CN105184777A - Painted design fabric defect detection method based on image decomposition - Google Patents

Abstract

The invention discloses a painted design fabric defect detection method based on image decomposition. The method implements specifically according to the following steps: step 1, acquiring images of a painted design fabric; step 2, pre-processing the images acquired in the step 1, that is, performing image enhancement to obtain a first target image; step 3, and using a Gaussian back substitution alternating direction method to decompose the first target image in the step 2, to break the image into a texture part v and a defect part u. The invention provides the painted design fabric defect detection method based on image decomposition, and the painted design fabric defect detection method based on image decomposition using a Gaussian back substitution alternating direction method is used. The method effectively analyzes and solves an image decomposition objective function through the Gaussian back substitution alternating direction method of a convex optimization model, so the defect part of the image is partially visual.

Description

A kind of decalcomania fabric defects detection method based on picture breakdown

Technical field

The invention belongs to image procossing, pattern-recognition and technical field of machine vision, be specifically related to a kind of decalcomania fabric defects detection method based on picture breakdown.

Background technology

Along with the fast development of science and technology, China's textile industry competition, the good and bad degree of cloth quality is quite big on textile manufacturing impact, will sell containing clothes defective by discounted price, thus Shi Ge great textile enterprise is faced with high standard, the tight immense pressure required.In textile product is produced, cloth cover flaw is the principal element affecting fabric quality, and the inspection of fabric face flaw is a very important link.At present, most domestic enterprise still adopts the method for traditional artificial visually examine to detect quality of textile products, because the impact by working environment and labour intensity makes detection efficiency lower, according to test, manual detection probably can only detect the flaw of 40%-60%, even if skilled perching workman also can only find the flaw of about 70%.The shortcomings such as traditional manual detection method labour intensity is large, and undetected and false drop rate is high, have become one of bottleneck improving textile enterprise's production efficiency.

Since nineteen seventies, along with the develop rapidly of digital integration technology and image processing techniques, machine vision has obtained applying more and more widely in industrial surface detection field, replace artificial vision not only can improve detection speed with computer vision, reduce labour cost, and carry out by PRINTED FABRIC flaw automatic checkout system the evaluation that Defect Detection is PRINTED FABRIC quality grade, provide the believable reference data of both sides.

At present, the crossing research field, forward position that the scholar having become weaving subject and information science based on the PRINTED FABRIC flaw on-line checkingi of machine vision plays an active part in.Domestic and international many researchers have proposed the multiple fabric defects detection algorithm based on machine vision, as auto-relativity function method, co-occurrence matrix method, the mathematics morphology of Corpus--based Method method; At the fourier transform method of frequency domain extraction eigenwert, Gabor filter method, Wavelet Transform and autoregressive model, markov random file method etc. based on model algorithm.Mak etc. utilize mathematical morphology filter to process fabric, complete the Defect Detection of fabric.Tsai and Hu proposes the Fourier model of four kinds of different flaw fabrics, and utilizes Fourier's feature of these model extraction fabric defects.The people such as XuY propose a kind of by using the unsupervised Defect Detection algorithm of the strange part of Gabor function.But these algorithms are mainly directed to the comparatively simple plain weave of texture structure and twills, and star-like for comprising, and pattern, the Defect Detection research of the decalcomania fabric of the relative complex such as ring-dot type is relatively less.Therefore, how Defect Detection is carried out to decalcomania fabric and there is more deep Research Significance.

Wavelet pretreatment gold template subtracts each other coupling (WGIS) method, based on pattern texture periodically rule band (RB) method, based on cloth forest belt (BB) method of image pixel standard deviation and be all the Defect Detection algorithm that several classes existed at present are directed to PRINTED FABRIC based on the Defect Detection algorithm etc. of pattern primitive, this several algorithm is all the algorithm that Corpus--based Method method combines with filtering mode.Wherein, rule band (RB) method based on the pattern texture cycle mainly adopts the fabric defects textural characteristics of two related complementary to realize the feature extraction of fabric window, but the setting of fabric window does not have unified method, be difficult to detect textile design flaw in real time; And be the PRINTED FABRIC for regular repetitive based on cloth forest belt (BB) rule of image pixel standard deviation, calculate the standard deviation of upper bound band and lower bound band, by training process and testing process, identify fabric defects, but for the fault also less than single repetitive, be difficult to accurately detect by cloth forest belt method.

Summary of the invention

The object of this invention is to provide a kind of decalcomania fabric defects detection method based on picture breakdown, solve the problem that prior art accurately can not detect relatively tiny fault.

The technical solution adopted in the present invention is, a kind of decalcomania fabric defects detection method based on picture breakdown, specifically implements according to following steps:

The image of step 1, collection decalcomania fabric;

Step 2, pre-service is carried out to the image that step 1 collects, namely target image I is obtained to image enhaucament;

Step 3, employing Gaussian back substitution alternating direction method are decomposed the target image I in step 2, are decomposed into texture part v and flaw part u.

Feature of the present invention is also:

Step 2 adopts the method for histogram equalization to carry out pre-service to image, and the process obtaining target image I is specially:

Suppose that image has S rank, through type (1) can obtain target image I and be:

$I=T\left(r_i\right)=\underset{i=0}{\overset{m}{\Σ}}{P}_r\left(r_i\right)=\underset{i=0}{\overset{m}{\Σ}}{n}_i/n,m=0,1,2,...,S-1---\left(1\right)$

Wherein, m is the gray level of image, and n is total number of pixels of image, n _ithe number of pixels in i-gray level, P (r _i) then represent probability density in i-gray level, T (r _m) be the non-linear transform function of pixel in m gray level.

In step 3, Gaussian back substitution alternating direction method to the concrete steps that target image I decomposes is:

First introduce convex Optimized model, namely solve min θ ₁(x ₁)+θ ₂(x ₂)+θ ₃(x ₃), submit to A ₁x ₁+ A ₂x ₂+ A ₃x ₃=b, x _i∈ X _i, i=1,2,3, wherein θ _i: for convex function, for giving set matrix, for the convex subset of non-NULL, b ∈ R ^lfor known vector; Wherein, the Lagrangian λ ∈ R of convex optimization problem ^lfunction is defined as:

$L\left(x_1,x_2,x_3,\mathrm{\λ}\right)=\underset{i=1}{\overset{3}{\Σ}}{\mathrm{\θ}}_i\left(x_i\right)-{\mathrm{\λ}}^T\left(\underset{i=1}{\overset{3}{\Σ}}{A}_i{x}_i-b\right)---\left(2\right)$

The spatial dimension of Lagrangian λ is Q=X ₁× X ₂× X ₃× R ^l;

Secondly, application Gaussian back substitution alternating direction method solves convex Optimized model problem, is specially:

1. defined parameters:

v＝(x ₂,x ₃,λ)(3)

$v^k=(x_2^k,x_3^k,{\mathrm{\λ}}^k)---\left(4\right)$

$\stackrel{-}{v^k}=(\stackrel{-}{x_2^k},\stackrel{-}{x_3^k},{\mathrm{\λ}}^k)---\left(5\right)$

$M=\left[\begin{array}{ccc}{\mathrm{\βA}}_2^T{A}_2& 0& 0\\ {\mathrm{\βA}}_3^T{A}_2& {\mathrm{\βA}}_3^T{A}_3& 0\\ 0& 0& 1/\mathrm{\β}E\end{array}\right]---\left(6\right)$

$H=diag({\mathrm{\βA}}_2^T{A}_2,{\mathrm{\βA}}_3^T{A}_3,1/\mathrm{\β}E)---\left(7\right)$

Wherein, E is unit matrix, punishment parameter beta > 0, V=X ₂× X ₃× R ^l;

2. alternating direction method is specially:

$\left\{\begin{array}{c}\stackrel{-}{x_1^k}=\mathrm{argmin}\{{\mathrm{\θ}}_1\left(x_1\right)+\mathrm{\β}/2||(A_1{x}_1+\underset{j=1}{\overset{3}{\Σ}}{A}_j{x}_j^k-b)-1/{\mathrm{\β\λ}}^k|{|}^2\}\\ \stackrel{-}{x_2^k}=\arg \min \{{\mathrm{\θ}}_2\left(x_2\right)+\mathrm{\β}/2||(A_1\stackrel{-}{x_1^k}+A_2{x}_2+\underset{j=2}{\overset{3}{\Σ}}{A}_j{x}_j^k-b)-1/{\mathrm{\β\λ}}^k|{|}^2\}\\ \stackrel{-}{x_3^k}=\mathrm{argmin}\{{\mathrm{\θ}}_3\left(x_3\right)+\mathrm{\β}/2||(A_1\stackrel{-}{x_1^k}+A_2\stackrel{-}{x_2^k}+A_3{x}_3+\underset{j=3}{\overset{3}{\Σ}}{A}_j{x}_j^k-b)-1/{\mathrm{\β\λ}}^k|{|}^2\}\\ \stackrel{-}{{\mathrm{\λ}}^k}={\mathrm{\λ}}^k-\mathrm{\β}(A_1\stackrel{-}{x_1^k}+A_2\stackrel{-}{x_2^k}+A_3\stackrel{-}{x_3^k}-b)\end{array}\right.---\left(8\right)$

3. Gaussian back substitution step is specially:

$\left\{\begin{array}{c}{H}^{-1}{M}^T\left(v^{k+1}-v^k\right)=\mathrm{\α}\left(\stackrel{-}{v^k}-v^k\right)\\ x_1^{k+1}=\stackrel{-}{x_1^k}\end{array}\right.---\left(9\right)$

Repeat 2., 3., until iteration terminates,

Wherein, α ∈ [0.5,1), tolerance ε > 0, and initial vector $v^0=(x_2^0,x_3^0,{\mathrm{\λ}}^0)\∈R^{m_2}\×R^{m_3}\×R^l;$

Hypothetical target image I ∈ R ⁿ, decompose following formula target image I in conjunction with the convex Optimized model of above-mentioned Gaussian back substitution alternating direction method:

$\underset{u\∈R^n,g\∈R^n\×R^n}{min}\mathrm{\τ}\left|\right|\left|\▿u\right||{|}_1+\frac{1}{2}||u+divg-I|{|}_2^2+\mathrm{\μ}\left|\right|\left|g\right||{|}_p---\left(10\right)$

Namely texture part v and the flaw part u of decalcomania textile image is obtained;

Wherein, p>=1, v=divg, ▽ represent first order derivative operator, div=-▽ ^tbe divergence operator, τ>=1, μ>=1 are used to the balance parameter of three ingredients weighing objective function (10) respectively;

Section 1 || | ▽ u||| ₁for the total variance norm of u, suppose for arbitrary z=(z ₁, z ₂..., z _n) ^t∈ R ⁿ, represent the p norm of z, and for arbitrary y=(y ₁, y ₂) ∈ R ⁿ× R ⁿ, | y| represents R ⁿin a vector, and to be provided by following formula:

${\left|y\right|}_i={({{\left(y_1\right)}_i}^2+{{\left(y_2\right)}_i}^2)}^{1/2},i=1,2,...,n---\left(11\right)$

From above formula $\left|\right|\left|y\right||{|}_p={\left({\mathrm{\Σ}}_{i=1}^n{{\left|y\right|}_i}^p\right)}^{1/p};$

Section 2 wherein, I ≈ u+divg;

Section 3 || | g||| _p, first we consider in negative exponent Sobolev space, for arbitrary u ∈ R ⁿ, || u|| _{1, p}=|| | u||| _p, that is in this space, total variance norm is exactly semi-norm || || _1,1, || || _{1, p}dual norm be denoted as || || _{-1, q}, 1/p+1/q=1, and be defined as: v _{-1, q}=inf{|||g|||q}, g ∈ R ⁿ× R ⁿ, so, for the Section 3 in formula (10) || | g||| _p, generally get p → ∞, can draw $\left|\right|\left|g\right||{|}_{\mathrm{\∞}}={\lim }_{p\→\mathrm{\∞}}|\left|\sqrt{{g_1}^2+{g_2}^2}\right|{|}_p.$

Also comprising step 4, the texture part v of calculating flaw fabric and the correlativity Corr (W, v (τ, μ)) of indefectible fabric W is:

$Corr(W,v(\mathrm{\τ},\mathrm{\μ}\left)\right)=\mathrm{cov}(W,v(\mathrm{\τ},\mathrm{\μ}\left)\right)/\sqrt{\mathrm{var}\left(W\right)\·\mathrm{var}\left(v\right(\mathrm{\τ},\mathrm{\μ}\left)\right)}---\left(12\right)$

Wherein, cov () and var () is respectively covariance and variance;

Corr (W, v (τ, μ)) close to 1 time (τ, μ) value be optimum balance parameter, now, target image is decomposed into texture part v' and flaw part u'.

Also comprise step 4, adopt the image partition method of the two-dimentional Otsu threshold value based on grey scale pixel value and neighborhood of pixel points gray-scale value to split the flaw part u that step 3 obtains, flaw part u is set to original image, the threshold value of getting image is T, bianry image f (x, y) then after segmentation is:

$f(x,y)=\left\{\begin{array}{cc}0& u\left(x,y\right)<T\\ 1& u\left(x,y\right)>T\end{array}\right.---\left(13\right)$

In formula: 0 represents that pixel is black, 1 represents that pixel is white.

Also comprising step 4, the texture part v of calculating flaw fabric and the correlativity Corr (W, v (τ, μ)) of indefectible fabric W is:

$Corr(W,v(\mathrm{\&tau;},\mathrm{\&mu;}\left)\right)=\mathrm{cov}(W,v(\mathrm{\&tau;},\mathrm{\&mu;}\left)\right)/\sqrt{\mathrm{var}\left(W\right)\&CenterDot;\mathrm{var}\left(v\right(\mathrm{\&tau;},\mathrm{\&mu;}\left)\right)}---\left(14\right)$

Wherein, cov () and var () is respectively covariance and variance;

Corr (W, v (τ, μ)) close to 1 time (τ, μ) value be optimum balance parameter, now, target image is decomposed into texture part v' and flaw part u';

Step 5, the image partition method of the two-dimentional Otsu threshold value based on grey scale pixel value and neighborhood of pixel points gray-scale value is adopted to split the flaw part u' that step 4 obtains, flaw part u' is set to original image, the threshold value of getting image is T, bianry image f (x, y) then after segmentation is:

$f(x,y)=\left\{\begin{array}{cc}0& u^{\&prime;}\left(x,y\right)<T\\ 1& u^{\&prime;}\left(x,y\right)>T\end{array}\right.---\left(13\right)$

In formula: 0 represents that pixel is black, 1 represents that pixel is white.

The invention has the beneficial effects as follows: the present invention is a kind of decalcomania fabric defects detection method based on picture breakdown, adopt the flaw detection method based on the decalcomania fabric of the picture breakdown of Gaussian back substitution alternating direction method, the method is mainly through the Gaussian back substitution alternating direction method effective analyze and solve picture breakdown objective function of convex Optimized model, target image is decomposed, thus makes the flaw partial visual of image.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of flaw detection method of the present invention;

Fig. 2 is star-like flaw original image and grey level histogram thereof in the present invention, the flaw image after equalization and grey level histogram thereof;

Fig. 3 be in the present invention star-like flaw image without/through pretreated picture breakdown result figure;

Fig. 4 is texture part and the flaw part of decomposition after adopting the heavy filling/pick type flaw image of the inventive method ring-dot type and equalization;

Fig. 5 is the flaw part adopting the inventive method fine filling type flaw image of pattern under different balance parameters;

Fig. 6 is the flaw part of the fine filling type flaw image adopting the inventive method star-like under different balance parameters;

Fig. 7 adopts the inventive method to the testing result figure mono-of star-like decalcomania flaw point fabric;

Fig. 8 adopts the inventive method to the testing result figure bis-of star-like decalcomania flaw point fabric;

Fig. 9 adopts the inventive method to the testing result figure mono-of pattern decalcomania flaw point fabric;

Figure 10 adopts the inventive method to the testing result figure bis-of pattern decalcomania flaw point fabric;

Figure 11 adopts the inventive method to the testing result figure mono-of ring-dot type decalcomania flaw point fabric;

Figure 12 adopts the inventive method to the testing result figure bis-of ring-dot type decalcomania flaw point fabric.

Embodiment

Below in conjunction with the drawings and specific embodiments, the present invention is described in detail.

A kind of decalcomania fabric defects detection method based on picture breakdown of the present invention, as shown in Figure 1, specifically implement according to following steps:

The image of step 1, collection decalcomania fabric;

When step 2, image acquisition, too bright or too dark, image acquisition element (as the ccd video camera) precision of light is forbidden and various noises etc. in image transmitting process all inevitably can reduce the PRINTED FABRIC picture quality collected, cause image fault, in order to reduce the impact of this distortion on successive image processing procedure, improve picture quality, the method of histogram equalization need be adopted to carry out pre-service to image, i.e. image enhaucament.Histogram equalization is that the uneven distribution histogram of these images is carried out Nonlinear extension, again distributes image pixel value, and pixel is uniformly distributed in the whole tonal range of image, thus reaches the object strengthening image visual effect.

Suppose that image has S rank, through type (1) can obtain target image I and be:

$I=T\left(r_i\right)=\underset{i=0}{\overset{m}{\&Sigma;}}{P}_r\left(r_i\right)=\underset{i=0}{\overset{m}{\&Sigma;}}{n}_i/n,m=0,1,2,...,S-1---\left(1\right)$

Wherein, m is the gray level of image, and n is total number of pixels of image, n _ithe number of pixels in i-gray level, P (r _i) then represent probability density in i-gray level, T (r _m) be the non-linear transform function of pixel in m gray level.

If Fig. 2 (a) is star-like fabric defects original image, the grey level histogram that Fig. 2 (b) is Fig. 2 (a), Fig. 2 (c) is for Fig. 2 (a) is through the pretreated flaw image of histogram equalization, the grey level histogram that Fig. 2 (d) is Fig. 2 (c), can find out through histogram equalization, image fault part is effectively strengthened.

If Fig. 3 (a) is star-like fabric defects original image, Fig. 3 (b) is Fig. 3 (a) without pretreated flaw part u, flaw image after the histogram equalization that Fig. 3 (c) is Fig. 3 (a), Fig. 3 (d) is for Fig. 3 (a) is through pretreated flaw part u, can find out that this pretreatment operation of histogram equalization is to the material impact of testing result, fabric defects position can be given prominence to more significantly through pretreated PRINTED FABRIC picture breakdown testing result.

Step 3, Gaussian back substitution alternating direction (AlternatingDirectionMethodwithGaussian, ADMG) method is utilized to solve picture breakdown objective function.Alternating direction method (AlternatingDirectionMethod, ADM) be perform on the multiplier method basis of Lagrangian function, this algorithm is actually the decomposition method of the decomposable asymmetric choice net structure of Utilizing question itself, namely, when subproblem can solve out effectively, solve by alternating iteration the normal solution that a series of subproblem obtains former problem.

First introduce convex Optimized model, namely solve min θ ₁(x ₁)+θ ₂(x ₂)+θ ₃(x ₃), submit to A ₁x ₁+ A ₂x ₂+ A ₃x ₃=b, x _i∈ X _i, i=1,2,3, wherein θ _i: for convex function, for giving set matrix, for the convex subset of non-NULL, b ∈ R ^lfor known vector; Wherein, the Lagrangian λ ∈ R of convex optimization problem ^lfunction is defined as:

$L(x_1,x_2,x_3,\mathrm{\&lambda;})=\underset{i=1}{\overset{3}{\&Sigma;}}{\mathrm{\&theta;}}_i\left(x_i\right)-{\mathrm{\&lambda;}}^T(\underset{i=1}{\overset{3}{\&Sigma;}}{A}_i{x}_i-b)---\left(2\right)$

The spatial dimension of Lagrangian λ is Q=X ₁× X ₂× X ₃× R ^l;

Secondly, application Gaussian back substitution alternating direction method solves convex Optimized model problem, and the flow process of Gaussian back substitution alternating direction method (ADMG) algorithm is as follows:

1. defined parameters:

v＝(x ₂,x ₃,λ)(3)

$v^k=(x_2^k,x_3^k,{\mathrm{\&lambda;}}^k)---\left(4\right)$

$\stackrel{-}{v^k}=(\stackrel{-}{x_2^k},\stackrel{-}{x_3^k},{\mathrm{\&lambda;}}^k)---\left(5\right)$

$M=\left[\begin{array}{ccc}{\mathrm{\&beta;A}}_2^T{A}_2& 0& 0\\ {\mathrm{\&beta;A}}_3^T{A}_2& {\mathrm{\&beta;A}}_3^T{A}_3& 0\\ 0& 0& 1/\mathrm{\&beta;}E\end{array}\right]---\left(6\right)$

$H=diag({\mathrm{\&beta;A}}_2^T{A}_2,{\mathrm{\&beta;A}}_3^T{A}_3,1/\mathrm{\&beta;}E)---\left(7\right)$

Wherein, E is unit matrix, punishment parameter beta > 0, V=X ₂× X ₃× R ^l;

2. alternating direction method (ADM) is specially:

$\left\{\begin{array}{c}\stackrel{-}{x_1^k}=\mathrm{argmin}\{{\mathrm{\&theta;}}_1\left(x_1\right)+\mathrm{\&beta;}/2||(A_1{x}_1+\underset{j=1}{\overset{3}{\&Sigma;}}{A}_j{x}_j^k-b)-1/{\mathrm{\&beta;\&lambda;}}^k|{|}^2\}\\ \stackrel{-}{x_2^k}=\arg \min \{{\mathrm{\&theta;}}_2\left(x_2\right)+\mathrm{\&beta;}/2||(A_1\stackrel{-}{x_1^k}+A_2{x}_2+\underset{j=2}{\overset{3}{\&Sigma;}}{A}_j{x}_j^k-b)-1/{\mathrm{\&beta;\&lambda;}}^k|{|}^2\}\\ \stackrel{-}{x_3^k}=\mathrm{argmin}\{{\mathrm{\&theta;}}_3\left(x_3\right)+\mathrm{\&beta;}/2||(A_1\stackrel{-}{x_1^k}+A_2\stackrel{-}{x_2^k}+A_3{x}_3+\underset{j=3}{\overset{3}{\&Sigma;}}{A}_j{x}_j^k-b)-1/{\mathrm{\&beta;\&lambda;}}^k|{|}^2\}\\ \stackrel{-}{{\mathrm{\&lambda;}}^k}={\mathrm{\&lambda;}}^k-\mathrm{\&beta;}(A_1\stackrel{-}{x_1^k}+A_2\stackrel{-}{x_2^k}+A_3\stackrel{-}{x_3^k}-b)\end{array}\right.---\left(8\right)$

3. Gaussian back substitution step is specially:

$\left\{\begin{array}{c}{H}^{-1}{M}^T\left(v^{k+1}-v^k\right)=\mathrm{\&alpha;}\left(\stackrel{-}{v^k}-v^k\right)\\ x_1^{k+1}=\stackrel{-}{x_1^k}\end{array}\right.---\left(9\right)$

Repeat 2., 3., until iteration terminates,

Wherein, α ∈ [0.5,1), tolerance ε > 0, and initial vector $v^0=\left(x_0^2,x_3^2,{\mathrm{\&lambda;}}^0\right)\&Element;R^{m_2}\&times;R^{m_3}\&times;R^l;$

Hypothetical target image I ∈ R ⁿ, decompose following formula target image I in conjunction with the convex Optimized model of above-mentioned Gaussian back substitution alternating direction method:

$\underset{u\&Element;R^n,g\&Element;R^n\&times;R^n}{min}\mathrm{\&tau;}\left|\right|\left|\&dtri;u\right||{|}_1+\frac{1}{2}||u+divg-I|{|}_2^2+\mathrm{\&mu;}\left|\right|\left|g\right||{|}_p---\left(10\right)$

Namely texture part v and the flaw part u of decalcomania textile image is obtained;

Wherein, p>=1, v=divg, ▽ represent first order derivative operator, div=-▽ ^tbe divergence operator, τ>=1, μ>=1 are used to the balance parameter of three ingredients weighing objective function (10) respectively;

Section 1 || | ▽ u||| ₁for the total variance norm (TV) of u, the advantage that TV norm is maximum in image processing process be it can Recovery image sectionally smooth and be unduly smoothly present in obvious uncontinuity in image, namely it can retain the marginal information of image.Suppose for arbitrary z=(z ₁, z ₂..., z _n) ^t∈ R ⁿ, represent the p norm of z, and for arbitrary y=(y ₁, y ₂) ∈ R ⁿ× R ⁿ, | y| represents R ⁿin a vector, and to be provided by following formula:

${\left|y\right|}_i={({{\left(y_1\right)}_i}^2+{{\left(y_2\right)}_i}^2)}^{1/2},i=1,2,...,n---\left(11\right)$

From above formula $\left|\right|\left|y\right||{|}_p={\left({\mathrm{\&Sigma;}}_{i=1}^n{{\left|y\right|}_i}^p\right)}^{1/p};$

Section 2 wherein, I ≈ u+divg;

Section 3 || | g||| _p, first we consider in negative exponent Sobolev space, for arbitrary u ∈ R ⁿ, || u|| _{1, p}=|| | u||| _p, that is in this space, total variance norm is exactly semi-norm || || _1,1, || || _{1, p}dual norm be denoted as || || _{-1, q}, 1/p+1/q=1 (namely as the p=1 that q=∞ is corresponding, vice versa), and be defined as: || v|| _{-1, q}=inf{|||g||| _q, g ∈ R ⁿ× R ⁿ, so, for the Section 3 in formula (10) || | g||| _p, generally get p → ∞, can draw $\left|\right|\left|g\right||{|}_{\mathrm{\&infin;}}={\lim }_{p\&RightArrow;\mathrm{\&infin;}}|\left|\sqrt{{g_1}^2+{g_2}^2}\right|{|}_p.$

Thus, the convex Optimized model of picture breakdown objective function in conjunction with Gaussian back substitution alternating direction method just can be obtained flaw part u and the texture part v of PRINTED FABRIC image by us.

As the original flaw image of heavy filling/pick type that Fig. 4 (a) is ring-dot type, the defect image of the histogram equalization that Fig. 4 (b) is Fig. 4 (a), Fig. 4 (c) adopts the texture part v of picture breakdown after the inventive method for Fig. 4 (b), and Fig. 4 (d) adopts the flaw part u of picture breakdown after the inventive method for Fig. 4 (b).Can find out, employing the inventive method can accurately by tiny Defect Detection out.

Can be flaw part u and texture part v by PRINTED FABRIC picture breakdown by above-mentioned steps, following three schemes all can identify fabric defects more accurately.

Scheme one,

Step 4, here, we need to consider correctly choosing of two optimum balances parameter (τ, μ) in formula (10).By available two Output rusults of formula (10): flaw part u and texture part v.But can identify fabric defects more accurately to accurately select balance parameter, we consider that the texture part v of flaw fabric and indefectible fabric W has higher correlativity, and both maximal correlation sexual intercourse computing formula are as follows:

$Corr(W,v(\mathrm{\&tau;},\mathrm{\&mu;}\left)\right)=\mathrm{cov}(W,v(\mathrm{\&tau;},\mathrm{\&mu;}\left)\right)/\sqrt{\mathrm{var}\left(W\right)\&CenterDot;\mathrm{var}\left(v\right(\mathrm{\&tau;},\mathrm{\&mu;}\left)\right)}---\left(12\right)$

In formula: cov () and var () is respectively covariance and variance.

In order to choose optimum balance parameter, generally, (τ, μ) obtain Corr (W, v (τ, μ)) close to 1 time value, now, target image is decomposed into texture part v' and flaw part u'.

As the original flaw image of fine filling type that Fig. 5 (a) is pattern, Fig. 5 (b) ~ Fig. 5 (e) is for decalcomania fabric is under different balance parameters, decompose the flaw part u' obtained, the balance parameter of Fig. 5 (b) ~ Fig. 5 (e) is respectively (1.1,1), (1.3,1), (1.5,1), (2,1).

If Fig. 6 (a) is the original flaw image of star-like fine filling type, Fig. 6 (b) ~ Fig. 6 (e) is for decalcomania fabric is under different balance parameters, decompose the flaw part u' obtained, the balance parameter of Fig. 6 (b) ~ Fig. 6 (e) is respectively (1.2,1), (1.5,1), (1.7,1), (2.1,1).

Scheme two,

Step 4, PRINTED FABRIC image carry out binaryzation, the image partition method of two-dimentional Otsu (maximum between-cluster variance) threshold value based on grey scale pixel value and neighborhood of pixel points gray-scale value is adopted to split the flaw part u that step 3 obtains, flaw part u is set to original image, the threshold value of getting image is T, bianry image f (x, y) then after segmentation is:

$f(x,y)=\left\{\begin{array}{cc}0& u\left(x,y\right)<T\\ 1& u\left(x,y\right)>T\end{array}\right.---\left(13\right)$

In formula: 0 represents that pixel is black, 1 represents that pixel is white.

Scheme three,

Step 4, here, we need to consider correctly choosing of two optimum balances parameter (τ, μ) in formula (10).By available two Output rusults of formula (10): flaw part u and texture part v.But can identify fabric defects more accurately to accurately select balance parameter, we consider that the texture part v of flaw fabric and indefectible fabric W has higher correlativity, and both maximal correlation sexual intercourse computing formula are as follows:

$Corr(W,v(\mathrm{\&tau;},\mathrm{\&mu;}\left)\right)=\mathrm{cov}(W,v(\mathrm{\&tau;},\mathrm{\&mu;}\left)\right)/\sqrt{\mathrm{var}\left(W\right)\&CenterDot;\mathrm{var}\left(v\right(\mathrm{\&tau;},\mathrm{\&mu;}\left)\right)}---\left(14\right)$

In formula: cov () and var () is respectively covariance and variance.

In order to choose optimum balance parameter, generally, (τ, μ) obtain Corr (W, v (τ, μ)) close to 1 time value, now, target image is decomposed into texture part v' and flaw part u'.

Step 5, PRINTED FABRIC image carry out binaryzation, the image partition method of two-dimentional Otsu (maximum between-cluster variance) threshold value based on grey scale pixel value and neighborhood of pixel points gray-scale value is adopted to split the flaw part u' that step 4 obtains, flaw part u' is set to original image, the threshold value of getting image is T, bianry image f (x, y) then after segmentation is:

$f(x,y)=\left\{\begin{array}{cc}0& u^{\&prime;}\left(x,y\right)<T\\ 1& u^{\&prime;}\left(x,y\right)>T\end{array}\right.---\left(13\right)$

In formula: 0 represents that pixel is black, 1 represents that pixel is white.

Fig. 7-Figure 12 adopts third aspect of the present invention to the testing result of decalcomania flaw point fabric.Fig. 7, Fig. 8 are star-like, and Fig. 9, Figure 10 are pattern, and Figure 11, Figure 12 are ring-dot type.(a) figure of Fig. 7-Figure 12 is original decalcomania flaw point fabric, (b) of Fig. 7-Figure 12 is the pretreating effect figure after histogram equalization, (c) of Fig. 7-Figure 12 is the flaw dot image obtained after picture breakdown algorithm, and (d) figure of Fig. 7-Figure 12 is the fault bianry image obtained through two-dimentional Otsu Threshold segmentation.As can be seen from the results, the position of fabric defects and shape have obtained good Visual retrieval, and in an experiment the detection time of ring-dot type fabric short compared with other two kind fabrics, detection efficiency is higher.

Table 1, table 2 and table 3 are respectively star-like, ring-dot type, pattern fabric be detected as power, sensitivity and specific result, not only show detection algorithm based on the picture breakdown of Gaussian back substitution alternating direction to the detection perform of decalcomania fault fabric, and also show the recognition capability without fault decalcomania fabric.Defect detection algorithm in this invention to star-like broken hole and fine filling, the broken hole of ring-dot type, tubercle, heavy filling/pick and fine filling Four types fabric defects recognition effect more satisfactory, be detected as power, sensitivity and specificity all reach 100%.Star-like and ring-dot type totally 55 width defect image all effectively can determine defect position, and for broken yarn, many net two kind fabric testing results are relatively poor, are detected as power, and sensitivity and specificity are respectively 96.7%, 96%, 100%.Comparatively speaking, the decalcomania fabric of pattern be detected as power, sensitivity and specificity are respectively 96.9%, 96.1%, 100%, poor relative to the testing result effect of first two fault fabric type, the algorithm effect result that we propose is unsatisfactory.Although its main cause is the defect position effectively can determining defect image, but part without background texture structure in defect image and fault part district pixel similarity higher, part normal region by approximate think result in defect regions algorithm testing result undesirable, there is error.

The star-like fabric of table 1 be detected as power, sensitivity and specificity

Table 2 ring-dot type fabric be detected as power, sensitivity and specificity

Table 3 pattern fabric be detected as power, sensitivity and specificity

Claims (6)

1., based on a decalcomania fabric defects detection method for picture breakdown, it is characterized in that, specifically implement according to following steps:

The image of step 1, collection decalcomania fabric;

Step 2, pre-service is carried out to the image that step 1 collects, namely target image I is obtained to image enhaucament;

Step 3, employing Gaussian back substitution alternating direction method are decomposed the target image I in step 2, are decomposed into texture part v and flaw part u.

2. a kind of decalcomania fabric defects detection method based on picture breakdown according to claim 1, it is characterized in that, described step 2 adopts the method for histogram equalization to carry out pre-service to image, and the process obtaining target image I is specially:

Suppose that image has S rank, through type (1) can obtain target image I and be:

$I=T\left(r_i\right)=\underset{i=0}{\overset{m}{\&Sigma;}}{P}_r\left(r_i\right)=\underset{i=0}{\overset{m}{\&Sigma;}}{n}_i/n,m=0,1,2,...,S-1---\left(1\right)$

Wherein, m is the gray level of image, and n is total number of pixels of image, n _ithe number of pixels in i-gray level, P (r _i) then represent probability density in i-gray level, T (r _m) be the non-linear transform function of pixel in m gray level.

3. a kind of decalcomania fabric defects detection method based on picture breakdown according to claim 1, it is characterized in that, in described step 3, Gaussian back substitution alternating direction method to the concrete steps that target image I decomposes is:

First introduce convex Optimized model, namely solve min θ ₁(x ₁)+θ ₂(x ₂)+θ ₃(x ₃), submit to A ₁x ₁+ A ₂x ₂+ A ₃x ₃=b, x _i∈ X _i, i=1,2,3, wherein θ _i: for convex function, for giving set matrix, for the convex subset of non-NULL, b ∈ R ^lfor known vector; Wherein, the Lagrangian λ ∈ R of convex optimization problem ^lfunction is defined as:

$L(x_1,x_2,x_3,\mathrm{\&lambda;})=\underset{i=1}{\overset{3}{\&Sigma;}}{\mathrm{\&theta;}}_i\left(x_i\right)-{\mathrm{\&lambda;}}^T(\underset{i=1}{\overset{3}{\&Sigma;}}{A}_i{x}_i-b)---\left(2\right)$

The spatial dimension of Lagrangian λ is Q=X ₁× X ₂× X ₃× R ^l;

Secondly, application Gaussian back substitution alternating direction method solves convex Optimized model problem, is specially:

1. defined parameters:

v＝(x ₂,x ₃,λ)(3)

$v^k=(x_2^k,x_3^k,{\mathrm{\&lambda;}}^k)---\left(4\right)$

$\stackrel{-}{v^k}=(\stackrel{-}{x_2^k},\stackrel{-}{x_3^k},{\mathrm{\&lambda;}}^k)---\left(5\right)$

$M=\left[\begin{array}{ccc}{\mathrm{\&beta;A}}_2^T{A}_2& 0& 0\\ {\mathrm{\&beta;A}}_3^T{A}_2& {\mathrm{\&beta;A}}_3^T{A}_3& 0\\ 0& 0& 1/\mathrm{\&beta;}E\end{array}\right]---\left(6\right)$

$H=diag({\mathrm{\&beta;A}}_2^T{A}_2,{\mathrm{\&beta;A}}_3^T{A}_3,1/\mathrm{\&beta;}E)---\left(7\right)$

Wherein, E is unit matrix, punishment parameter beta > 0, V=X ₂× X ₃× R ^l;

2. alternating direction method is specially:

$\left\{\begin{array}{c}\stackrel{-}{x_1^k}=\mathrm{argmin}\{{\mathrm{\&theta;}}_1\left(x_1\right)+\mathrm{\&beta;}/2||(A_1{x}_1+\underset{j=1}{\overset{3}{\&Sigma;}}{A}_j{x}_j^k-b)-1/{\mathrm{\&beta;\&lambda;}}^k|{|}^2\}\\ \stackrel{-}{x_2^k}=\arg \min \{{\mathrm{\&theta;}}_2\left(x_2\right)+\mathrm{\&beta;}/2||(A_1\stackrel{-}{x_1^k}+A_2{x}_2+\underset{j=2}{\overset{3}{\&Sigma;}}{A}_j{x}_j^k-b)-1/{\mathrm{\&beta;\&lambda;}}^k|{|}^2\}\\ \stackrel{-}{x_3^k}=\mathrm{argmin}\{{\mathrm{\&theta;}}_3\left(x_3\right)+\mathrm{\&beta;}/2||(A_1\stackrel{-}{x_1^k}+A_2\stackrel{-}{x_2^k}+A_3{x}_3+\underset{j=3}{\overset{3}{\&Sigma;}}{A}_j{x}_j^k-b)-1/{\mathrm{\&beta;\&lambda;}}^k|{|}^2\}\\ \stackrel{-}{{\mathrm{\&lambda;}}^k}={\mathrm{\&lambda;}}^k-\mathrm{\&beta;}(A_1\stackrel{-}{x_1^k}+A_2\stackrel{-}{x_2^k}+A_3\stackrel{-}{x_3^k}-b)\end{array}\right.---\left(8\right)$

3. Gaussian back substitution step is specially:

$\left\{\begin{array}{c}{H}^{-1}{M}^T\left(v^{k+1}-v^k\right)=\mathrm{\&alpha;}\left(\stackrel{-}{v^k}-v^k\right)\\ x_1^{k+1}=\stackrel{-}{x_1^k}\end{array}\right.---\left(9\right)$

Repeat 2., 3., until iteration terminates,

Wherein, α ∈ [0.5,1), tolerance ε > 0, and initial vector $v^0=(x_2^0,x_3^0,{\mathrm{\&lambda;}}^0)\&Element;R^{m_2}\&times;R^{m_3}\&times;R^l;$

Hypothetical target image I ∈ R ⁿ, decompose following formula target image I in conjunction with the convex Optimized model of above-mentioned Gaussian back substitution alternating direction method:

$\underset{u\&Element;R^n,g\&Element;R^n\&times;R^n}{min}\mathrm{\&tau;}\left|\right|\left|\&dtri;u\right||{|}_1+\frac{1}{2}||u+divg-I|{|}_2^2+\mathrm{\&mu;}\left|\right|\left|g\right||{|}_p---\left(10\right)$

Namely texture part v and the flaw part u of decalcomania textile image is obtained;

Wherein, p>=1, v=divg, ▽ represent first order derivative operator, div=-▽ ^tbe divergence operator, τ>=1, μ>=1 are used to the balance parameter of three ingredients weighing objective function (10) respectively;

Section 1 || | ▽ u||| ₁for the total variance norm of u, suppose for arbitrary z=(z ₁, z ₂..., z _n) ^t∈ R ⁿ, represent the p norm of z, and for arbitrary y=(y ₁, y ₂) ∈ R ⁿ× R ⁿ, | y| represents R ⁿin a vector, and to be provided by following formula:

${\left|y\right|}_i={({{\left(y_1\right)}_i}^2+{{\left(y_2\right)}_i}^2)}^{1/2},i=1,2,...,n---\left(11\right)$

From above formula $\left|\right|\left|y\right||{|}_p={\left({\mathrm{\&Sigma;}}_{i=1}^n{{\left|y\right|}_i}^p\right)}^{1/p};$

Section 2 wherein, I ≈ u+divg;

Section 3 || | g||| _p, first we consider in negative exponent Sobolev space, for arbitrary u ∈ R ⁿ, that is in this space, total variance norm is exactly semi-norm || || _1,1, || || _{1, p}dual norm be denoted as || || _{-1, q}, 1/p+1/q=1, and be defined as: || v|| _{-1, q}=inf{|||g||| _q, g ∈ R ⁿ× R ⁿ, so, for the Section 3 in formula (10) || | g||| _p, generally get p → ∞, can draw $\left|\right|\left|g\right||{|}_{\mathrm{\&infin;}}={\lim }_{p\&RightArrow;\mathrm{\&infin;}}|\left|\sqrt{{g_1}^2+{g_2}^2}\right|{|}_p.$

4. a kind of decalcomania fabric defects detection method based on picture breakdown according to any one of claim 1-3, it is characterized in that, also comprising step 4, the texture part v of calculating flaw fabric and the correlativity Corr (W, v (τ, μ)) of indefectible fabric W is:

$Corr(W,v(\mathrm{\&tau;},\mathrm{\&mu;}\left)\right)=\mathrm{cov}(W,v(\mathrm{\&tau;},\mathrm{\&mu;}\left)\right)/\sqrt{\mathrm{var}\left(W\right)\&CenterDot;\mathrm{var}\left(v\right(\mathrm{\&tau;},\mathrm{\&mu;}\left)\right)}---\left(12\right)$

Wherein, cov () and var () is respectively covariance and variance;

Corr (W, v (τ, μ)) close to 1 time (τ, μ) value be optimum balance parameter, now, target image is decomposed into texture part v' and flaw part u'.

5. a kind of decalcomania fabric defects detection method based on picture breakdown according to any one of claim 1-3, it is characterized in that, also comprise step 4, adopt the image partition method of the two-dimentional Otsu threshold value based on grey scale pixel value and neighborhood of pixel points gray-scale value to split the flaw part u that step 3 obtains, flaw part u is set to original image, the threshold value of getting image is T, bianry image f (x, y) then after segmentation is:

$f(x,y)=\left\{\begin{array}{cc}0& u\left(x,y\right)<T\\ 1& u\left(x,y\right)>T\end{array}\right.---\left(13\right)$

In formula: 0 represents that pixel is black, 1 represents that pixel is white.

6. a kind of decalcomania fabric defects detection method based on picture breakdown according to any one of claim 1-3, it is characterized in that, also comprising step 4, the texture part v of calculating flaw fabric and the correlativity Corr (W, v (τ, μ)) of indefectible fabric W is:

$Corr(W,v(\mathrm{\&tau;},\mathrm{\&mu;}\left)\right)=\mathrm{cov}(W,v(\mathrm{\&tau;},\mathrm{\&mu;}\left)\right)/\sqrt{\mathrm{var}\left(W\right)\&CenterDot;\mathrm{var}\left(v\right(\mathrm{\&tau;},\mathrm{\&mu;}\left)\right)}---\left(14\right)$

Wherein, cov () and var () is respectively covariance and variance;

Corr (W, v (τ, μ)) close to 1 time (τ, μ) value be optimum balance parameter, now, target image is decomposed into texture part v' and flaw part u';

Step 5, the image partition method of the two-dimentional Otsu threshold value based on grey scale pixel value and neighborhood of pixel points gray-scale value is adopted to split the flaw part u' that step 4 obtains, flaw part u' is set to original image, the threshold value of getting image is T, bianry image f (x, y) then after segmentation is:

$f(x,y)=\left\{\begin{array}{cc}0& u^{\&prime;}\left(x,y\right)<T\\ 1& u^{\&prime;}\left(x,y\right)>T\end{array}\right.---\left(15\right)$

In formula: 0 represents that pixel is black, 1 represents that pixel is white.