Supervised defect detection on textile fabrics via optimal Gabor filter

Abstract

An effective defect detection scheme for textile fabrics is designed in this article. Interestingly, this approach is particularly useful for patterned fabric. In the proposed method, firstly, Gabor filter is adjusted to match with the texture information of non-defective fabric image via genetic algorithm. Secondly, adjusted optimal Gabor filter is used for detecting defects on defective fabric images and defective fabric images to be detected have the same texture background with corresponding defect-free fabric images. The significance of the proposed approach lies in selecting Gabor filter parameters with an abundance of choices to build the optimal Gabor filter by means of genetic algorithm and achieving accurate defect detection on patterned fabric. High success rate and accuracy with little computational time online are obtained in the defect detection on fabrics, which indicate that the suggested method can be put to use in practice.

Introduction

Flaws on textile fabrics have a great influence on selling price and price reduction ranges from 45% to 65% [1] in the original price of a product. At present, artificial detection occupies main position in the real fabric detection but has a lower detection success rate at the slower speed of 15–20 m/min [2]. It is investigated that the accuracy of artificial detection is merely 60–70% [3]. As a result, many commercial detection systems are considered to replace artificial detection, for instance, employment of I-TEX inspection system [4,5]. However, high hardware maintenances lead to the fact that application of I-TEX inspection system is limited. Realizing fabric detection method in software as well as turning costs lower on hardware equipments and maintaining from fabric detection systems are the goals to attain in the future.

A series of algorithms on the basis of software are presented in fabric detection now. Thereinto, three general types of fabric detection approaches are, respectively, based on the statistical, the model [6] and the spectral methods [7,8]. Statistical approach puts fabric images into the operation that the properties of texture features of input fabric images defined by a measurement of ‘energy’ [9] in a window about each pixel in every response image are captured. Conci and Proenca have utilized the estimation of fractal dimension (FD) [10] on input images for the sake of inspecting fabric defects. In order to dispose image information, different boxes are counted with a few modifications to minimize the complexity of computation and improve the efficiency. But the only weakness is poor localization accuracy in defect detection with high FA. The advantage of model method is that semblable textures can be structured to match the observed textures. Cohen from Drexel University of American devotes himself to automated inspection on textile fabrics using Gauss Markov random field [11] whose parameters could be obtained from defect-free fabric images with ideal detection results. But this method has its own disadvantage, such as hardly decreasing the complexity of analysis on input images. Therefore, fast detection on textile fabrics could not be realized. Spectral method is unsuitable for random textured materials. Tsai et al. [12,13] inspect defects in the directional textures with a combination of discrete Fourier transform, which can preserve the local defects and remove all homogeneous and directional textures from the initial gray-level images. However, manipulating the frequency components associated with homogeneous non-defective regions could bring enormous influences on frequency components of defective regions.

Proofs in many research works prove that Gabor filter widely used in the field of fabric defect detection uniquely has an optimal localization in both space domain and frequency domain with multiple orientations and dimensions. In general, defect detection methods based on Gabor function could be classified into two portions: one category is adding a succession of Gabor filters to characterize channels to draw a fine detection results on fabrics and the other method is selecting optimal filters. In fact, this article proposes an effective method by way of building optimal Gabor filter with selected parameters to solve encountered problems in fabric detection. Gabor filters are coordinated by stainless fabric images in objective function, and genetic algorithm is wielded to get the minimum of objective function, thus finding suitable parameters to generate optimal Gabor filters. Extracting effective texture features via optimal Gabor filters on textile fabrics can lead to an excellent consequence on fabric defect detection. The performance of Gabor filter depends on the parameters, which could be selected by genetic algorithm automatically. Based on this idea, the new method for defect detection on fabrics could be obtained. The whole proposed method includes the training part and the defect detection part, whose descriptions are shown in Figure 1. Escofet et al. [14] have used a mass of multi-scale and multi-orientation Gabor filters to detect fabric defects, which could prove that a bank of Gabor filters are suitable to characterize texture features from textile fabrics. The disadvantage of above-mentioned approach is that using plenty of filters causes a huge computational burden, thus preventing real-time effective implementation. Compared with Escofet’s method, two advantages of the proposed method are that ideal defect detection results on pattern fabrics are obtained and less calculated quantities are implemented.

Figure 1.

Fabric defect detection method on constituting optimal Gabor filter by using genetic algorithm.

Gabor function

A two-dimensional (2-D) Gabor function is a complex exponential function assigned by the given sinusoidal wave frequency u₀ and rotated orientation θ. Meanwhile, Gabor function is modulated by 2-D Gaussian function [15,16] which involves three parameters in spatial domain. The parameters are expressed as ( ${\sigma }_x$ , ${\sigma }_y$ ) and orientation θ which rotates the values x and y to the corresponding $x\text{'}$ and $y\text{'}$ , and they have variances along the x-axis and y-axis, respectively. Objective response of Gabor function in the 2-D space domain can be defined as follows:

$g(x,y)=\frac{1}{2\pi {\sigma }_x{\sigma }_y}\exp \{-\frac{1}{2}[(\frac{x\text{'}}{{\sigma }_x})2+(\frac{y\text{'}}{{\sigma }_y})2]\}\exp (j2\pi u_{0}x\text{'}).$

(1) and

$[\begin{array}{c}\hfill x\text{'}\hfill \\ \multicolumn{1}{c}{y\text{'}}\end{array}]=[\begin{array}{cc}\hfill \cos \theta \hfill & \hfill -\sin \theta \hfill \\ \multicolumn{1}{c}{\sin \theta }& \hfill \cos \theta \hfill \end{array}][\begin{array}{c}\hfill x\hfill \\ \multicolumn{1}{c}{y}\end{array}]$

The real part of 2-D Gabor function shown as equation (3) acts as an even symmetric Gabor filter [17] to detect fabric blob section. While, the imaginary part of 2-D Gabor function indicated as equation (4) is used for detecting fabric edge part as an odd symmetric filter. The relationship of two portions and integrated Gabor filter can be described as in equation (2). General responses of the real part and the imaginary part from 2-D Gabor function are exhibited in Figure 2.

$g(x,y)=g_e(x,y)+{\mathrm{jg}}_0(x,y).$

(2)

$g_e(x,y)\exp \{-\frac{1}{2}[(\frac{x\text{'}}{{\sigma }_x})2+(\frac{y\text{'}}{{\sigma }_y})]\}\cos (2\pi u_{0}x\text{'})$

(3)

${\text{g}}_o(x,y)=\exp \{-\frac{1}{2}[(\frac{x\text{'}}{{\sigma }_x})2+(\frac{y\text{'}}{{\sigma }_y})2]\}\sin (2\pi u_{0}x\text{'})$

(4) Gabor function in frequency domain defined as equation (5) can be obtained via Fourier transform of 2-D Gabor function in space domain. Practice [18] has proved that Gabor function can be used as a low pass filter to remove high-frequency components from fabric images.

$\text{F}(u,\upsilon )=\exp \{-\frac{1}{2}[(\frac{u-u_0}{{\sigma }_u})2+(\frac{\upsilon }{{\sigma }_{\upsilon }})2]\}$

(5) where ${\sigma }_u=\frac{1}{2\pi {\sigma }_x},{\sigma }_{\upsilon }=\frac{1}{2\pi {\sigma }_y}$ , and u₀ is equivalent to mid-frequency.

Figure 2.

Outline drawing for the real part (a) and imaginary part (b) of a basic Gabor function.

Structure optimal Gabor filter and flaws detection

Select proper Gabor function

Based on 2-D Gabor function equation (1), the real part of 2-D Gabor function is sufficient to defect detection, and thus only the real part is used as filter function. The main reason is that the imaginary part not only requires a mass of calculations but also contributes little to defect detection. Therefore, Gabor filter function can be formulated as equation (6):

${\text{g}}_e(x,y)=\exp \{-\frac{1}{2}[(\frac{x\text{'}}{{\sigma }_x})2+(\frac{y\text{'}}{\lambda {\sigma }_x})2]\}\cos (2\pi u_{0}x\text{'})$

(6) among

$[\begin{array}{c}\hfill x\text{'}\hfill \\ \multicolumn{1}{c}{y\text{'}}\end{array}]=[\begin{array}{cc}\hfill \cos \theta \hfill & \hfill -\sin \theta \hfill \\ \multicolumn{1}{c}{\sin \theta }& \hfill \cos \theta \hfill \end{array}][\begin{array}{c}\hfill x-T_1\hfill \\ \multicolumn{1}{c}{y-T_2}\end{array}]{\sigma }_y=\lambda {\sigma }_x$

where $T_1$ and $T_2$ are conversion parameters along the x-axis and y-axis respectively. λ is the variance ratio between x-axis and y-axis.

2-D Gabor functions can be built by rotating and zooming the basic Gabor function. The specific direction and size have strong influence on fabric defects. Therefore it is important to search optimal Gabor filter in arbitrary orientations and sizes. The superb effect of real part of 2-D Gabor function via increasing center frequency with $\sqrt[5]{4}$ multiples and angles rotation with a $\pi /6$ pace in spatial domain is shown in Figure 3. From Figure 3, Gabor function shows the most suitable effect in spatial domain which can be concluded in Figure 2(a). Gabor function with adaptable parameters u₀ and θ presents various shapes in Figure 3. The goal of proposed method is to choose suitable shapes for various textures within the shapes.

Figure 3.

A group of Gabor filters from five dimensions (center frequencies) and six orientations in space.

Determine optimal Gabor filter parameters

A similar idea mentioned in the former research [19] is selecting optimal Gabor filter, According to this thought, it is concluded that optimal Gabor filter decided by parameters should own the most similar envelope with gray-level distribution of non-defective fabric images to conform to texture feature information. To build an optimal Gabor filter, the following objective function shown in equation (7) should be optimized:

$E={min}_{\omega ,T_x,T_y,\lambda ,\theta ,u_0}[\sum _{x,y}(\text{IM}(x,y)-\omega g_e(x,y))2]$

(7) where IM is a defect-free fabric image, ω is the Gabor coefficient to harmonize the relevance between non-defective image gray-level value IM (x, y) and Gabor function result ${\text{g}}_e(x,y)$ . In the optimization process, variance ratio λ is limited to [1.0, 2.0]. The range of radial frequency u₀ with a good experimental consequence is [1.9, 5.7]. According to the experimental findings, Gaussian envelope window covers around 1 $\times \lambda$ . On account of balanced Gabor function, orientation usually lies within [0,π].

Genetic algorithm

Genetic algorithm [20] is a random search method. It is structured by imitating genes. One of the characteristics of genetic algorithm is doing nothing with decisive variables straightforward but to intersect and mutate codes from individuals. Finally, optimal or approximate solution with higher fitness would be sought out by selection, crossover and mutation, thus practical problems can be solved. Genetic algorithm is used in the previous research [21] to search the optimal parameters. But unlike parameters and diverse way of individual, structures in proposed genetic algorithm are designed. Genetic algorithm can be divided into four steps as follows:

Initial population: Initial population [22] is constructed by binary codes in line with genes from chromosomes to achieve operations effortlessly in algorithms.

Selection: Optimal group in population is inclined to the lower results of objective function E in equation (7) which owns the high fitness among initial or new population.

Crossover: Crossover is mutual exchange in two selected individuals with a certain probability at some point of two individuals. The example recorded in Table 1 shows the process of crossing binary codes.

Mutation: Mutation operator takes some point from each individual into a reverse operation with a certain probability, namely exchange 1 to 0 or 0 to 1 [23].

Table 1.

Crossover operation in two individuals.

The selected individuals	The new individuals
A	1001|0001	1001|1100
B	1010|1100	1010|0001

The whole program of genetic algorithm is shown in detail in Figure 4. Through the process of genetic algorithm, the most suitable parameters would be obtained to make great contributions to the construction of optimal Gabor filters

Figure 4.

Block diagram of genetic algorithm.

In genetic algorithm, Gabor filter parameters in objective function E in equation (7) constitute the whole parameter group. Genetic algorithm searches the minimum of objective function E to obtain the optimal Gabor parameters. The four steps in genetic algorithm provide an effective way to search other optimal Gabor parameters in the extent of u₀ and θ shown in Figure 3.

Table 2(a) and (b) presents two shapes of parameters with binary codes in genetic algorithm. Contents in Table 2 display the composition of each individual and serve expressions of minimum and maximum. The forty-eight ‘0’ represent minimum in binary codes. The forty-eight ‘1’ mean maximum in binary codes. All parameters appear as a whole in genetic algorithm to realize crossover and mutation. The corresponding parameters in the first line are from equation (6) and equation (7). Binary codes in the second line act as a complete parameter group in population and would be produced randomly between minimum and maximum. When the suitable binary codes are selected, then they would be changed into decimal numbers applied in the Gabor filter. In the whole algorithm, an individual is binary codes of a parameter and parameter group means binary codes of all parameters in Table 2, population is made of all parameter groups.

Table 2.

(a) Expression of a minimum parameter group and (b) exhibition of a maximum parameter group.

ω	$T_1$	$T_2$	λ	θ	u 0
00000000	00000000	00000000	00000000	00000000	00000000
ω	$T_1$	$T_2$	λ	θ	u 0
11111111	11111111	11111111	11111111	11111111	11111111

ω is a coefficient for controlling the relationship of Gabor function and normal fabric.

$T_1$ is the conversion parameter along the x-axis.

$T_2$ is the conversion parameter along the y-axis.

λ is the variance ratio between x-axis and y-axis.

θ rotates the values x and y to the corresponding $x\text{'}$ and $y\text{'}$ .

u₀ is the sinusoidal wave frequency.

The experimental results show that the parameters obtained by genetic algorithm have to be dealt with the following procedure [24] in equation (8). The aim of operation is to adapt to fabric texture and end with perfect defect detection. $\pi /6$ is the minimum variational angle in Figure 3. The minimum cycle of $u_{0\text{ga}}$ reflected in Figure 3 is 1.9.

$\{\begin{array}{cc}\hfill \theta =\hfill & \hfill {\theta }_{\text{ga}}-\frac{5}{6}\pi \hfill \\ \multicolumn{1}{c}{u_0=}& \hfill u_{0\text{ga}}-1.9\hfill \end{array}$

(8) Parameters ${\theta }_{\text{ga}}$ and $u_{0\text{ga}}$ are derived from genetic algorithm. Orientation θ and center frequency u₀ captured by parameters ${\theta }_{\text{ga}}$ and $u_{0\text{ga}}$ would be implemented in optimal Gabor filters. The other parameters obtained directly from genetic algorithm are also applied in optimal filters.

Filtering an image with optimal Gabor filter

For a sample fabric image I(x, y), amplitude response of a filtered image with optimal Gabor filter can be gained from equation (9) [25,26]:

$I_i(x,y)=\{[g_e(x,y)*I(x,y)]2+[g_o(x,y)*I(x,y)]2\}\frac{1}{2}$

(9) Output image $I_i(x,y)$ is a filtered fabric image. Asterisk (*) is the mark of convolution operation. ${\text{g}}_e(x,y)$ and ${\text{g}}_o(x,y)$ denote the real part and the imaginary part of Gabor function. In this article, a simplified convolution formula expressed as equation (10) can be employed to filter images, but only the real part of Gabor function is adopted.

$I_i(x,y)=\{[g_e(x,y)*I(x,y)]2\}\frac{1}{2}$

(10)

Binarization in filtered images

Before binarization, a simple $7\times 7$ median filter is used to smooth filtered fabric image for the sake of lessening various noises. Binarization in filtered fabric images can be divided into two independent steps, namely thresholds determination part and defects segmentation part.

Thresholds determination

In this step, we choose central widow W from non-defective filtered image B, then take out the maximum gray-level value ${\lambda }_{\text{max}}$ and minimum gray-level value ${\lambda }_{\text{min}}$ in the central widow W. Thresholds ${\lambda }_{\text{max}}$ and ${\lambda }_{\text{min}}$ are determined in accordance with the following equation (11):

$\{\begin{array}{cc}\hfill {\lambda }_{max}={max}_{x,y\in W}\hfill & \hfill |B(x,y)|\hfill \\ \multicolumn{1}{c}{{\lambda }_{min}={min}_{x,y\in W}}& \hfill |B(x,y)|\hfill \end{array}$

(11)

Defects segmentation

In this procedure, gray values between thresholds ${\lambda }_{\text{max}}$ and ${\lambda }_{\text{min}}$ in filtered defective image B are replaced with 0, other image gray values are endowed with 255. Output binary images D(x, y) can be obtained by equation (12):

$D(x,y)=\{\begin{array}{cc}\hfill 255\hfill & \hfill B(x,y)>{\lambda }_{max}\mathrm{\hspace{1em}\hspace{1em}\hspace{1em}}\text{or}\mathrm{\hspace{1em}\hspace{1em}\hspace{1em}}B(x,y)<{\lambda }_{min}\hfill \\ \multicolumn{1}{c}{0}& \hfill B(x,y)\le {\lambda }_{max}\mathrm{\hspace{1em}\hspace{1em}\hspace{1em}}\text{or}\mathrm{\hspace{1em}\hspace{1em}\hspace{1em}}B(x,y)\ge {\lambda }_{min}\hfill \end{array}$

(12)

Experimental results

Numerous common fabric samples including 80 fabric images with 40 non-defective images are needed in defect detection experiments to evaluate the performance of the proposed method. The experimental images acquired by using a CCD camera satisfy the definition of fabric defects from TILDA database [27] in the textile industry.

In parameters selection procedure of genetic algorithm, the target is choosing a minimum result E of equation (7) by selection, crossover and mutation in initial population with 100 parameter groups. Selection step reduces 20 parameter groups one time until the number of population becomes zero. Thus 300 parameter groups are created in whole procedure, and 300 statistical results of objective function E from patterned fabric Figure 5(a) are depicted in Figure 5(a1), (a2) and (a3). Figure 5(b1), (b2) and (b3) shows 300 statistical objective function results E from patternless fabric Figure 5(b), and three different pairs of crossover probabilities (pc) and mutation probabilities (pm) are, respectively, shown in Figure 5(a1), (a2) and (a3) as well as Figure 5(b1), (b2) and (b3). It is seen in Figure 5 that using a crossover probability (pc) value 0.6 and a mutation probability (pm) value 0.05 in genetic algorithm could receive ideal objective function results E in both patterned image and patternless image.

Figure 5.

(a) normal patterned image, (a1), (a2) and (a3) homologous statistical results E of equation (7) from 300 parameter groups in genetic algorithm on image (a), (b) normal patternless image, (b1), (b2) and (b3) homologous statistical results E of equation (7) from 300 parameter groups in genetic algorithm on image (b).

Possible results from fabric defect detection obtained in binary images are of four types [28]: namely overall detection (OD), true detection (TD), misdetection (MD) and false alarm (FA). True detection (TD) is the white area of binary images as same as the corresponding defects in original fabric image. FA binary images contain the white area of the corresponding defect regions in the fabric image and include the other white regions away from the defective areas. OD is the combination of TD and FA. MD regards defects as normal textures, which has no white areas in the binary output image.

In this article, 40 defective images are applied to fabric defect detection. Meanwhile, the corresponding defect-free fabric images are utilized in genetic algorithm for selecting the tuned Gabor filters to specific fabric textures. Statistical data offered in Table 3 can signify the performance of the proposed method.

Table 3.

Fabric detection types in the output binary images.

Types of detection results (in output binary images)	Percentage of various etection results
Overall detection	100% (40/40)
True detection	95% (38/40)
Misdetection	0% (0/40)
False alarm	5% (2/40)

Optimal Gabor filters with selected parameters gain from the training step by virtue of genetic algorithm. It is interesting that one optimal Gabor filter could only demonstrate the perfect defect detection on the specific fabric texture, and various defect inspections using the optimal Gabor filter on the specific texture fabric are pretty well. Perfect consequences of diversiform flaw detections on patterned fabric images distribute in Figure 6 including defect-free images, blemish images, filtered images and binarization images. Figure 7 shows corresponding experimental results from patternless fabric images. The whole images from detection results relate to 11 fabric textures and serve multifarious flaws on each fabric texture, for example, Figure 6(a) and (b) possess an identical fabric texture but disparate stains. The parameters of determined optimal Gabor filters from 11 unlike fabric textures are spread out in Table 4.

Figure 6.

The TILDA database images: (a) c3r1edvn, (b) c3r1edzw, (c) c3r1eeaa, (d) c3r3eexn, (e) c4r1efqg, (f) c4r1e4n8, (g) c4r3egpa, (h) c4r3eglz, (i) lockeaal, (j) ziese1 and (k) ziese2. Corresponding consequences with Gabor filters include non-defective images, defective images.

Figure 7.

The TILDA database images: (a) c2r3eczc, (b) c2r2eckm, (c) c2r2econ, (d) c2r2ecme, (e) c1r1eajo, (f) c1r1eadd, (g) c1r1eajr, (h) c1r3ebnw, (i) c1r1e4n1, (j) c1r1eaep, (k) c1r3ebox, (l) c1r3ebmh, (m) c1r3ebrh and (n) c1r3ebmu. Corresponding consequences with Gabor filters include non-defective images, defective images, filtered images and binarization images (a–n).

Table 4.

Parameters of optimal Gabor filters from 11 fabric textures.

Fabric images with different textures	ω	$T_1$	$T_2$	λ	θ	u 0
Figure 6(a) and (b)	445.4545	122.8739	152.7859	1.0303	0.3757	3.5819
Figure 6(c)	445.4545	122.8739	152.7859	1.0303	1.9457	4.5152
Figure 6(d)	206.6471	170.2835	115.6403	1.5484	0.3409	2.4944
Figure 6(e) and (f)	206.6471	170.2835	115.6403	1.5484	0.3409	2.4944
Figure 6(g) and (h)	591.8866	181.2317	148.9736	1.8104	0.3260	2.5801
Figure 6(i)	479.6676	121.0166	155.0342	1.1065	0.3813	3.5472
Figure 6(j)	212.1212	191.3978	156.0117	1.6413	0.3286	2.5911
Figure 6(k)	212.1212	191.3978	156.0117	1.6413	0.3286	2.5911
Figure 7(a)	479.6676	121.0166	155.0342	1.1065	0.3813	3.5472
Figure 7(b) to (d)	477.6149	153.1769	108.7977	1.8641	0.2491	3.5777
Figure 7(e) to (j)	212.1212	102.3460	164.6139	1.3627	0.2615	2.0637
Figure 7(k) to (n)	479.6676	121.0166	155.0342	1.1065	0.3813	3.5472

The parameters of Table 4 in Gabor filter could obtain ideal defect detection results. Most diverse textures have different parameter groups. Sometimes, inequable textures may hold same parameter group. The main reason is that fabric images have relative similar pixel distributions, although textures are different. Compared with the same textures Figure 6(a) and (b), Figure 6(c) with a distinctive filtered image roots from the settings of parameters ${\sigma }_x$ ${\sigma }_y$ , θ and u₀.

Conclusion

A supervised method has been proposed in this article including training and detection. In the training section, Gabor filter ${\text{g}}_e(x,y)$ could be supervised by a defect-free image IM(x,y) in the objective function E from equation (7). When objective function E reaches the minimum, optimal Gabor filter parameters can be obtained from applied Gabor filter $g_e(x,y)$ . An effective way to search the minimum of objective function E is genetic algorithm. Wide spaces are searched and every point is tested to search the most suitable parameters for constituting optimal Gabor filter in genetic algorithm. The fruit of objective function E is an obvious testimony that genetic algorithm has a benign search capability which occupies an important part in the whole optimal Gabor filter selection. In the detection section, selected optimal Gabor filter would be applied in defect detection on corresponding defective fabrics. Perfect detection results can be fulfilled on textile fabrics, especially defect detections on patterned fabric present good results in this work, which are fractionally done in research works. Parameters from optimal Gabor filters simultaneously are enumerated in this article and offer references for research on fabric defect detection in future. A verdict can be concluded that one optimal Gabor filter can have perfect flaw detection results on a specific texture from statistical parameters. In addition, high speed in defect detection on fabrics offers the possibility of being put into use in the modern technical industry. Likewise, the proposed method has its own disadvantages, and the main disadvantage is that defects caused by destroying the fabric and having the same color as the normal texture could not be perfectly detected on fabrics. We would put much effort into the improvement of implementation on the proposed method and the range of application.