i=1}{\overset{C}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{C}{\mathrm{\&Sigma;}}}(u_i-u_j){(u_i-u_j)}^T---\left(8\right)$

$S_B=\frac{1}{C}\underset{i=1}{\overset{C}{\mathrm{\&Sigma;}}}\frac{1}{N}\underset{j=1}{\overset{N_i}{\mathrm{\&Sigma;}}}(x_j^i-u_i){(x_j^i-u_i)}^T---\left(9\right)$

C is total class number, N _ithe sample number that represents i class,

be j sample in i class, it is the sample average in i class;

On mathematics, the optimum solution that solves Fisher criterion function just equals to solve

eigenvalue problem; Ask and make

eigenwert while obtaining maximal value, corresponding proper vector is exactly the base of LDA subspace; Feature set in PCA proper subspace, to LDA subspace projection, is just obtained to the final PLA feature space that represents former Traffic Sign Images;

(4) adopt the recognition effect of minimum distance classification checking institute feature extraction feature.

Images