Evaluation model of color difference for dyed fabrics based on the Support Vector Machine

Abstract

In the color difference inspection system based on machine vision, two types of dyeing effects need to be evaluated quantitatively according to color measurement results: the color consistency – the color matching degree between the dyeing product and the target; and the color levelness – the color uniformity in different regions of the same dyeing product. The purpose of this paper is to develop the color consistency and levelness evaluation algorithms and a new evaluation model of dyed fabrics based on the Support Vector Machine (SVM). Firstly, the evaluation goals were quantitatively classified into five different levels according to ISO 105-A02:1993; secondly, six color difference-related features from two color spaces were defined as the evaluation indexes, among which several independent ones were chosen using the Principal Components Analysis method from the training data and test data to improve the speed of the evaluation while retaining the accuracy. Finally, the evaluation model was built by employing the SVM method and its parameters were optimized with the Genetic Algorithm. The SVM model was then used to evaluate the dyeing effects according to the measured color difference-related features. Experimental results show that compared with the traditional Naive Bayesian algorithm, the proposed evaluation algorithms and model in this paper can evaluate the color quality of dyed fabrics quickly and decisively, with prediction accuracy increasing by 9% and relative error reducing by 0.0985.

Keywords

color difference evaluation evaluation model Support Vector Machine

Color difference refers to the difference between two color samples in color perception, that is, the integrated performance of chrome, lightness and hue.¹ In the textile dyeing and printing industry, color difference evaluation is a very important process during the dyeing process and before the final dyed fabrics leave from the factory. The purpose of color difference evaluation is to find the following: (1) the color matching degree between the dyeing product and the sample; and (2) the color uniformity of the dyeing product.

At present, the color difference evaluation of dyed fabrics in many dyeing factories is mostly done by workers, depending on their eyes and instruments, which can be greatly improved in accuracy and speed. The adoption of the color difference evaluation system based on machine vision is becoming popular because it can not only improve evaluation efficiency better, but also can overcome the subjective influence of human beings, making the evaluation results more objective. Many research institutions and companies have studied and developed many color difference inspection systems based on machine vision. For example, Nobbs and Connolly² proposed a colorimeter based on a video camera. Yang and Sun³utilized the Digital Signal Processing (DSP) and Complex Programmable Logic Device (CPLD) embedded processing platform with a PC structure to develop a machine vision color difference measurement system. Other similar systems included the Qtex system⁴ developed by Sedo Treepoint GmbH in the city of Mengerskirchen in Germany.

In the machine vision system of color difference evaluation, the evaluation results, that is, color consistency and color levelness, should be classified and quantified first. Then, the algorithms for determining how to calculate the values of color consistency and levelness of the dyed fabrics, as well as color difference-related features used for evaluation, should be designed and chosen carefully. Finally, a color difference evaluation model should be designed to obtain the evaluation results in terms of the chosen evaluation indexes. So far researches^2,3 have paid more attention to the evaluation system itself, but less to the classification and quantification of color difference evaluation results, as well as the selection of evaluation indexes and the evaluation model. There were many disadvantages in previous color evaluation systems;⁴ for example, only single evaluation feature in single color space was used without considering the effects of lighting conditions and background noise. Standard algorithms for color consistency and levelness have been insufficient up to now. Many systems⁴ only provided certain color difference specific data, so manpower still was necessary for classification and quantification of evaluation results, leading to them being unable to realize automatic color difference evaluation.

The evaluation model of color difference aims to create a mapping from the color difference-related features to the evaluation results, which essentially is a kind of nonlinear classification model. For this model, many machine learning methods, such as the Bayesian, neural network, Support Vector Machine (SVM), etc., can be very effective. Ji and Qi⁵ proposed color classification using the Bayesian method and the image classification based on an image texture feature; Kuo et al.⁶ analyzed the color system of embroidery fabric using the neural network method; Chen et al.⁷ also carried out color evaluation and clustering in the color measuring system using a neural network; The SVM algorithm proposed by Vapnik and his collaborator is widely used in many fields, such as pattern recognition, image processing and nonlinear process modeling and intelligent control,⁸ which can be used as the classifier with obviously higher performance than that of the Radial Basis Function (RBF) Neural Network.⁹

The purpose of this paper is to develop the color difference evaluation model for dyeing products in three important steps: (1) classifying and quantifying the evaluated results; (2) developing the color evaluation algorithms and selecting color difference-related features; (3) establishing a color difference evaluation model based on the SVM. This study is the first attempt to resolve the problem for the machine vision color difference inspection system, which has important significance for improving the evaluation speed and credibility of dyed fabrics.

Research methods and color difference evaluation algorithms

The experiment equipments used in this paper include three kinds of light source: A, D65 and D50; a SSC-DC398BP color industrial camera with SSV0358GNB industrial lens made by SONY company; a VT-FA300 image acquisition card; and a common PC installed with image processing software. The finished polyester woven fabrics were used for evaluation. The experimental platform is shown in Figure 1.
Figure 1.
Experimental platform of color difference evaluation.

The algorithms involved in this paper were programmed with MATLAB 7.1 under Microsoft Windows XP. The research framework of this paper is shown in Figure 2.
Figure 2.
Framework of this paper.

Color space and color difference formula

It is important for a color difference evaluation model to select the appropriate color space. In a machine vision system of the color difference inspection, the color values of the acquired original images are expressed by red, green, blue (RGB) values. However, the RGB color space cannot reflect the color cognitive attributes intuitively, and moreover it is one of the most uneven color spaces. Therefore, this paper selected the color difference features from both hue saturation value (HSV) and CIE 1976 (L, a, b) color spaces for developing the evaluation model, which can better make use of humans' color feelings and also take the independency of the device into consideration compared with the single color space.

HSV color space

The HSV color space defines color information in a way more familiar to human beings. It is made up of three components: H, S and V, where the H component represents hue, S saturation and V brightness. The V component is independent of the color information, but H and S are closely related to the manner of color feeling by human beings. The transformation equation from RGB space to HSV space is shown:
$H = {\frac{π}{3} [\frac{B - R}{V - min (R, G, B)}] if G = V \frac{π}{3} [2 + \frac{R - G}{V - min (R, G, B)}] if B = V \frac{π}{3} [4 + \frac{G - B}{V - min (R, G, B)}] if R = V S = [V - min (R, G, B)] / V V = max (R, G, B)$
(1)

CIELAB color space

CIELAB space is a uniform color space⁹ based on human vision and independent of device. The CIELAB color space (also called CIE 1976 (L, a, b)) contains three vertical color coordinate axes, where column coordinate L* represents lightness (0–100), a* is the red–green coordinate and b* is the yellow–blue coordinate. These three values are obtained by nonlinear transformation from the XYZ tristimulus space (obtained through linear transformation of RGB space) as shown:¹⁰
$L * = 116 (Y / Y Y_{n} Y_{n}) 1 / 13 3 - 16, if Y / Y Y_{n} Y_{n} > 0.008856 L * = 903.3 (Y / Y Y_{n} Y_{n}), if Y / Y Y_{n} Y_{n} > 0.008856 a * = 500 [(X / X X_{n} X_{n}) - (Y / Y Y_{n} Y_{n})] b * = 0.4 \times 500 [(Y / Y Y_{n} Y_{n}) - (Z / Z Z_{n} Z_{n})]$
(2)
where X_n, Y_n, Z_n are the tristimulus of the ideal white object.

Color difference formula

There are many color difference formulas, among which the preferred color difference formula in textile industries is $CM C_{(l : c)}$ , which is obtained by modification and improvement of JPC79¹¹ in the color space CIE 1976 (L, a, b). Many color difference evaluation instruments employ just the $CM C_{(l : c)}$ value as the evaluation index without considering the HSV color space, which is calculated by
$Δ E_{CMC (l : c)} = [(Δ L / Δ L * l S_{L} / S_{L}) 2 + (Δ C_{ab}^{} / / Δ C_{ab}^{} S_{c} S_{c}) 2 + (Δ H_{ab}^{} / / Δ H_{ab}^{} S_{H} S_{H}) 2] 1 / 2$
(3)
where $S_{L}, S_{C}, S_{H}$ are the weighting coefficients of lightness difference $Δ L $ , saturation difference $Δ C_{ab} $ and color difference $Δ H_{ab} $ , respectively; l, c are two coefficients used to adjust the relatively wide capacity of brightness and saturation, respectively. In the dyeing industry, the $CM C_{(2 : 1)}$ formula is employed often, that is, $l = 2, c = 1$ .

Color difference evaluation indexes and levels

The evaluation index is used to describe certain features in different aspects that the evaluated object owns. Different from the traditional color difference measurement instruments, this paper used six color-related attributes in two color spaces: lightness difference $Δ L , Δ a * and Δ b $ ; hue difference $Δ H$ , saturation difference $Δ S$ and brightness difference $Δ V$ . Among them, the first three indexes ( $Δ L , Δ a * and Δ b $ ) are defined in CIELAB space reflecting the color uniformity effect independent of device, and other three ( $Δ H, Δ S$ and $Δ V$ ) are defined in HSV space representing the humans' color feeling. Due to the fact that the linear dependence exists in some indexes above, the Principal Component Analysis (PCA) method was employed to refine them carefully for improving the evaluating speed and accuracy.

The purpose of color difference evaluation is to obtain the consistency and levelness results for dyed fabrics. Both of them are expressed with different levels of color difference. The ISO 105-A02:1993¹⁰ standard describes the gray scale for determining changes in dyed fabrics before and after color fastness tests. In this paper, we used this standard to express the levels of color difference evaluation, which are divided into five fading and staining fastness levels according to the $CM C_{(l : c)}$ color difference formula, as shown in Table 1. Based on this standard, the evaluation results of consistency and levelness can be similarly quantified into five levels, as shown in Table 2. It should be pointed out that levelness evaluating is more rigorous because it will be useless unless the evaluated object passed the consistency evaluation.
Table 1.
Relationship between color difference and fastness level¹⁰

Color difference Fastness level Color difference Fastness level

>11.85 1 2.16–3.05 3–4

8.41–11.85 1–2 1.27–2.15 4

5.96–8.40 2 0.20–1.26 4–5

4.21–5.95 2–3 <0.20 5

3.06–4.20 3

Table 2.
Evaluation levels

Evaluation level Class 1 Class 2 Class 3 Class 4 Class 5

Levelness Fastness level 1 Fastness level 2 Fastness level 3 Fastness level 4 Fastness level 5

Consistency Fastness level 1 to 2 Fastness level 2 to 3 Fastness level 3 to 4 Fastness level 4 to 5 Fastness level 5

Evaluation algorithm

For consistency evaluation, the size of the inspection region was 10 cm × 10 cm, where the evaluation region is chosen as 2.5 cm × 2.5 cm ( $295 \times 295 pixels$ ), so an inspected region is separated into four evaluation regions, as shown in Figure 3. Each evaluation region is compared with the standard sample of the same size, and if the number of evaluation regions with consistency level less than or equal to 3 is more than three, the inspection region of 10 cm × 10 cm is treated as inconsistent. The evaluation algorithm is as follows:
adopting the mean filter template $h [i, j]$ ( $295 \times 295 pixels$ ), and calculating the color mean values of the pixels $p_{n} [i, j]$ (n = 1,2,3,4) in the sample region covered by the template;

adopting the mean filter template $h [i, j]$ , and calculating the color mean values of the pixels $s [i, j]$ in the standard region covered by the template;

calculating $Δ [i, j] = | p [i, j] - s [i, j] |$ and the color difference evaluation indexes, and establishing the evaluation model based on the SVM to evaluate the region;

making $i = i + 295, j = j + 295$ , where $i, j <$ the length of the inspection region;

for the next 10 cm × 10 cm region, the above steps are repeated.

Figure 3.
Inspection region.

For levelness evaluation, the selected inspection region is the same as the consistency evaluation. In this region, the color mean values of the four regions (2.5 cm × 2.5 cm) are compared with that of the whole region (10 cm × 10 cm), and then the levelness levels are determined using the evaluation model based on the SVM. If the number of evaluation regions with levelness level less than or equal to 3 is more than three, the inspection region of 10 cm × 10 cm is treated as unlevel. The levelness evaluation process is similar to the consistency evaluation.

Related algorithms for the evaluation model

SVM algorithm

The SVM algorithm is a machine learning approach for classification and regression problems. So far, research progress shows that the SVM demonstrates superior performance gains and robustness in many applications over traditional methods.¹² The SVM has a learning ability that is independent of the dimensionality of the feature space, because the SVM measures the complexity of hypotheses based on the margin with which it separates the data, not the number of features. So it is an ideal candidate for addressing the classification problem on high precision and high dimensionality with a small sample. In the color difference evaluation system based on machine vision, the mapping relationship between the evaluation indexes and the evaluation results is complex because many factors, such as selections of color space, illumination condition and background noise, etc., can influence the evaluation process. In this paper, we used the standard SVM and the Least Squares SVM (LS-SVM) algorithms to develop the nonlinear evaluation model. In terms of the learning ability of the SVM, the influences exerted by environmental conditions can be reduced, making the evaluation results more objective.

Standard SVM

The SVM is based on the Structural Risk Minimization principle from computational learning theory. The idea is to find a hyper-plane that separates the positive examples from negative ones in the training set while maximizing the distance of them from the hyper-plane. For classification problems, the SVM calculates the classification surface of a region according to the attributes of samples in it, so that the categories of the samples could be determined through that surface.

Suppose that the sample x is an m-dimension vector and there are n samples in a certain region, given by a set of n data pairs:
$(x_{1}, y_{1}), (x_{2}, y_{2}), \dots, (x_{n}, y_{n}), x_{i} \in R_{n}, y_{i} \in {\pm 1}, i = 1, 2, \dots, n$
(4)

If a hyper-plane that can separate the training samples without error, it will satisfy
$y_{i} [ω T \cdot φ (x_{i}) + b] \geq 1, i = 1, 2, \dots, n$
(5)
where φ is the mapping function that maps the training samples into a feature space, and b is the parameter to be solved. When the hyper-plane makes the separating margin $2 / ‖ ω ‖$ maximal, it is the optimal one. In addition, considering the existence of samples that may not be classified with the hyper-plane correctly, a slack variable $ξ_{i} \geq 0, i = 1, \dots, n$ is introduced. So the hyper-plane satisfies
$y_{i} [ω T \cdot φ (x_{i}) + b] \geq 1 - ξ_{i}, i = 1, 2, \dots, n$
(6)

A minimum objective function is defined as
$\frac{1}{2} ‖ ω ‖ 2 + C \cdot \sum_{i = 1}^{n} ξ_{i}$
(7)
where the nonnegative parameter C is the penalty factor, the larger value of which shows that the degree of penalty on the error of the SVM classification is larger. By use of the Lagrange multiplier combined with –the Kuhn–Tucker theorem, it can be transformed into the maximum objective function:
$max W (α) = \sum_{i = 1}^{n} α_{i} - \frac{1}{2} \sum_{i = 1}^{n} \sum_{j = 1}^{n} α_{i} y_{i} α_{j} y_{j} (φ (x_{i}) T \cdot φ (x_{j})) s . t . \sum_{i = 1}^{n} α_{i} y_{i} = 0 α_{i} \in [0, C], i = 1, \dots, n$
(8)

For the nonlinear case, it can be transformed into the linear case with a kernel function K(·,·) in a higher dimensional feature space, where the kernel K(·,·) must satisfy the condition stated in Mercer's theorem so as to correspond to some type of inner product in the transformed (higher) dimensional feature space Φ(X). So the new maximum objective function is
$max W (α) = \sum_{i = 1}^{n} α_{i} - \frac{1}{2} \sum_{i = 1}^{n} \sum_{j = 1}^{n} α_{i} y_{i} α_{j} y_{j} K (x_{i} \cdot x_{j}) s . t . \sum_{i = 1}^{n} α_{i} y_{i} = 0 α_{i} \in [0, C], i = 1, \dots, n$
(9)
and the corresponding classification decision function is
$f (x) = sgn [\sum_{i = 1}^{n} α_{i} y_{i} K (x_{i} \cdot x) + b]$
(10)
where the training samples corresponding to the nonzero $α_{i}$ are the so-called support vectors. Equation (10) is then employed to develop the color difference evaluation model.

Least Squares SVM

The LS-SVM is a reformulation of the standard SVM that uses equality constraints (instead of the inequality constraints implemented in the standard SVM) and a quadratic error term to obtain a linear set of equations in a dual space. In this way the LS-SVM allows one to reduce the learning cost and speed up the operation compared to the SVM.

The LS-SVM expresses the classification problem as the optimization problem constrained by equality according to the structural risk minimization principle. The objective function to solve the optimization problem of the LS-SVM is
$min \frac{1}{2} ‖ ω ‖ 2 + C \cdot \sum_{i = 1}^{n} ξ_{i}^{2} s . t . y_{i} [ω T \cdot φ (x_{i}) + b] = 1 - ξ_{i}, i = 1, 2, \dots, n$
(11)

The optimization problem in (11) can be solved using the Lagrange method:
$L (ω, b, ξ_{i}; α) = \frac{1}{2} ‖ ω ‖ 2 + C \sum_{i = 1}^{n} ξ_{i}^{2} - \sum_{i = 1}^{n} α_{i} {y_{i} [ω T φ (x_{i}) + b] + ξ_{i} - 1}$
(12)

According to the optimizing condition $\frac{\partial L}{\partial ω} = 0$ , $\frac{\partial L}{\partial b} = 0$ , $\frac{\partial L}{\partial ξ_{i}} = 0$ and $\frac{\partial L}{\partial α_{i}} = 0$ , the following set of equations is obtained:
$ω = \sum_{i = 1}^{n} α_{i} y_{i} φ (x_{i}), \sum_{i = 1}^{n} α_{i} y_{i} = 0, α_{i} = C ξ_{i}, y_{i} [ω T φ (x_{i}) + b] + ξ_{i} - 1 = 0$
(13)

After eliminating $ξ_{i}$ and ω by (12) with (13), the realization form of the LS-SVM can be given:
$[0 y T y Ω + C - 1 I] [b \bar{α}] = [0 1_{N}]$
(14)
where $y = [y_{1}, y_{2}, \dots, y_{n}] T$ , $1_{N} = [1, 1, \dots, 1] T$ , $\bar{α} = [α_{1}, α_{2}, \dots, α_{n}] T$ and I is the identity matrix, and
$Ω_{ij} = y_{i} y_{j} ϕ (x_{i}) T ϕ (x_{j}) = y_{i} y_{j} K (x_{i}, x_{j}), i, j = 1, 2, \dots, n$
(15)
where $K (x_{i}, x_{j})$ is the kernel function. The corresponding classification decision function is transformed into
$f (x) = sgn [\sum_{i = 1}^{n} α_{i} y_{i} K (x_{i} \cdot x) + b]$
(16)

There is no doubt that the efficient performance of the LS-SVM model depends on an optimal selection of the kernel function $K (x_{i} \cdot x)$ and penalty factor C. The most usual kernel functions include the linear function, polynomial function and RBF. This paper used the RBF function because it can better deal with the nonlinear relationship between the evaluation index and the evaluation level:
$K (x_{i}, x_{j}) = e - γ ‖ x_{i} - x_{j} ‖ 2$
(17)

The optimal selection of the parameters of penalty factor C and γ in kernel function is implemented by using the Genetic Algorithm (GA).

Principal Components Analysis

In this paper, we used the PCA method to refine the evaluation indexes. PCA is a mathematical procedure¹³ that converts a group of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components by using the orthogonal transformation.

The number of original variables is more than or equal to the number of principal components. The first principal accounts for as much of the variability in the data as possible (that is, it has the largest possible variance); in addition, each succeeding component in turn has the highest variance possible under the constraint that it be orthogonal to (i.e., uncorrelated with) the preceding components. If the data set is jointly normally distributed, principal components are guaranteed to be independent.

Genetic Algorithm

In this paper, we used the GA to search the optimal parameters of the SVM, which is a search heuristic that mimics the process of natural selection in the field of artificial intelligence. This heuristic is routinely used to generate useful solutions to optimization and search problems.

In a GA, a population of candidate solutions (called individuals) to an optimization problem is evolved toward better solutions. Each candidate solution has a set of properties (its chromosomes or genotype) that can be mutated and altered. The evolution usually starts from a population of randomly generated individuals, and is an iterative process, with the population in each iteration called a generation. In each generation, the fitness of every individual in the population is evaluated. The more fit individuals are stochastically selected from the current population, and each individual's genome is modified to form a new generation. The new generation of candidate solutions is then used in the next iteration of the algorithm.

Experimental details

In the experiments, the inspected materials were woven plain polyester fabrics, which were dyed with Disperse Red FB, Disperse Yellow M-4GL and Disperse Blue 2BLN. The dyed fabrics were then clipped to a size of 10 cm × 10 cm for evaluation modeling.

The experiments were performed in two steps. The first step was to determine the evaluation indexes. As described in the Color difference evaluation indexes and levels* section, six evaluation indexes were initially chosen as inputs of the evaluation model, but they are relevant. By using the PCA algorithm, these indexes were screened to fewer independent indexes, and consequently the training time of the evaluation model was reduced. Eleven sample images were acquired under the same light condition for screening. Table 3 shows color difference values of the original six evaluation indexes between the 11 samples and the standard sample, which is assigned randomly. Four new independent evaluation indexes, $F_{i} (i = 1, 2, 3, 4)$ , where $F_{i} = a_{i 1} Δ L * + a_{i 2} Δ a * + a_{i 3} Δ b * + a_{i 4} Δ H + a_{i 5} Δ S + a_{i 6} Δ V$ , which are the normalized feature vectors corresponding to the first four larger eigenvalues of the original variable covariance matrix, were deduced by using the PCA to analyze the attributes of those original indexes. The reduced four new evaluation indexes are shown in Table 4 for the same image set.
Table 3.
Original evaluation indexes of 11 dyed fabric samples

Serial number $Δ L $ $Δ a $ $Δ b $ $Δ H$ $Δ S$ $Δ V$

1 1.8604 1.6988 0.4808 0.0446 0.0138 0.0193

2 4.928 2.6343 4.3533 0.014 0.1122 0.0402

3 2.5417 1.1126 2.9942 0.0025 0.045 0.0301

4 1.7418 4.1576 3.6772 0.0163 0.0576 0.0232

5 1.89 1.4155 3.278 0.0034 0.0268 0.0183

6 1.3771 1.585 0.6995 0.1664 0.0162 0.0243

7 4.8841 4.1878 2.8448 0.0048 0.1094 0.0585

8 1.6286 1.9069 2.8156 0.0032 0.0446 0.0234

9 1.2704 2.936 0.5823 0.0017 0.0293 0.0193

10 4.1321 3.836 2.3166 0.0189 0.0476 0.0618

11 3.0263 0.6928 11.092 0.0016 0.094 0.0375

Table 4.
Four new evaluation indexes through Principal Component Analysis

Serial number $F_{1}$ $F_{2}$ $F_{3}$ $F_{4}$

1 0.0138 1.7587 0.4808 0.0446

2 0.1122 1.0702 4.3533 0.014

3 0.045 0.0301 2.9942 0.0025

4 0.0576 0.0232 3.6772 0.0163

5 0.0268 0.0183 3.278 0.0034

6 0.0162 0.0243 0.6995 0.1664

7 0.1094 0.0585 2.8448 0.0048

8 0.0446 0.0234 2.8156 0.0032

9 0.0293 0.0193 0.5823 0.0017

10 0.0476 0.0618 2.3166 0.0193

11 0.0138 0.0375 11.092 0.0402

The next step was to develop the color difference evaluation model using the new four independent evaluation indexes. Here, nine images of dyed fabrics were acquired under three kinds of light sources D65, A and D50 using a charge-couple device (CCD) camera, and thus in total 27 images were obtained. The images under D50 are shown in the appendices.

Results and discussion

Results of evaluation model based on the standard SVM

The parameters of penalty factors C and γ in the kernel function of the standard SVM model are optimally determined with the GA method. The population size, the maximum iterating times, the crossover and the mutation probability for the GA are 20, 100, 0.4 and 0.01 respectively. After optimization of parameters, a 10-fold cross-validation is executed 10 times, that is, the color difference set of dyed fabrics is divided into 10 sub-parts, with nine parts training data and one part testing data in turn. The average of 10 validations is used as the accuracy estimation of SVM parameters.

Modeling of color consistency

In order to construct more experimental data for training the evaluation model, an image was chosen randomly from 27 images as a standard sample and others were compared with it for calculating the evaluation indexes according to the color consistency algorithm described in the Evaluation algorithm* section, and then in total $C_{27 * 4}^{2}$ sets of data were obtained. One thousand sets of data were chosen as the training data, where the color difference levels were determined according to the expert's experience after being measured by a DataColor 650® color measurement instrument. Appendices I and II respectively show the 28 groups of training data evenly selected from a total of 1000 groups and 36 groups of test data selected randomly. Because the test data were randomly selected, some of the color difference levels are absent in Appendix II .

The training results with six and four evaluation indexes are shown in Tables 5 and 6, respectively. It can be concluded that if the model is trained with sample data that has six attributes in Appendix I, the training precision is lower and the parameter optimization time is longer, compared with those that have fewer attributes screened by PCA, because some attributes for the color difference evaluation model are redundant and secondary.
Table 5.
Training results with six evaluation indexes

Training data quantity Parameter c Parameter g Kernel functions Parameter optimization time Model training time Training accuracy

1000 groups 68.135 15.164 RBF 2239s 1s 69%

Table 6.
Training results with evaluation indexes screened by Principal Component Analysis

Training data Test data C γ Kernel functions Parameter optimization time Training accuracy Prediction accuracy

1000 groups 36 groups 30.095 4.8623 RBF 239.8 s 78.8% 77%

RBF: Radial Basis Function.

Modeling of color levelness

The same 27 images as in the Modeling of color consistency section were acquired under three kinds of light sources – D65, A, D50 – a total of 108 sets of data were used as the training data for modeling of color levelness. Thirty-six sets of data under light sources A and D50 were selected for testing. The modeling algorithm was described in Evaluation algorithm section and the modeling process is similar to that in the Modeling of color consistency section. Appendices III and IV respectively show 28 sets (evenly selected from a total of 1000 sets) of training data and 36 sets of testing data.

Experimental results of the color levelness evaluation model are shown in Tables 7 and 8.
Table 7.
Model training results of six indexes

Training data quantity C γ Kernel functions Parameter optimization time Model training time Training accuracy

108 groups 2.3841 716.16 RBF 61 s 1 s 62%

RBF: Radial Basis Function.

Table 8.
Model training and testing results of four indexes screened by Principal Component Analysis

Training data Test data C γ Kernel functions Parameter optimization time Training accuracy Prediction accuracy

108 groups 36 groups 10.474 45.256 RBF 40.69 s 66% 83.4%

RBF: Radial Basis Function.

Validation of the evaluation model developed by the standard SVM

Comparison between the SVM and Naive Bayesian algorithm

The performances of color consistency and levelness models based on the SVM were validated compared to the Naive Bayesian (NB) algorithm. The same data sets in the Results of evaluation model based on the standard SVM section were modeled using the Weka-3-6¹² Bayesian toolbox and the color difference levels were classified again. The prediction accuracy and relative error for the two data sets are listed in Table 9. It can be seen that the instability exists in the NB especially when different training sets with the same number are experimented on, where the larger the testing sample number is, the lower the classification accuracy is. The main reason is that the NB depends on the prior probability of the training samples. The performance of the SVM is obviously superior to the NB since it can keep a higher prediction accuracy without regard to the prior probability of dyeing samples.
Table 9.
Comparison between two methods

Algorithm Consistency data set
Levelness data set

Prediction accuracy Relative error Prediction accuracy Relative error

Naive Bayesian 62.0% 0.1052 76.0% 0.0928

SVM 71.0% 0.0065 78.8% 0.001

SVM: Support Vector Machine.

Table 10.
Prediction effect of evaluation model of the Least Squares Support Vector Machine

Training data Test data C γ Kernel function Parameter optimization time Model training time Training accuracy Prediction accuracy

1000 groups 36 groups $1 \times 45$ Vector $1 \times 45$ Vector RBF 8 s 1 s 97.9% 98.2%

RBF: Radial Basis Function.

Comparison between the SVM and LS-SVM

It can be seen from the former experiments that the performance of the SVM is not so good. In this section, the LS-SVM was used again to model the same data sets in Appendices I and II with the same parameter optimization algorithm as the standard SVM, where the initial penalty factor was set to be 10 and the kernel function parameter γ to be 2. The results are shown in Table10, where the accuracy of the LS-SVM is improved significantly.

Conclusions

The purpose of this paper is to propose the evaluation algorithm of color difference in the machine vision system for evaluating the dyed fabrics and developing the evaluation model based on the SVM. While comprehensively considering the characteristics of humans' color perception and the need for color consistency and levelness, six evaluation indexes were chosen from the HSV and CIELAB color space. In order to improve the speed of parameter optimization and model training, the PCA was employed to extract four independent evaluation indexes, which can compress the redundant and secondary information in the six evaluation indexes. The evaluation algorithms of color consistency and color levelness were proposed and the color difference levels were defined based on ISO 105-A02:1993. For evaluating the color difference accurately and automatically, the standard SVM and the LS-SVM algorithms were used to develop the model between the evaluation indexes and the color difference levels. Compared to the NB algorithm, the SVM model has better stability and can maintain higher prediction accuracy without considering the prior probability of the samples. Moreover, its performance can be highly improved by using the Least Squares algorithm. In conclusion, the SVM model has many prominent characteristics so that it can adapt to such conditions as different light sources or background noise in the machine vision inspection system, and maintain better accuracy. In future research, the evaluation index and the division of the evaluation region for the color difference of the dyeing product sample can be optimized further.

Color difference	Fastness level	Color difference	Fastness level
>11.85	1	2.16–3.05	3–4
8.41–11.85	1–2	1.27–2.15	4
5.96–8.40	2	0.20–1.26	4–5
4.21–5.95	2–3	<0.20	5
3.06–4.20	3

Evaluation level	Class 1	Class 2	Class 3	Class 4	Class 5
Levelness	Fastness level 1	Fastness level 2	Fastness level 3	Fastness level 4	Fastness level 5
Consistency	Fastness level 1 to 2	Fastness level 2 to 3	Fastness level 3 to 4	Fastness level 4 to 5	Fastness level 5

Serial number	$Δ L *$	$Δ a *$	$Δ b *$	$Δ H$	$Δ S$	$Δ V$
1	1.8604	1.6988	0.4808	0.0446	0.0138	0.0193
2	4.928	2.6343	4.3533	0.014	0.1122	0.0402
3	2.5417	1.1126	2.9942	0.0025	0.045	0.0301
4	1.7418	4.1576	3.6772	0.0163	0.0576	0.0232
5	1.89	1.4155	3.278	0.0034	0.0268	0.0183
6	1.3771	1.585	0.6995	0.1664	0.0162	0.0243
7	4.8841	4.1878	2.8448	0.0048	0.1094	0.0585
8	1.6286	1.9069	2.8156	0.0032	0.0446	0.0234
9	1.2704	2.936	0.5823	0.0017	0.0293	0.0193
10	4.1321	3.836	2.3166	0.0189	0.0476	0.0618
11	3.0263	0.6928	11.092	0.0016	0.094	0.0375

Serial number	$F_{1}$	$F_{2}$	$F_{3}$	$F_{4}$
1	0.0138	1.7587	0.4808	0.0446
2	0.1122	1.0702	4.3533	0.014
3	0.045	0.0301	2.9942	0.0025
4	0.0576	0.0232	3.6772	0.0163
5	0.0268	0.0183	3.278	0.0034
6	0.0162	0.0243	0.6995	0.1664
7	0.1094	0.0585	2.8448	0.0048
8	0.0446	0.0234	2.8156	0.0032
9	0.0293	0.0193	0.5823	0.0017
10	0.0476	0.0618	2.3166	0.0193
11	0.0138	0.0375	11.092	0.0402

Training data quantity	Parameter c	Parameter g	Kernel functions	Parameter optimization time	Model training time	Training accuracy
1000 groups	68.135	15.164	RBF	2239s	1s	69%

Training data	Test data	C	γ	Kernel functions	Parameter optimization time	Training accuracy	Prediction accuracy
1000 groups	36 groups	30.095	4.8623	RBF	239.8 s	78.8%	77%

Training data quantity	C	γ	Kernel functions	Parameter optimization time	Model training time	Training accuracy
108 groups	2.3841	716.16	RBF	61 s	1 s	62%

Training data	Test data	C	γ	Kernel functions	Parameter optimization time	Training accuracy	Prediction accuracy
108 groups	36 groups	10.474	45.256	RBF	40.69 s	66%	83.4%

Algorithm	Consistency data set	Levelness data set
Naive Bayesian	62.0%	0.1052	76.0%	0.0928
SVM	71.0%	0.0065	78.8%	0.001

Training data	Test data	C	γ	Kernel function	Parameter optimization time	Model training time	Training accuracy	Prediction accuracy
1000 groups	36 groups	$1 \times 45$ Vector	$1 \times 45$ Vector	RBF	8 s	1 s	97.9%	98.2%

Footnotes

Funding

This material is partially based upon work funded by National Natural Science Foundation of China under Grant No.61074154, and by the Program for Changjiang Scholars and Innovative Research Team in University (PCSIRT) under grant No.IRT13097.

References

Dong

Zheng

. Color measurement and computer color matching, 2nd ed. Beijing: China Textile, 2007, pp. 48.

Nobbs

Connolly

. Camera-based colour inspection. Sensor Rev 2000; 20: 14–20.

Yang

Sun

. The design of the shading variation measurement system based on machine vision. ME Thesis 2009. Huazhong University of Science and Technology, CHN.

Relevant introduce to the Qtex system, http://www.sedo-treepoint.com/ (2003, accessed 13 February 2014).

. A colour management system for textile based on HSV model and Bayesian classifier. In: 10th international conference on control, automation, robotics and vision, Hanoi, Vietnam, 17–20 December 2008, paper no. ISBN 978-1-4244-2286-9, pp. 1878–1883.

Kuo

CFJ

Jian

Tung

. Automatic machine embroidery image color analysis system, Part II: Application of the genetic algorithm in search of a repetitive pattern image. Textil Res J 2012; 82: 1099–1106.

Chen

. Color perception of the textile and clothing. J Dong Hua Univ (English Edition) 2004; 21: 166–170.

Xue

Yan

Zheng

. Classifications of EEG during mental task based on Support Vector Machine with optimal kernel-parameter. Biophys J 2003; 19: 322–326.

Kobus

Lindsay

Brian

. Colour by correlation in a three dimensional colour space (A). In: the 6th European conference on computer vision 2000, Dublin, Ireland, 26 June–1 July 2000, pp. 275–289.

10.

ISO105-A02. Textile-tests for colour fastness-Part A02: Grey scale for assessing change in colour.

11.

Clarke

FJJ

McDonald

Rigg

. Modification to the JPC79 colour-difference formula. J Soc Dyer Colourist 1984; 100: 128–132.

12.

Witten

Frank

. Data mining: Practical machine learning tools and technique, 2nd ed. Amsterdam: Elsevier Inc, 2005.

13.

Wikipedia, the free encyclopedia. http://en.wikipedia.org/wiki/Principal_component_analysis (2014, accessed 3 April 2014).

Algorithm	Consistency data set		Levelness data set
Algorithm	Prediction accuracy	Relative error	Prediction accuracy	Relative error
Naive Bayesian	62.0%	0.1052	76.0%	0.0928
SVM	71.0%	0.0065	78.8%	0.001