CN105205828A - Warp knitted fabric flaw detection method based on optimal Gabor filter - Google Patents

Abstract

The invention relates to a warp knitted fabric flaw detection method based on an optimal Gabor filter. The warp knitted fabric flaw detection method is characterized by comprising the following steps: step 1, constructing a Gabor filter and extracting Gabor filtering parameters; step 2, performing Gabor convolution processing on the image of a flawless warp knitted fabric, adopting a Fisher norm to construct a fitness function, and utilizing an quantum-behaved particle swarm optimization algorithm to optimize the Gabor filtering parameters extracted in the step 1 to obtain the optimal parameters of the Gabor filter; step 3, according to the optimal parameters of the Gabor filter, obtained in the step 2, performing Gabor convolution processing the image of the warp knitted fabric to be detected; step 4, performing binarization processing to obtain a flaw detection result of the warp knitted fabric. The flaw detection method can improve the flaw detection efficiency and accuracy of the warp knitted fabric.

Description

Based on the WARP-KNITTING flaw detection method of Optimal Gabor Filters

Technical field

The present invention relates to a kind of WARP-KNITTING flaw detection method based on Optimal Gabor Filters, belong to technical field of image processing.

Background technology

Domestic obtaining through volume industry develops fast, and while becoming the major production base of the world through compiling product, external Countries also emerges gradually through compiling industry, as some countries in Southeast Asia such as India, Vietnam, impels competition to strengthen.Be faced with competition, improve the quality of products and reduce the key that production cost becomes Business survival.Fabric defect is the principal element affecting cloth quality.According to investigations, due to the existence of fault, make fabric price reduce 45-65%, enterprise income is subject to very large loss.Current textile enterprise great majority still take the mode of artificial visually examine to detect fabric defects.The shortcoming of manual detection is: the restriction of (1) visual acuity and easy fatigue cause detecting instability; (2) artificial visually examine's Detection accuracy is low, and the Detection accuracy of skilled labor is difficult to more than 85%; (3) limited view of people, can not detect very wide region, the energy of people is limited simultaneously, often undetected situation can occur; (4) testing cost is higher, comprises the expenditures such as the training cost of a large amount of workman, wage.Therefore, the use of defect detection system in enterprise practical production run based on machine vision can improve the quality that tricot machine goes out cloth greatly, can reduce artificial simultaneously, save the production cost of enterprise, thus increase Competitive Products.

In general, after gathering WARP-KNITTING image, need preprocessing process be carried out, then carry out feature extraction and flaw differentiation.Pre-service, mainly in order to strengthen the contrast of image, making flaw information and the contrast of image background information obviously, needing in addition to carry out image denoising, remove the noise in image.Feature extraction, carries out analyzing and processing to image exactly, therefrom extracts suitable proper vector.Flaw differentiates, defect areas is detected exactly by certain sorter.Wherein feature extraction is the core link of flaw detection method, and in general, the method for feature extraction mainly contains statistic law, modelling and frequency domain method etc.Corpus--based Method method extracts feature can be divided into autocorrelation function, gray level co-occurrence matrixes, the methods such as Mathematical Morphology method and fractal theory.Extract feature based on modelling and have Wold model and Markov random field model etc.Extract feature based on frequency domain method and can be divided into Fourier transform, wavelet transformation and Gabor transformation etc.Gabor function is one group of similar measure through over-rotation and flexible process, it is one group of narrow band filter, good resolution characteristic is all had in spatial domain and frequency field, there are obvious set direction and frequency selective characteristic, can realize the best co-located of spatial domain and frequency domain, therefore Gabor transformation is applicable to the analysis of texture image.

Summary of the invention

The object of the invention is to overcome the deficiencies in the prior art, a kind of WARP-KNITTING flaw detection method based on Optimal Gabor Filters is provided, accuracy rate and the real-time of detection can be improved.

According to technical scheme provided by the invention,

In an embodiment, a kind of WARP-KNITTING flaw detection method based on Optimal Gabor Filters, feature is, comprises the following steps:

Step 1, structure Gabor filter, extract Gabor filtering parameter;

Step 2, Gabor process of convolution is carried out to indefectible WARP-KNITTING image, adopt Fisher criterion structure fitness function, utilization sub-line is that particle group optimizing (QPSO) algorithm carries out optimal treatment to the Gabor filtering parameter that step 1 is extracted, and obtains the optimized parameter of Gabor filter;

Step 3, the Gabor filter optimized parameter obtained by step 2, carry out Gabor process of convolution to WARP-KNITTING image to be detected;

Step 4, binary conversion treatment of carrying out obtain the Defect Detection result of WARP-KNITTING.

Further, described step 1 is implemented according to following steps:

Step 1.1, set up Gabor filter function, specifically implement in accordance with the following methods:

Gabor filter function G (x, y) is formed by two-dimentional Gaussian kernel function g (x, the y) modulation that the multiple sine function of directivity is tuning, and in the spatial domain, Gaussian kernel function relates to three parameter δ _x, δ _y, θ, wherein δ _xfor the scale parameter on Gaussian kernel function x-axis direction, δ _yfor the scale parameter on Gaussian kernel function y-axis direction, θ is the anglec of rotation of Gaussian kernel function, (x ', y ') be the coordinate that (x, y) rotates after θ angle; In frequency field, three parameters that Fourier transform relates to frequency are F ₀, u ₀, v ₀, wherein F ₀the centre frequency of oval Gabor filter function, u ₀the centre frequency of Gabor filter function on x-axis direction, v ₀it is the centre frequency of Gabor filter function on y direction;

Gabor filter function in two-dimensional space is expressed as:

$G(x,y)=g(x^{\′},y^{\′})\exp \left(2\mathrm{\π}j\left(F_0\sqrt{x^{\′2}+\frac{y^{\′2}}{{\mathrm{\γ}}^2}}+u_0{x}^{\′}+v_0{y}^{\′}\right)\right)---\left(1\right);$

Wherein,

$g\left(x^{\′},y^{\′}\right)=\frac{1}{2{\mathrm{\π\δ}}_x{\mathrm{\δ}}_y}\exp \left(-\frac{1}{2}\left(\frac{x^{\′2}}{{{\mathrm{\δ}}_x}^2}+\frac{y^{\′2}}{{{\mathrm{\δ}}_y}^2}\right)\right);$

$\left[\begin{array}{c}{x}^{\′}\\ y^{\′}\end{array}\right]=\left[\begin{array}{cc}\cos \mathrm{\θ}& -\sin \mathrm{\θ}\\ \sin \mathrm{\θ}& \cos \mathrm{\θ}\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right];$

$\mathrm{\γ}=\frac{{\mathrm{\δ}}_y}{{\mathrm{\δ}}_x};$

Step 1.2, Gabor filter function in spatial domain is obtained the Gabor filter function of frequency field through Fourier transform

$\hat{G}\left(u,v\right)=\frac{\sqrt{2\mathrm{\π}}\mathrm{\α}}{2}\exp \left(-\frac{{\left(\sqrt{{\left(u-u_0\right)}^{\′2}+\mathrm{\γ}{\left(v-v_0\right)}^{\′2}}-F_0\right)}^2}{2{\mathrm{\α}}^2}\right);$

Wherein, $\mathrm{\α}=\frac{1}{2{\mathrm{\π\δ}}_x},\left[\begin{array}{c}{\left(u-u_0\right)}^{\′}\\ {\left(v-v_0\right)}^{\′}\end{array}\right]=\left[\begin{array}{cc}cos\mathrm{\θ}& -sin\mathrm{\θ}\\ \sin \mathrm{\θ}& \cos \mathrm{\θ}\end{array}\right]\left[\begin{array}{c}\left(u-u_0\right)\\ \left(v-v_0\right)\end{array}\right];$

Step 1.3, the Gabor filter function constructed from step 1.2 middle extraction 6 Gabor filtering parameters (alpha, gamma, u ₀, v ₀, F ₀, θ).

Further, the middle coefficient F of Gabor filter function G (x, y) of described step 1.1 structure _owhen=0, be then modulated to 2-DGabor filter function G (x, y); u ₀=0, v ₀when=0, be then modulated to oval Gabor filter function G (x, y).

Further, described step 2 is implemented according to following steps:

Step 2.1, initialization population, comprise and determine maximum iteration time, search volume, the number of particle, the position of random initializtion particle;

Step 2.2, when first time iteration, the initial position of each particle is current individual desired positions; Gabor process of convolution is carried out to indefectible WARP-KNITTING image, adopts Fisher criterion structure fitness function, calculate the functional value that each particle is corresponding; The fitness function value of all particles finds the particle with minimum fitness function value after comparing, and the position of this particle is overall desired positions;

Step 2.3, the position of each particle to be upgraded, adopt the fitness function value obtaining each particle with step 2.2 same procedure, upgrade individual desired positions and overall desired positions;

Step 2.4, when reaching iteration termination condition, training terminate, overall desired positions is the optimal value of Gabor filtering parameter to be determined; Otherwise iterations adds 1, forward step 2.3 to.

Further, described step 2.1 is implemented according to following steps: iterations n=0 when establishing initial, and maximum iteration time is max_n; Gabor filtering parameter has (alpha, gamma, u ₀, v ₀f ₀, θ), then search volume is 6 dimensions; The number of particle is M, and the initial position of each particle is wherein i=1,2 ..., M/

Further, in described step 2.2, the image R (x, y) of image after Gabor convolution can be expressed as:

$R\left(x,y\right)=T\left(x,y\right)*G\left(x,y\right)=IDEF\left(\hat{T}\left(u,v\right)\hat{G}\left(u,v\right)\right);$

Wherein, T (x, y) is indefectible WARP-KNITTING image, and R (x, y) is the image after Gabor filter convolution, and * is the convolution operation of image, be the Fourier transform of image T (x, y), IDFT is that inverse discrete Fourier transform changes;

The energy of the image R (x, y) after described Gabor convolution is expressed as:

$E_r(x,y)={\[R_e{\left(x,y\right)}^2+R_o{\left(x,y\right)}^2\]}^{\frac{1}{2}};$

Wherein, $R_e(x,y)=IDFT\left(\hat{T}\left(u,v\right)\widehat{G_e}\left(u,v\right)\right),R_o(x,y)=IDFT\left(\hat{T}\left(u,v\right)\widehat{G_o}\left(u,v\right)\right),$ with g respectively _e(x, y) and G _othe discrete Fourier transformation of (x, y);

The described objective function according to Fisher criterion structure is expressed as:

$F\left(\mathrm{\Φ}\right)=-{\left(\frac{\mathrm{\μ}\left(\mathrm{\Φ}\right)}{\mathrm{\σ}\left(\mathrm{\Φ}\right)}\right)}^2;$

Wherein, Gabor filtering parameter Φ=(alpha, gamma, u ₀, v ₀, F ₀θ), the average energy value of the image of μ (Φ) and σ (Φ) to be size be respectively X × Y after Gabor convolution and standard deviation;

$\mathrm{\μ}\left(\mathrm{\Φ}\right)=\frac{1}{XY}\underset{x=1}{\overset{X}{\Σ}}\underset{y=1}{\overset{Y}{\Σ}}{E}_r(x,y);$

$\mathrm{\σ}\left(\mathrm{\Φ}\right)={\[\frac{1}{XY-1}\underset{x=1}{\overset{X}{\Σ}}\underset{y=1}{\overset{Y}{\Σ}}{\left(E_r\left(x,y\right)-\mathrm{\μ}\left(\mathrm{\Φ}\right)\right)}^2\]}^{\frac{1}{2}};$

Thus, have 6 decision variables, the nonlinear programming problem of 5 constraint conditions can be described as:

$\underset{\mathrm{\Φ}}{\min }F\left(\mathrm{\Φ}\right)=\underset{\mathrm{\α},\mathrm{\γ},u_0,v_0,F_0,\mathrm{\θ}}{\min }F\left(\mathrm{\α},\mathrm{\γ},u_0,v_0,F_0,\mathrm{\θ}\right);$

s.t.

$\frac{2}{\sqrt{2\mathrm{\π}}N}\≤a\≤\frac{1}{\sqrt{2\mathrm{\π}}};$

$\frac{2}{\sqrt{2\mathrm{\π}}N}\≤\frac{a}{\mathrm{\γ}}\≤\frac{1}{\sqrt{2\mathrm{\π}}};$

$0\≤u_0,v_0\≤\frac{1}{4};$

$0\≤F_0\≤\frac{\sqrt{2}}{4};$

0≤θ≤π；

When first time iteration, the initial position of each particle is current individual desired positions, namely the objective function constructed by Fisher criterion calculates fitness function value corresponding to each particle;

The fitness function value of all particles finds the particle with minimum fitness function value after comparing, and the position of this particle is overall desired positions.

Further, in described step 2.3, the location updating equation of particle is:

$x_{id}^{n+1}=p_{id}^n\±\mathrm{\β}|C_d^n-x_{id}^n|\ln \[\frac{1}{u_{id}^n}\];$

The probability got "+" in formula or get "-" is all 0.5, and wherein β is called converging diverging coefficient, for the uniform random number on interval (0,1), the convergence process of particle i is with point for attractor, its coordinate is:

Wherein it is the upper equally distributed random number in an interval (0,1);

Following formula is adopted when upgrading individual desired positions in described step 2.3:

$P_i^{n+1}=\{\begin{array}{ccc}{x}_i^{n+1},& if& F\left(x_i^{n+1}\right)<F\left(P_i^n\right)\\ P_i^n,& if& F\left(x_i^{n+1}\right)\&GreaterEqual;F\left(P_i^n\right)\end{array};$

After the individual desired positions of each particle is determined, according to upgrade overall desired positions.

Further, be that S (x, y) carries out Gabor process of convolution to WARP-KNITTING image to be detected in described step 3, obtain the image Q (x, y) after convolution:

$Q(x,y)=S(x,y)*G^{*}(x,y)=IDFT\left(\hat{S}(u,v)\widehat{G^{*}}(u,v)\right).$

Further, in described step 4, binary conversion treatment adopts following formula to carry out:

$B(x,y)=\left\{\begin{array}{ccc}0& if& |E_r(x,y)-\mathrm{\&mu;}|<c\mathrm{\&sigma;}\\ 1& if& |F_r(x,y)-\mathrm{\&mu;}|\&GreaterEqual;c\mathrm{\&sigma;}\end{array}\right.;$

Wherein B (x, y) is bianry image, is the net result of Defect Detection, if the value of B (x, y) is 1, then the pixel bit that image to be detected is corresponding is equipped with flaw; If the value of B (x, y) is 0, then the location of pixels that image to be detected is corresponding is indefectible; μ be convolution after the average energy value of image, σ is that energy scale is poor, and c is experimental constant, is obtained by experiment.

The present invention has following beneficial effect:

(1) the present invention adopts the Gabor filter of modulation arbitrarily can be modulated into 2-D-Gabor wave filter, also can be modulated into oval Gabor filter, make the different types of flaw of the more effective detection of Gabor constructed;

(2) the present invention utilizes QPSO Algorithm for Training Gabor filter parameter, uses the single Optimal Gabor Filters of structure, can detect WARP-KNITTING flaw efficiently, accurately, more be used in commercial production during detection;

(3) the present invention is by Fisher criterion structure objective function, obtain Gabor filtering parameter structure Gabor filter and flawless textile image texture more agree with, make the Gabor filter more effective detection WARP-KNITTING flaw constructed.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of WARP-KNITTING flaw detection method of the present invention.

Embodiment

Below in conjunction with concrete accompanying drawing, the invention will be further described.

WARP-KNITTING flaw detection method based on Optimal Gabor Filters of the present invention, as shown in Figure 1, specifically comprises the following steps:

The Gabor filter that step 1, structure can be modulated arbitrarily, obtains the Gabor filtering parameter needing to determine optimal value;

The Gabor filter function that step 1.1, described foundation are modulated arbitrarily, specifically implement in accordance with the following methods:

Setting up Gabor filter function G (x, y), is modulated by the two-dimentional Gaussian kernel function g (x, y) that a kind of multiple sine function of directivity is tuning.The time-frequency combination location of Gabor filter, multiple dimensioned, multidirectional characteristic, makes Gabor filter function through suitable dilation or rotation, can obtain the Gabor filter function of the different directions different scale of self similarity.

In two-dimensional space, Gabor filter function is expressed as:

$G(x,y)=g(x^{\&prime;},y^{\&prime;})\exp \left(2\mathrm{\&pi;}j\left(F_0\sqrt{x^{\&prime;2}+\frac{y^{\&prime;2}}{{\mathrm{\&gamma;}}^2}}+u_0{x}^{\&prime;}+v_0{y}^{\&prime;}\right)\right)---\left(1\right);$

Gabor filter function G (x, y) of 2-D or ellipse can be modulated into arbitrarily, coefficient F in formula (1) according to formula (1) _owhen=0, be modulated to 2-DGabor filter function G (x, y); u ₀=0, v ₀when=0, be modulated to oval Gabor filter function G (x, y);

Wherein,

$g\left(x^{\&prime;},y^{\&prime;}\right)=\frac{1}{2{\mathrm{\&pi;\&delta;}}_x{\mathrm{\&delta;}}_y}\exp \left(-\frac{1}{2}\left(\frac{x^{\&prime;2}}{{{\mathrm{\&delta;}}_x}^2}+\frac{y^{\&prime;2}}{{{\mathrm{\&delta;}}_y}^2}\right)\right)---\left(2\right);$

$\left[\begin{array}{c}{x}^{\&prime;}\\ y^{\&prime;}\end{array}\right]=\left[\begin{array}{cc}\cos \mathrm{\&theta;}& -\sin \mathrm{\&theta;}\\ \sin \mathrm{\&theta;}& \cos \mathrm{\&theta;}\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]---\left(3\right);$

$\mathrm{\&gamma;}=\frac{{\mathrm{\&delta;}}_y}{{\mathrm{\&delta;}}_x}---\left(4\right);$

In the spatial domain, Gaussian kernel function relates to three parameter δ _x, δ _y, θ, wherein δ _xfor the scale parameter on Gaussian kernel function x-axis direction, δ _yfor the scale parameter on Gaussian kernel function y-axis direction, θ is the anglec of rotation of Gaussian kernel function, (x ', y ') be the coordinate that (x, y) rotates after θ angle.In frequency field, three parameters of frequency involved by Fourier transform are F ₀, u ₀, v ₀, wherein F ₀the centre frequency of oval Gabor filter function, u ₀the centre frequency of Gabor filter function on x-axis direction, v ₀it is the centre frequency of Gabor filter function on y direction.

This any modulation Gabor filter is multiplied by multiple sine function by Gaussian kernel function and obtains, and can be rewritten as:

G(x，y)＝G _e(x，y)+jG _o(x，y)(5)；

Wherein, G _e(x, y) is the real part of Gabor filter, G _o(x, y) is the imaginary part of Gabor filter, can be expressed as follows respectively:

$G_e(x,y)=\exp \left(-\frac{1}{2}\left(\frac{x^2}{{{\mathrm{\&delta;}}_x}^2}+\frac{y^2}{{{\mathrm{\&delta;}}_y}^2}\right)\right)\cos \left(2\mathrm{\&pi;}\left(F_0\sqrt{x^2+\frac{y^2}{{\mathrm{\&gamma;}}^2}}+u_{0}x+v_{0}y\right)\right);$

$G_o(x,y)=\exp \left(-\frac{1}{2}\left(\frac{x^2}{{{\mathrm{\&delta;}}_x}^2}+\frac{y^2}{{{\mathrm{\&delta;}}_y}^2}\right)\right)\sin \left(2\mathrm{\&pi;}\left(F_0\sqrt{x^2+\frac{y^2}{{\mathrm{\&gamma;}}^2}}+u_{0}x+v_{0}y\right)\right).$

Step 1.2, Gabor filter present powerful image characteristics extraction ability, but calculated amount is larger.In order to simplify calculating, meet requirement of real-time, in spatial domain, Gabor filter function obtains the Gabor filter function of frequency field through Fourier transform

$\hat{G}\left(u,v\right)=\frac{\sqrt{2\mathrm{\&pi;}}\mathrm{\&alpha;}}{2}\exp \left(-\frac{{\left(\sqrt{{\left(u-u_0\right)}^{\&prime;2}+\mathrm{\&gamma;}{\left(v-v_0\right)}^{\&prime;2}}-F_0\right)}^2}{2{\mathrm{\&alpha;}}^2}\right)---\left(6\right);$

Wherein, $\mathrm{\&alpha;}=\frac{1}{2{\mathrm{\&pi;\&delta;}}_x},\left[\begin{array}{c}{\left(u-u_0\right)}^{\&prime;}\\ {\left(v-v_0\right)}^{\&prime;}\end{array}\right]=\left[\begin{array}{cc}cos\mathrm{\&theta;}& -sin\mathrm{\&theta;}\\ \sin \mathrm{\&theta;}& \cos \mathrm{\&theta;}\end{array}\right]\left[\begin{array}{c}\left(u-u_0\right)\\ \left(v-v_0\right)\end{array}\right].$

6 Gabor filtering parameters (alpha, gamma, u are had in step 1.3, formula (6) ₀, v ₀, F ₀, θ) need to determine optimal value.

Step 2, Gabor process of convolution is carried out to indefectible WARP-KNITTING image, adopt Fisher criterion structure fitness function, utilization sub-line is that particle group optimizing (QPSO) algorithm carries out optimal treatment to the Gabor filtering parameter extracted, and obtains the optimized parameter of Gabor filter;

Step 2.1, initialization population, comprise and determine maximum iteration time, search volume, the number of particle, the position (being a class value of Gabor filtering parameter) of random initializtion particle.

If iterations n=0 time initial, maximum iteration time is max_n.The parameter determining optimal value is needed to have (alpha, gamma, u ₀, v ₀, F ₀, θ), then search volume is 6 dimensions.The number of particle is M, and the initial position of each particle is wherein i=1,2 ..., M.

Step 2.2, when first time iteration, the initial position of each particle is current individual desired positions.Gabor process of convolution is carried out to indefectible WARP-KNITTING image, adopts Fisher criterion structure fitness function, calculate the functional value that each particle is corresponding.The fitness function value of all particles finds a particle with minimum fitness function value after comparing, and the position of this particle is overall desired positions.

For extracting WARP-KNITTING feature, structure fitness function, carries out Gabor process of convolution to indefectible WARP-KNITTING image.In the spatial domain, calculating convolution will carry out convolution to real part and imaginary part respectively, and then merges.By formula (6), in spatial domain, Gabor filter function obtains the Gabor filter function of frequency field through Fourier transform the Fourier transform of convolution of functions is the product of function Fourier transform, the product in the convolution respective frequencies territory namely in spatial domain.The image R (x, y) of image after Gabor convolution can be expressed as:

$R\left(x,y\right)=T\left(x,y\right)*G\left(x,y\right)=IDEF\left(\hat{T}\left(u,v\right)\hat{G}\left(u,v\right)\right)---\left(7\right);$

Wherein, T (x, y) is indefectible WARP-KNITTING image, and R (x, y) is the image after Gabor filter convolution, and * is the convolution operation of image, be the Fourier transform of image T (x, y), IDFT is that inverse discrete Fourier transform changes.

In general, the image after the Gabor convolution defined by formula (7) is the image of a plural form, and its energy can be expressed as:

$E_r(x,y)={\&lsqb;R_e{\left(x,y\right)}^2+R_o{\left(x,y\right)}^2\&rsqb;}^{\frac{1}{2}}---\left(8\right);$

Wherein, $R_e(x,y)=IDFT\left(\hat{T}\left(u,v\right)\widehat{G_e}\left(u,v\right)\right),R_o(x,y)=IDFT\left(\hat{T}\left(u,v\right)\widehat{G_o}\left(u,v\right)\right),$ with g respectively _e(x, y) and G _othe discrete Fourier transformation of (x, y).

Fitness function can construct according to Fisher criterion, constructs the objective function of optimization problem according to the cost function of Fisher criterion:

$F\left(\mathrm{\&Phi;}\right)=-{\left(\frac{\mathrm{\&mu;}\left(\mathrm{\&Phi;}\right)}{\mathrm{\&sigma;}\left(\mathrm{\&Phi;}\right)}\right)}^2---\left(9\right);$

Wherein, Gabor filtering parameter Φ=(alpha, gamma, u ₀, v ₀, F ₀, θ), average energy value after Gabor convolution of the image of μ (Φ) and σ (Φ) to be size be respectively x × Y and standard deviation.

$\mathrm{\&mu;}\left(\mathrm{\&Phi;}\right)=\frac{1}{XY}\underset{x=1}{\overset{X}{\&Sigma;}}\underset{y=1}{\overset{Y}{\&Sigma;}}{E}_r(x,y)---\left(10\right);$

$\mathrm{\&sigma;}\left(\mathrm{\&Phi;}\right)={\&lsqb;\frac{1}{XY-1}\underset{x=1}{\overset{X}{\&Sigma;}}\underset{y=1}{\overset{Y}{\&Sigma;}}{\left(E_r\left(x,y\right)-\mathrm{\&mu;}\left(\mathrm{\&Phi;}\right)\right)}^2\&rsqb;}^{\frac{1}{2}}---\left(11\right);$

Thus, have 6 decision variables, the nonlinear programming problem of 5 constraint conditions can be described as:

$\underset{\mathrm{\&Phi;}}{\min }F\left(\mathrm{\&Phi;}\right)=\underset{\mathrm{\&alpha;},\mathrm{\&gamma;},u_0,v_0,F_0,\mathrm{\&theta;}}{\min }F\left(\mathrm{\&alpha;},\mathrm{\&gamma;},u_0,v_0,F_0,\mathrm{\&theta;}\right)---\left(12\right);$

s.t.

$\frac{2}{\sqrt{2\mathrm{\&pi;}}N}\&le;a\&le;\frac{1}{\sqrt{2\mathrm{\&pi;}}}---\left(12a\right);$

$\frac{2}{\sqrt{2\mathrm{\&pi;}}N}\&le;\frac{a}{\mathrm{\&gamma;}}\&le;\frac{1}{\sqrt{2\mathrm{\&pi;}}}---\left(12b\right);$

$0\&le;u_0,v_0\&le;\frac{1}{4}---\left(12c\right);$

$0\&le;F_0\&le;\frac{\sqrt{2}}{4}---\left(12d\right);$

0≤θ≤π(12e)；

When first time iteration, the initial position of each particle is current individual desired positions, namely fitness function value corresponding to each particle is calculated by formula (9).

The fitness function value of all particles finds a particle with minimum fitness function value after comparing, and the position of this particle is overall desired positions.If the overall desired positions of whole population wherein,

$g=\arg \underset{1\&le;i\&le;M}{\min }F\left(P_i^n\right)---\left(13\right).$

Step 2.3, the position of each particle to be upgraded, adopt the fitness function value obtaining each particle with step 2.2 same procedure, upgrade individual desired positions and overall desired positions.

By QPSO algorithm, the location updating equation of particle is:

$x_{id}^{n+1}=P_{id}^n\&PlusMinus;\mathrm{\&beta;}\left|C_d^n-x_{id}^n\right|\ln \&lsqb;\frac{1}{u_{id}^n}\&rsqb;---\left(14\right);$

The probability got "+" in formula or get "-" is all 0.5.Wherein β is called converging diverging coefficient, and generally, parameter beta can adopt the mode linearly reduced with iterations to control. for the uniform random number on interval (0,1).The convergence process of particle i is with point for attractor, its coordinate is:

Wherein it is the upper equally distributed random number in an interval (0,1).

In formula (14) be called average desired positions, be defined as the average of the individual desired positions of all particles, namely

$C_d^n=\frac{1}{M}\underset{i=1}{\overset{M}{\&Sigma;}}{P}_{id}^n---\left(16\right);$

After the position of each particle is upgraded, adopt the fitness function value obtaining each particle with step 2.2 same procedure, then upgrade individual desired positions by following formula:

$P_i^{n+1}=\{\begin{array}{ccc}{x}_i^{n+1},& if& F\left(x_i^{n+1}\right)<F\left(P_i^n\right)\\ P_i^n,& if& F\left(x_i^{n+1}\right)\&GreaterEqual;F\left(P_i^n\right)\end{array}---\left(17\right);$

The individual desired positions of each particle obtained by above formula is preserved: to current, have the position of minimum fitness function value.

The individual desired positions of each particle just can upgrade overall desired positions according to formula (13) after determining.

Step 2.4, when reaching iteration termination condition, training terminate, overall desired positions is one group of optimal value of Gabor filtering parameter to be determined; Otherwise iterations adds 1, forward step 2.3 to.

Iteration termination condition is generally that iterations n equals max_n.

Step 3, construct Optimal Gabor Filters by optimized parameter, Gabor process of convolution is carried out to WARP-KNITTING image to be detected;

Optimized parameter structure Optimal Gabor Filters G* (x, y) obtained by step 2, is that S (x, y) carries out Gabor process of convolution to WARP-KNITTING image to be detected, obtains the image Q (x, y) after convolution:

$Q(x,y)=S(x,y)*G^{*}(x,y)=IDFT\left(\hat{S}(u,v)\widehat{G^{*}}(u,v)\right)---\left(18\right).$

Step 4, carry out binary conversion treatment and obtain Defect Detection result.

In image Q (x, y) after convolution, flawless region and area image defective have different energy response values, can be obtained the energy value E of each location of pixels by formula (8) _r(x, y).Binary conversion treatment is carried out again by following formula:

$B(x,y)=\{\begin{array}{ccc}0& if& |E_r(x,y)-\mathrm{\&mu;}|<c\mathrm{\&sigma;}\\ 1& if& |F_r(x,y)-\mathrm{\&mu;}|\&GreaterEqual;c\mathrm{\&sigma;}\end{array}---\left(19\right);$

Wherein B (x, y) is bianry image, according to formula (10) (11), μ be convolution after the average energy value of image, σ is that energy scale is poor, and c is an experimental constant, is obtained by experiment.

B (x, y) is exactly the net result of Defect Detection, is judged whether containing flaw by B (x, y).If the value of B (x, y) is 1, then the pixel bit that image to be detected is corresponding is equipped with flaw; If the value of B (x, y) is 0, then the location of pixels that image to be detected is corresponding is indefectible.

Claims (9)

1., based on a WARP-KNITTING flaw detection method for Optimal Gabor Filters, it is characterized in that, comprise the following steps:

Step 1, structure Gabor filter, extract Gabor filtering parameter;

Step 2, Gabor process of convolution is carried out to indefectible WARP-KNITTING image, adopt Fisher criterion structure fitness function, utilization sub-line is that particle group optimizing (QPSO) algorithm carries out optimal treatment to the Gabor filtering parameter that step 1 is extracted, and obtains the optimized parameter of Gabor filter;

Step 3, the Gabor filter optimized parameter obtained by step 2, carry out Gabor process of convolution to WARP-KNITTING image to be detected;

Step 4, binary conversion treatment of carrying out obtain the Defect Detection result of WARP-KNITTING.

2., as claimed in claim 1 based on the WARP-KNITTING flaw detection method of Optimal Gabor Filters, it is characterized in that: described step 1 is implemented according to following steps:

Step 1.1, set up Gabor filter function, specifically implement in accordance with the following methods:

Gabor filter function G (x, y) is formed by two-dimentional Gaussian kernel function g (x, the y) modulation that the multiple sine function of directivity is tuning, and in the spatial domain, Gaussian kernel function relates to three parameter δ _x, δ _y, θ, wherein δ _xfor the scale parameter on Gaussian kernel function x-axis direction, δ _yfor the scale parameter on Gaussian kernel function y-axis direction, θ is the anglec of rotation of Gaussian kernel function, (x ', y ') be the coordinate that (x, y) rotates after θ angle; In frequency field, three parameters that Fourier transform relates to frequency are F ₀, u ₀, v ₀, wherein F ₀the centre frequency of oval Gabor filter function, u ₀the centre frequency of Gabor filter function on x-axis direction, v ₀it is the centre frequency of Gabor filter function on y direction;

Gabor filter function in two-dimensional space is expressed as:

Wherein,

Step 1.2, Gabor filter function in spatial domain is obtained the Gabor filter function of frequency field through Fourier transform

Wherein,

Step 1.3, the Gabor filter function constructed from step 1.2 middle extraction 6 Gabor filtering parameters (alpha, gamma, u ₀, v ₀, F ₀, θ).

3. as claimed in claim 2 based on the WARP-KNITTING flaw detection method of Optimal Gabor Filters, it is characterized in that: coefficient F in Gabor filter function G (x, y) that described step 1.1 constructs _owhen=0, be then modulated to 2-DGabor filter function G (x, y); u ₀=0, v ₀when=0, be then modulated to oval Gabor filter function G (x, y).

4., as claimed in claim 1 based on the WARP-KNITTING flaw detection method of Optimal Gabor Filters, it is characterized in that: described step 2 is implemented according to following steps:

Step 2.1, initialization population, comprise and determine maximum iteration time, search volume, the number of particle, the position of random initializtion particle;

Step 2.2, when first time iteration, the initial position of each particle is current individual desired positions; Gabor process of convolution is carried out to indefectible WARP-KNITTING image, adopts Fisher criterion structure fitness function, calculate the functional value that each particle is corresponding; The fitness function value of all particles finds the particle with minimum fitness function value after comparing, and the position of this particle is overall desired positions;

Step 2.3, the position of each particle to be upgraded, adopt the fitness function value obtaining each particle with step 2.2 same procedure, upgrade individual desired positions and overall desired positions;

Step 2.4, when reaching iteration termination condition, training terminate, overall desired positions is the optimal value of Gabor filtering parameter to be determined; Otherwise iterations adds 1, forward step 2.3 to.

5., as claimed in claim 4 based on the WARP-KNITTING flaw detection method of Optimal Gabor Filters, it is characterized in that: described step 2.1 is implemented according to following steps: iterations n=0 when establishing initial, maximum iteration time is max_n; Gabor filtering parameter has (alpha, gamma, u ₀, v ₀, F ₀, θ), then search volume is 6 dimensions; The number of particle is M, and the initial position of each particle is wherein i=1,2 ..., M/.

6., as claimed in claim 4 based on the WARP-KNITTING flaw detection method of Optimal Gabor Filters, it is characterized in that: in described step 2.2, the image R (x, y) of image after Gabor convolution can be expressed as:

Wherein, T (x, y) is indefectible WARP-KNITTING image, and R (x, y) is the image after Gabor filter convolution, and * is the convolution operation of image, be the Fourier transform of image T (x, y), IDFT is that inverse discrete Fourier transform changes;

The energy of the image R (x, y) after described Gabor convolution is expressed as:

Wherein, with g respectively _e(x, y) and G _othe discrete Fourier transformation of (x, y);

The described objective function according to Fisher criterion structure is expressed as:

Wherein, Gabor filtering parameter Φ=(alpha, gamma, u ₀, v ₀, F ₀, θ), average energy value after Gabor convolution of the image of μ (Φ) and σ (Φ) to be size be respectively X × Y and standard deviation;

Thus, have 6 decision variables, the nonlinear programming problem of 5 constraint conditions can be described as:

s.t.

0≤θ≤π；

When first time iteration, the initial position of each particle is current individual desired positions, namely the objective function constructed by Fisher criterion calculates fitness function value corresponding to each particle;

The fitness function value of all particles finds the particle with minimum fitness function value after comparing, and the position of this particle is overall desired positions.

7., as claimed in claim 4 based on the WARP-KNITTING flaw detection method of Optimal Gabor Filters, it is characterized in that: in described step 2.3, the location updating equation of particle is:

The probability got "+" in formula or get "-" is all 0.5, and wherein β is called converging diverging coefficient, for the uniform random number on interval (0,1), the convergence process of particle i is with point for attractor, its coordinate is:

Wherein it is the upper equally distributed random number in an interval (0,1);

Following formula is adopted when upgrading individual desired positions in described step 2.3:

After the individual desired positions of each particle is determined, according to upgrade overall desired positions.

8. as claimed in claim 1 based on the WARP-KNITTING flaw detection method of Optimal Gabor Filters, it is characterized in that: be S (x to WARP-KNITTING image to be detected in described step 3, y) carry out Gabor process of convolution, obtain the image Q (x, y) after convolution:

9. as claimed in claim 1 based on the WARP-KNITTING flaw detection method of Optimal Gabor Filters, it is characterized in that: in described step 4, binary conversion treatment adopts following formula to carry out:

Wherein B (x, y) is bianry image, is the net result of Defect Detection, if the value of B (x, y) is 1, then the pixel bit that image to be detected is corresponding is equipped with flaw; If the value of B (x, y) is 0, then the location of pixels that image to be detected is corresponding is indefectible; μ be convolution after the average energy value of image, σ is that energy scale is poor, and c is experimental constant, is obtained by experiment.