Objective evaluation of fabric smoothness appearance with an ordinal classification framework based on label noise estimation

Abstract

Objective fabric smoothness appearance evaluation plays an important role in the textile and apparel industry. In most previous studies, objective fabric smoothness appearance evaluation is defined as a general pattern classification problem. However, the labels in this problem exhibit a natural ordering. Nominal classification ignores the ordinal information, which may cause overfitting in model training. In addition, for the existence of subjective errors, measurement errors, manual errors, etc., the labels in the data might be noisy, which has been rarely discussed previously. This paper proposes an ordinal classification framework based on label noise estimation (OCF-LNE) to objectively evaluate the fabric smoothness appearance degree, which takes the ordinal information and noise of the label in the training data into consideration. The OCF-LNE uses the basic classifier in pre-training as a label noise estimator, and uses the estimated label noise to adjust the labels in further training. The adjusted labels can introduce the ordinal constrain implicitly and reduce the negative impact of label noise in model training. Within a 10 × 10 nested cross-validation, the proposed OCF-LNE achieves 82.86%, 94.29%, and 100% average accuracies under errors of 0, 0.5, and 1 degree, respectively. Experiments on different fabric image features and basic classification models verify the effectiveness of the OCF-LNE. In addition, the proposed method outperforms the state-of-the-art methods for fabric smoothness evaluation and ordinal classification. Promisingly, the OCF-LNE can provide novel ideas for image-based fabric smoothness evaluation.

Keywords

fabric smoothness textile testing ordinal classification noise estimation

Fabric smoothness after laundering is treated as a vital characteristic of the fabric to evaluate the tendency for the fabric to wrinkle, which quantizes the wrinkles on the fabric after being subjected to laundering procedures and has a bearing on ‘ease-of-care’ related properties (durable press, easy-care, minimum-iron, after-wash appearance, etc.) in the textile and garment industry.¹ Conventionally, the smoothness of the fabric samples after standard laundering is assessed manually in accordance with smoothness appearance replicas in six smoothness degrees (SA-1, SA-2, SA-3, SA-3.5, SA-4, SA-5, as given in Figure 1) referring to the industry standards.^2,3 However, human vision is affected by individual physical, psychological, and environmental factors, showing low precision and poor reproducibility.⁴ In addition, with a heavy reliance on human testers, to ensure the stability of evaluation result, the traditional method needs more than three testers to evaluate every single sample. This is quite time-consuming and labor-intensive. To avoid such adverse issues, objective evaluating methods have been proposed by researchers in recent years. Previous researches regarding fabric smoothness evaluation have treated it as a typical classification problem, which generally includes three main steps: fabric surface data acquisition, appearance feature extraction, and smoothness degree classification.

Figure 1.

American Association of Textile Chemists and Colorists fabric smoothness appearance replicas in different degrees: (a) SA-1; (b) SA-2; (c) SA-3; (d) SA-3.5; (e) SA-4; (f) SA-5.

According to the data forms, the existing methods can be divided into two types: the two-dimensional (2D) method and the three-dimensional (3D) method. The 2D methods take 2D digital images of the fabric samples as input data, which can be captured by scanners or industrial cameras.^5–12 Researchers propose to use various image features to characterize wrinkled fabric images, such as features based on image edges,^9,10 features of the gray-level co-occurrence matrix (GLCM),^7,8 features from the Fourier spectral space¹¹ and the wavelet spectral space,¹² and features from the visual masking model.¹³ The wrinkle information in 2D fabric images is presented in the form of uneven brightness distribution in the image, which appears as shadow regions in vision. This form of information is a direct measurement of the geometry of the fabric surface, and is easily affected by the image acquisition environment and camera parameters. Thus, 2D methods are kinds of indirection observation of the fabric surface. To access the direct observation of the fabric surface, researchers turns to the use of technologies such as laser triangulation,^14–18 the photometric stereo method,^19,20 and binocular stereo-vision^21–24 to obtain depth maps of fabric samples.

The 3D methods are, theoretically, much more accurate than their counterparts, that is, 2D methods, on the one hand; on the other hand, there are numerous devices and techniques for achieving the low-cost, user-friendly 3D evolution methods in the current stage. However, accuracy, cost, and efficiency still contradict each other. The depth change on the fabric surface can always be lower than 0.5 mm. In our early exploration, Kinect V2, as a representative of low-cost and high-efficiency 3D imaging equipment, could not accurately reconstruct the fabric surface. In addition, the binocular stereo-vision method has become the most widely used method due to its high accuracy and low cost. However, in our early exploration, it took more than 20 minutes to reconstruct the surface of a standard $380 mm \times 380 mm$ fabric sample by binocular stereo-vision, which is difficult to accept in real application. Moreover, the accuracy of binocular stereo-vision depends heavily on its complex calibration. In the opinion of this study, although the 2D methods can only gather an indirect observation of the fabric surface, they still can provide sufficient information for the fabric smoothness evaluation. Such opinion can be supported by the phenomenon that a trained tester can well assess the specimen with only 2D images observed by eyes. As a result, the 2D method is adopted to acquire fabric surface data.

In the aspect of classification models, the minimum distance algorithm,¹¹ fuzzy priority similarity comparison method,⁸ neural network,^7,15 and support vector machine (SVM),^12,25 are widely used. In addition, differing from the traditional machine learning algorithms, which depend heavily on the representation of the input image, the deep learning algorithms can extract the high-level abstract features from the input images by introducing representations that are expressed in terms of other simpler representations.²⁶ Such algorithms have been widely used in the image classification area. However, the performance of the deep learning algorithms depends heavily on the amount of training data, which do not satisfy the small sample problem well in this research. In the experiments of this research, the performances of a series of famous deep learning models are discussed.

In summary, the previous research in the field suffered the following two issues. Firstly, most researchers solve the problem by general pattern classification models. However, it is not entirely reasonable to characterize this problem as a typical classification problem. The fabric smoothness evaluation is a process of classifying fabric samples into a number of discrete degrees in order, while the typical classification models the process of classifying samples into independent categories. The target that needs to be predicted by the machine learning model is called the label, which is the smoothness degree of the fabric samples in this research. The classification problem definition loses the sequence information in the labels and may cause overfitting during the training process. Thus, the problem should be viewed as an ordinal classification problem, which lies between multi-class classification and metric regression. On the other hand, caused by the individual physical, psychological, and environmental factors of human testers, the smoothness labels of the fabric samples could be noisy. The noise can induce the model to learn the incorrect underlying mapping. For example, when an SA-3 fabric sample $x^{s}$ is mislabeled as SA-3.5 (as its label $y^{s} = 3.5$ ), a model $r^{s}$ trained on it would learn the inner mapping from the input sample $x^{s}$ to the label $y^{s}$ . It is obvious that for the existing label noise, the learned mapping would be mis-leaded, and thus $r^{s}$ would predict other SA-3 fabric samples with a wrong prediction of SA-3.5. If the labels of the mislabeled samples, such as $(x^{s}, y^{s})$ , are adjusted into the correct ones, the model training will be more effective. However, current researches lack the discussion of label errors.

In this paper, we proposed an ordinal classification model framework to solve the fabric smoothness evaluation problem. In the framework, the errors of sample labels were estimated and utilized to adjust the labels. Classification models were then trained on the sample sets with different label adjustment strategies. The deviation of the adjusted labels constrained the training process to consider the ordinal property implicitly. Finally, the outputs of the classification models were constructed into an ensemble to predict the labels of the testing samples.

Process chain overview

Our research proposed a computer vision system to evaluate the fabric smoothness appearance automatically. It can effectively take the place of labor-intensive manual evaluation methods. In addition, the accurate and stable objective evaluation of the sample smoothness degree can effectively guide production quality control. The digital system can save the fabric images and reproduce the previous tests, which helps the informative control of the industry. Although the fabric smoothness appearance test is usually an off-line test, as the automation of textile production and sample preparation equipment increases, our computer vision system can help online monitoring as the sensing end.

The main objective of this study is to evaluate the fabric smoothness appearance by a computer vision system. The main contribution of this paper is proposing an ordinal classification framework based on label noise estimation (OCF-LNE). A flow chart of the workflow of this study is given in Figure 2. The process steps of the fabric surface data acquisition, appearance feature extraction, and smoothness degree evaluation are shown in orange, green, and blue, respectively. Specifically, the OCF-LNE is trained by the steps in the blue dotted frame, and the trained OCF-LNE in testing outputs the specific smoothness appearance degree of the testing sample, that is, SA-1, SA-1.5, SA-2,…, SA-5.

Figure 2.

Workflow of the proposed fabric smoothness appearance evaluation system. DoG: difference-of-Gaussian; OCF-LNE: ordinal classification framework based on label noise estimation. (Color online only).

Theoretical basis

The workflow of the whole fabric smoothness appearance evaluation system of this study includes image acquisition and preprocessing, feature extraction, and ordinal classification. This section introduces the theoretical basis of the whole system.

Image acquisition and image preprocessing

An image acquisition device that can capture images of objects under different light source position angles was used in this study, whose system parameters were optimized in our previous study.²⁷ As shown in Figure 3, the device includes a light box with black flocking fabrics covered inside, an objective table at the bottom center, a charge-coupled device (CCD) camera (Point Grey Chameleon CMLN-13S2C) at the top center, and a light control module around the objective table to control the light source position angle (including a strip led light source, a step-motor, and a rotating arm). The image set of a fabric sample captured by this device is given in the first row of Figure 4.

Figure 3.

The fabric image acquisition system: (a) schematic diagram of the system structure; (b) photo of the system. CCD: charge-coupled device; LED: light-emitting diode.

Figure 4.

Image of a fabric sample with different light source position angles: (a) 0°, (b) 90°; and their preprocessing results: (c), (d).

To rectify the uneven illumination background in images caused by the one-sided light source, an image preprocessing operation is applied to the origin image I_o as follows

I = I_{o} / I_{f}

(1)

where I_f is the 2D binomial fitting of I_o. Based on such progress, the uneven illumination background can be rectified well. The preprocessing results are shown in the second row of Figure 4.

Feature extraction

The smoothness appearance of fabrics is a subjective concept, which is mainly concerned with human vision perception under a specific environment and quantified by the degree of the smoothness. However, most of the image features proposed in previous studies did not consider the mechanism of the human vision system (HVS).¹³ In this study, a multi-scale spatial masking feature (MS-SMF)¹³ is used to describe the fabric smoothness appearance, with the consideration of the relationship between the HVS perceptual characteristics and the fabric smoothness appearance in images.

Difference-of-Gaussian scale space decomposition

In the subjective grading for fabric smoothness appearance, it was found that the testers tend to acquire information from more perceptual scales by changing the observation distance or refocusing their eyes. This phenomenon is caused by the accommodation function of the HVS, and shows the significance of the information in different scales for humans to evaluate the smoothness. In the MS-SMF, the image is decomposed into the difference-of-Gaussian (DoG) scale space to model the multi-scale perception ability of the human testers.

Figure 5 shows the process of DoG scale space construction. For an image I, the Gaussian scale space can be generated from a series of low-pass filtering and down-sampling, and expressed as a sequence of images $D = {I_{0}, I_{1}, \dots, I_{N_{g}}}$ formulated as follows^28,29

I_{n} = G_{q^{n} σ} * I_{n - 1}, n = 1, 2, \dots, N_{g}, I_{0} = I

(2)

where

G_{q^{n} σ}

is a Gaussian kernel with the scale

q^{n} σ

(variation of Gaussian); σ is a constant basic scale factor;

*

is the convolution operator; q is a constant multiplicative factor that determines the interval of decomposition; N_g is the scale parameter that determines the number of images in the decomposition result. The DoG scale space can be expressed as a sequence of images

D^{-} = {I_{1}^{-}, I_{2}^{-}, \dots, I_{N_{g} - 1}^{-}}

calculated from the difference between every two consecutive images in the Gaussian scale space as follows³⁰

I_{n}^{-} = I_{n} - I_{n + 1}, n = 0, 1, 2, \dots, N_{g} - 1

(3)

Figure 5.

Process of the difference-of-Gaussian pyramid construction.

In the experiment, the basic scale factor σ is selected as $\sqrt{2}$ , as it widely used in image processing. In addition, the scale length N_g is set as 35 based on experience while taking both the operation efficiency and decomposition accuracy into account. The raw image of the fabric in this study is $350 \times 350$ pixels, and the final scale $q^{n} σ$ (the variation of the last Gaussian kernel) should be no larger than 350. The multiplicative factor k is calculated as 1.2. Figure 7 gives a series of DoG images in different scales of SA-1 and SA-3 fabric smoothness appearance replicas. As can be seen, wrinkle information is distributed on different scales.

Spatial masking map calculation

In the HVS, the spatial masking effect is a very important phenomenon that describes the interactions between stimuli. Masking refers to the phenomenon that a visible stimulus (target stimulus) turns to undetectable due to the presence of another (masking stimulus).³¹ In fabric smoothness appearance perception, a more wrinkled fabric surface can causes a stronger spatial masking effect.¹³ As given in Figure 6, the same Gaussian noise (viewed as the target stimulus) is added to images of the standard fabric smoothness appearance replicas in the degrees of SA-1, SA-3, and SA-4. Observation shows that as the smoothness appearance level decreases, the noise becomes difficult to perceive. This reveals the relationship between fabric smoothness appearance and the spatial masking effect.

Figure 6.

Images of the surface appearance replicas with different smoothness degrees: SA-1(a), SA-3(c), SA-4(e); and their corresponding contaminated images (b), (d), (f).

Figure 7.

The difference-of-Gaussian (DoG) images in different scales of SA-1 and SA-3 fabric smoothness appearance replicas and their spatial masking maps.

In perceptual digital imaging studies, the spatial masking effect can be attributed to two aspects, that is, the image contrast and image pattern.³¹ This speculation comes from the phenomenon that the target stimulus is difficult to be perceived by human vision when superimposed by a masking stimulus with a larger contrast or a more complicated pattern. Thus, the spatial masking model can be built with two main components, that is, the contrast masking model and pattern masking model.^32–35

In the MS-SMF extraction,¹³ once the DoG scale space $D^{-}$ is constructed, for every scale $n \in {0, 1, 2, \dots, N_{g}}$ , the spatial masking effect is estimated by a spatial masking model and expressed as a spatial masking map $M_{s}^{n}$ . The calculation steps of the spatial masking map from the nth scale space images I_n and $I_{n}^{-}$ includes the following steps: pattern complexity calculation; luminance contrast calculation; pattern masking map calculation; contrast masking map calculation; and spatial masking map calculation. As the spatial masking map calculation is the same in every scale, the sequential variable n is omitted in the following detailed description.

Pattern complexity calculation

In the MS-SMF model,¹³ pattern complexity of the image is one of the main factors in the pattern masking effect. To model the pattern masking effect, the image pattern complexity needs to be estimated first. The pattern complexity of a pixel $x^{p} \in X^{p}$ is described as the gradient direction irregularity in the local region $R (x^{p})$ centered on $x^{p}$ . For a scale n, with the scale images I_n, $I_{n + 1}$ , and $I_{n}^{-}$ , the orientation θ (the subscript n is omitted) for each pixel $x^{p} \in X^{p}$ can be formulated as follows

θ (x^{p}) = \frac{1}{2} (\arctan \frac{G_{v}^{0} (x^{p})}{G_{h}^{0} (x^{p})} + \arctan \frac{G_{v}^{1} (x^{p})}{G_{h}^{1} (x^{p})}) x^{p} \in X^{p}

(4)

where

G_{v}^{0} (x^{p})

and

G_{h}^{0} (x^{p})

are the vertical horizontal gradient of the image I_n at pixel

x^{p}

;

x^{p}

is the coordinate space of I_n; and

G_{v}^{1} (x^{p})

and

G_{h}^{1} (x^{p})

are the vertical and horizontal gradients, respectively, of the image calculated from

I_{n + 1}

. Then the histogram

H (t | x^{p})

of θ in every local region

R (x^{p})

centered on

x^{p}

with the interval T can be calculated as

H (t | x^{p}) = \sum_{r \in R (x^{p})} δ (θ (r), t) t = 1, 2, 3, \dots, 360^{\circ} / T

(5)

where

x^{p} \in X^{p}

is the image coordinate;

r \in R (x^{p})

is the pixel coordinate in local region

R

centered on

x^{p}

;

\underline{δ} (\cdot)

is a pulse function, for which

δ (θ (r), t) = {\begin{matrix} 1 θ (r) / T \in [(t - 1), t) \\ 0 elsewhere \end{matrix}

(6)

where

t = 1, 2, 3, \dots, 360^{\circ} / T

is the index in the histogram; T is the histogram interval, which is selected as

12^{\circ}

. The value is determined by the subjective masking experiments,³⁴ which indicates that when the orientation difference between two oriented gratings is smaller than

12^{\circ}

, the human observers show a very low recognition ability. The pattern complexity C_p for a local region

R (x^{p})

is calculated as the sparsity of its corresponding histogram as follows

C_{p} (x^{p}) = \sum ‖ H (t | x^{p}) ‖_{0}

(7)

where

‖ \cdot ‖_{0}

denotes the L₀ norm computing on t for every pixel

x^{p}

, which counts the number of non-zero elements in H. Thus, C_p describes the irregularity (complexity) of the orientation θ in every local region R.

Luminance contract calculation

In the MS-SMF model,¹³ the pattern masking effect and contrast masking effect are modeled with the luminance contrast of the image. The luminance contrast C_l is calculated as follows³⁴

C_{l} (x^{p}) = | I_{n}^{-} |

(8)

In this equation, the local contrast of an image is calculated as the magnitude of the DoG image $I_{n}^{-}$ , which is generally used as a close approximation to the scale-normalized Laplacian of Gaussian (LoG).²⁹ It describes the local gradient of a Gaussian image.

Pattern masking effect calculation

As an important component in the spatial masking effect, the pattern masking effect is firstly computed. Based on the subjective experiment about the visual gain control and pattern masking, the pattern masking effect M_p is modeled as^34,36

M_{p} = f_{l} (C_{l}) \cdot f_{p} (C_{p}) = log_{2} (1 + C_{l}) \cdot \frac{a_{1} C_{p}^{a_{2}}}{C_{p}^{2} + a_{3}^{2}}

(9)

where a₁ is a constant of proportion indicating the output gain of the visual stimuli in the HVS; a₂ is an exponential parameter representing the excitatory component of human visual neurons; and a₃ is a small constant to avoid the zero denominator, which helps describe the strength of the pattern masking effect when the pattern complexity is zero. In the subjective test,^34,36 pattern masking strengths (expressed as the contrast gain of human testers) caused by different visual input patterns are recorded. The parameters in the model are then obtained by the fitting method as

a_{1} = 0.8

a_{2} = 2.7

, and

a_{3} = 0.1

Contract masking effect calculation

As another important component in the spatial masking effect, the contrast masking effect M_c in the MS-SMF is modeled. In perceptual studies, the spatial masking caused by the luminance contrast should be expressed by a nonlinear transducer for luminance contrast^37,38

M_{c} = 0.115 \cdot \frac{α \cdot C_{l}^{2.4}}{C_{l}^{2} + β^{2}}

(10)

where α is a constant of proportion and β represents the positively accelerating and compressive regions of the nonlinearity. In subjective experiments, the luminance masking effect strength is evaluated by the just noticeable difference (JND) in images perceived by human testers. By fitting the model with the JND in different luminance contrasts, the parameters are set as

α = 16

and

β = 26

Spatial masking effect formulation

The spatial masking model in the MS-SMF takes both the contrast masking and pattern masking into account. For the stronger one of the two types, the masking effect plays a dominant role in some in general, while the combination of contrast masking and pattern masking is calculated by a maximum function to express spatial the masking effect M_s

M_{s} (x^{p}) = max {M_{p} (x^{p}), M_{c} (x^{p})}

(11)

As the sequential variable $n \in {0, 1, 2, \dots, N_{g} - 1}$ is omitted in the above model expressions, M_s should have a sequence superscript n. Thus, $M_{s}^{n}$ is the spatial masking map for the fabric image in the nth scale. A series of DoG images in different scales of SA-1 and SA-3 fabric smoothness appearance replicas and their spatial masking map are given in Figure 7. It can be intuitively observed that the spatial masking intensity distribution of fabric images in different smoothness appearance levels has a significant difference.

Multi-scale spatial masking feature

As a result, the sequence ${M_{s}^{0}, M_{s}^{1}, \dots, M_{s}^{N_{g} - 1}}$ can describe the spatial masking effect in different scales. To characterize the fabric surface smoothness features, in this paper, the 60th, 70th, 80th, and 90th percentiles of the values in every masking effect map $M_{s}^{k}$ are calculated. Thus, the feature vector $F_{smk}$ can be expressed as follows

\begin{matrix} F_{smk} = [f_{p} (M_{s}^{0}, 60), f_{p} (M_{s}^{0}, 70), f_{p} (M_{s}^{0}, 80), f_{p} (M_{s}^{0}, 90), \\ = f_{p} (M_{s}^{1}, 60), f_{p} (M_{s}^{1}, 70), f_{p} (M_{s}^{1}, 80), f_{p} (M_{s}^{1}, 90), \\ = \dots, \\ = f_{p} (M_{s}^{N_{g} - 1}, 60), f_{p} (M_{s}^{N_{g} - 1}, 70), \\ f_{p} (M_{s}^{N_{g} - 1}, 80), f_{p} (M_{s}^{N_{g} - 1}, 90)]^{T} \end{matrix}

(12)

where

f_{p} (M, p)

is the percentile calculation function that returns the pth percentile of data set M. In the experiment in this study, the scale length N_g is set as 35 and the feature dimension is 140 for one fabric image.

Ordinal classification

Differing from most of the previous research on solving fabric smoothness evaluation by nominal classification, the problem is assigned as an ordinal classification problem in this paper. Ordinal classification, also named ordinal regression, is a type of problem that lies between multi-class classification and metric regression. The problem can be defined as predicting the label y of an input $x$ , where $x \in ℝ^{k}$ and $y \in {C_{1}, C_{2}, \dots, C_{L}}$ , where the labels are in order, that is, $C_{1} ≺ C_{2} ≺ \dots ≺ C_{L}$ , where ≺ is an order relation.

As the ordinal classification problem lies between multi-class classification and metric regression, it can be simply solved by nominal classification methods or standard regression methods. However, the nominal classification method ignores the ordering of the labels, thus requiring more training data. In addition, the main problem of standard regression is that the discrete labels may hinder the performance of the regression.³⁹

In the ordinal classification area, the approaches can be divided into two main categories, that is, approaches from the regression perspective or from the classification perspective. The approaches from the regression perspective map the inputs to a real line and predict the boundaries between ordinal categories to discretize it, for example, support vector ordinal regression with implicit constraints (SVORIM)⁴⁰ and the neural network based on proportional odd model (NNPOM).⁴¹ The approaches from the classification perspective are based on decomposing the ordinal target variable into several binary ones with ordinal information embedded, which are then solved by nominal classification models, for example support vector machines with ordered-partitions (SVMOP),⁴² the neural network with ordered-partitions (NNOP),⁴³ and the extreme learning machine with ordered-partitions (ELMOP).⁴⁴

For the existence of subjective errors, measurement errors, manual errors, etc., in fabric appearance smoothness evaluation, the labels in the data might be noisy. The noise can induce the model to learn the incorrect underlying mapping. However, few studies have explored such an issue in ordinal classification. In this paper, from the classification perspective, we propose a method to estimate the label noise, and then use it to build an ordinal classification framework.

Ordinal classification framework based on label noise estimation

As introduced above, the ordinal classification problem aims to find a ranker r to predict the ranked label $y \in Y = {C_{1}, C_{2}, \dots, C_{L}}$ of the input sample $x \in X \subseteq ℝ^{k}$ , that is, $r : X \to Y$ . With a cost-sensitive setting,⁴⁵ a cost vector $c \in ℝ^{L}$ can be defined by $(x, y)$ from a distribution $P (x, y, c)$ on $X \times Y \times ℝ^{L}$ . The lth element $c [l]$ of the vector is the penalty when predicting the input x as label C_k, which reaches the minimum when l is equal to y. For a training set $S = {(x_{i}, y_{i}, c_{i})}_{i = 1}^{N}$ , whose elements are independent and identically distributed in $P (x, y, c)$ , the objective of the problem can be formulated as finding the ranker r minimizing the expected test cost as follows

min E (r) =_{(x, y, c) \sim P} (c [r (x)])

(13)

For nominal classification models, the value of cost vector $c [l]$ is 0 when $l = y$ and 1 when $l \neq y$ . In the ordinal classification problem, the ordinal information in the ranked label suggests the mislabeling cost change depending on the closeness of the prediction. For example, predicting a SA-3 fabric sample as SA-3.5 is less costly than predicting it as SA-5. Thus, the cost vector $c$ should be V-shaped, that is⁴⁵

\begin{matrix} \begin{matrix} c [l - 1] \geq c [l] 2 \leq l < y \\ c [l] = 0 l = y \\ c [l + 1] \geq c [l] y < l \leq C_{L} - 1 \end{matrix} \end{matrix}

(14)

Most studies define the cost vector $c$ from the classification or regression prospective. However, the studies rarely consider the error in label y.

As the labels of the samples in fabric smoothness appearance evaluation are evaluated by human testers, there must be noises in the labels caused by individual physical, psychological, and environmental factors. This kind of issue also occurs in other ordinal classification tasks. Denote ${\tilde{y}}_{i} = y_{i} + Δ y_{i}$ as the observed label, and the training set labels are contaminated by a specific noise $Δ y$ , that is, $S = {(x_{i}, y_{i} + Δ y_{i}, c_{i})}_{i = 1}^{N}$ , and the aforementioned model performance would deteriorate. For the ordinal attributes of the task, human testers are more likely to rate the sample at a level near the ground truth value y_i. As a result, we can reasonably assume that $\cdot y$ is distributed around zero. Under these conditions, the cost vector $c$ constrained in Equation (14) appears overly confident on the label to set $c [y]$ as zero.

Assuming we can get $m - 1$ different estimations of the label error $Δ y_{i}$ for each sample, that is, $\cdot {\hat{y}}_{i, j}, j = 1, 2, \dots, m - 1$ , the training set can be modified as $S = {(x_{i}, {\tilde{y}}_{i}, {\hat{y}}_{i, j} |_{j = 1}^{m - 1}, c_{i})}_{i = 1}^{N}$ , where ${\hat{y}}_{i, j} = {\tilde{y}}_{i} - Δ {\hat{y}}_{i, j}$ is the adjusted label from the error estimation. Taking ${\tilde{y}}_{i}$ as an adjusted label with zero error estimation, the training set can be simplified to $S = {(x_{i}, {\hat{y}}_{i, j} |_{j = 1}^{m}, c_{i})}_{i = 1}^{N}$ . The $Δ \hat{y}$ can be overestimated or underestimated, and ${\tilde{y}}_{i}$ and ${\hat{y}}_{i}$ distribute around y_i. Thus, the problem can be redefined as finding the ranker r minimizing the expected test cost on every estimated label, which can be formulated as follows

min E (r) = \frac{1}{m} \sum_{j = 1}^{m}_{(x, {\hat{y}}_{j}, c) \sim P_{j}} (c [r (x)])

(15)

where

P_{j} (x, {\hat{y}}_{j}, c)

is the distribution on

X \times Y \times ℝ^{L}

for the jth label-adjusted samples

(x, {\hat{y}}_{j}, c)

. In this model, the adjusted labels can soften the strict constraint in Equation (14) to satisfy the label noise and guide the training process with ordinal information. The redefined model can be solved by a greedy strategy as in the following steps.

Step 1: optimize each term in the accumulation function as in Equation (15) individually to find m different rankers r_j

min E (r_{j}) =_{(x, {\hat{y}}_{j}, c) \sim P_{j}} (c [r_{j} (x)]) j = 1, 2, \dots, m

(16)

Step 2: construct an ensemble of the rankers to be the final ranker $r^{e}$ . In the experiment of this paper, a voting ensemble strategy was applied.

The construction of the proposed OCF-LNE has been introduced above. The process workflow is illustrated in Figure 8. As given in the illustration, in the noise estimation process, cross-validation of the basic model r on the input training set is applied, and the validation prediction of all samples in the cross-validation are used as the estimated label $r (x)$ . Then, different label adjustment strategies are applied to generate a new extended training set $S = {(x_{i}, {\hat{y}}_{i, j} |_{j = 1}^{m}, c_{i})}_{i = 1}^{N}$ , and a set of new basic models ${(r_{j})}_{j = 1}^{m}$ are trained on it. Finally, the ranker $r^{e}$ is constructed by the voting ensemble of the basic models. The noise estimation, label adjustment, and the basic model used in this paper are introduced in the follow sections.

Figure 8.

The work flow of the proposed ordinal classification framework based on label noise estimation (OCF-LNE).

The proposed OCF-LNE uses the noise estimation to generate a series of label-adjusted data sets $S = {(x_{i}, {\hat{y}}_{i, j} |_{j = 1}^{m}, c_{i})}_{i = 1}^{N}$ A number of classification models ${(r_{j})}_{j = 1}^{m}$ are trained on the data sets. As the label information was adjusted differently in $S$ , every model r_j learns different knowledge of the fabric smoothness evaluation. Firstly, from the aspect of ensemble learning theory, by combining multiple classifiers, the ensemble can often obtain significantly superior generalization performance than a single learner. In addition, from a macro point of view, the OCF-LNE can learn more purified information from the data set, as the label adjustment process can reduce the label error in the data set.

Label noise estimation and label adjustment

In this section, we propose an error estimation algorithm for an ordinal classification training set $S = {(x_{i}, {\tilde{y}}_{i} = y_{i} + Δ y_{i}, c_{i})}_{i = 1}^{N}$ with label noise $Δ y$ . The rating progress of the samples in the sample collection is generally operated by human testers. For the ordinal information of the problem, testers are more likely to rate the sample $x$ as the class near the ground truth y. Taking fabric smoothness evaluation as an example, an SA-3 fabric sample is more likely to be rated as SA-3.5 rather than SA-4, although there must be a specific error existing. Thus, we can assume that the distribution of error is around zero and decreases as the distance from zero increases.

When the label noise is small, the trained classification model r can be viewed as a ground truth estimator. In addition, the estimated output can be used to estimate the noise in the testing set as follows

Δ y^{. . .} = r (x) - y

(17)

Then the estimated noise can be used to adjust the label and construct the new training set. In this paper, we propose four label adjustment strategies as follows.

Strategy 1: adjust the samples’ label whose estimated error $Δ y^{. . .}$ is greater than 0.5 degrees by 0.5 degrees in the error direction, formulated as follows

\begin{matrix} {\hat{y}}_{i, 1} = \begin{matrix} {\tilde{y}}_{i} + 0.5 & {y^{. . .}}_{i} > 0.5 \\ {\tilde{y}}_{i} - 0.5 & {y^{. . .}}_{i} < - 0.5 \\ {\tilde{y}}_{i} & elsewhere \end{matrix} \end{matrix}

(18)

Strategy 2: adjust the samples’ label whose estimated error $Δ y^{. . .}$ is greater than 0 degrees by 0.5 degrees in the error direction, formulated as follows

\begin{matrix} {\hat{y}}_{i, 2} = \begin{matrix} {\tilde{y}}_{i} + 0.5 & {y^{. . .}}_{i} > 0 \\ {\tilde{y}}_{i} - 0.5 & {y^{. . .}}_{i} < 0 \\ {\tilde{y}}_{i} & elsewhere \end{matrix} \end{matrix}

(19)

Strategy 3: eliminate the samples with estimated error $Δ y^{. . .}$ greater than 0.5 degrees

\begin{matrix} {\hat{y}}_{i, 3} = \begin{matrix} none & | {y^{. . .}}_{i} | > 0.5 \\ {\tilde{y}}_{i} & elsewhere \end{matrix} \end{matrix}

(20)

Strategy 4: eliminate the samples with estimated error $Δ y^{. . .}$ greater than 0 degrees

\begin{matrix} {\hat{y}}_{i, 4} = \begin{matrix} none & | {y^{. . .}}_{i} | > 0 \\ {\tilde{y}}_{i} & elsewhere \end{matrix} \end{matrix}

(21)

Thus, the modified training set can be generated by including the original label as ${\hat{y}}_{i, 5} = {\tilde{y}}_{i}$ , that is, $S = {(x_{i}, {\hat{y}}_{i, j} |_{j = 1}^{m}, c_{i})}_{i = 1}^{N}$ . Such an adjusted training set can be then used in the ordinal classification framework proposed previously.

Basic classification model

In this paper, the SVM model is used as the basic classification model in the framework. For a training set of instance-label pairs $(x_{i}, y_{i}), i = 1, 2, \dots, N$ where $x_{i} \in R^{m}$ and $y_{i} \in {1, - 1}^{N}$ , the SVM maps input features $x$ to high-dimensional space with the kernel function, with the goal of maximizing the interval between classes. Then the optimized interval can be used to divide the samples into different categories. The objective function of the SVM model is defined as follows⁴⁶

\begin{matrix} {min}_{w, b, ξ} \frac{1}{2} w^{T} w + C \sum_{i = 1}^{N} ξ_{i} \\ subject to y_{i} (w^{T} φ (x_{i}) + b) \geq 1 - ξ_{i} \\ ξ_{i} \geq 0 . \end{matrix}

(22)

where training vectors

x_{i}

are mapped into a higher dimensional space by the function

φ (\cdot)

;

w

is the weight of every feature element in the linear model; b is the constant term in the linear model;

C > 0

is the penalty parameter of the error term

ξ_{i}

;

K (x_{i}, x_{j}) \equiv φ (x_{i})^{T} φ (x_{j})

is the kernel function. In this paper, the radial basis function is used as the kernel function, which is formulated as follows

K (x_{i}, x_{j}) = exp (- γ | x_{i} - x_{j} |^{2}), γ > 0

(23)

where γ is the kernel parameter. Once the model (22) is trained on the training data set,

w

and b are optimized. The classification

y^{test}

of an input testing data

x^{test}

can be given by the decision function

\begin{matrix} \begin{matrix} y^{test} = \begin{matrix} 1 & w^{T} φ (x) + b \geq 1 \\ - 1 & w^{T} φ (x) + b \leq - 1 \end{matrix} \end{matrix} \end{matrix}

where the prediction

y^{test}

may take two values, 1 and −1, respectively corresponding to the two different prediction categories. Then the model can be generalized into a multi-class problem by the OneVsAll decomposition strategy. The performance of the framework with other different basic classification models is discussed in our experiment.

Experimental details

Experiment setup

Except for the image acquisition system we proposed previously, all the experiments in this study were conducted on a personal computer with Intel(R) Core(TM) I7-4790 CPU(3.6 GHz) 16GB RAM and GPU of Nvidia(R) GTX 1080Ti. All the algorithms were implemented by MATLAB under the Windows 10 and Linux operating systems. The SVM was implemented by the LIBSVM.⁴⁶ The deep learning algorithms were implemented by the PyTorch.⁴⁷

Materials

To evaluate the performance of the proposed fabric smoothness evaluation system, four different fabrics in different weave structures and fiber compositions were selected from a textile enterprise and cut into the size of 380 mm × 380 mm according to the AATCC standard,² in total 385 samples. The fabrics were pretreated and undyed, without any size or finishing. The resized samples were then laundered in different modes to generate diverse fabric smoothness appearances and were graded by the experts. For the laundering process, the details are set as follows: 2003 AATCC Standard Reference Liquid Detergent; 25° rinse temperature; one to three washing cycles in three different modes; 70° drying temperature; 500–1200 hydroextractor rpm. The differentiated washing mode produces different smoothness degrees of the samples. Finally, images of the samples were captured by the image acquisition system. According to our previous research,¹³ we captured images of every fabric sample under two orthogonal light source position angles, which contain most of the fabric smoothness information.

Detailed information of the final fabric data set is given in Table 1. The samples have different weaves, fiber contents, yarn counts, and weave densities. Actually, in our experiment, the characteristics of white fabrics reveal quite a negligible effect in the fabric images. The reason could be that the image resolution is relatively too low to be sensitive enough to the visual effects caused by fabric characteristic change except for the color patterns. In our experiment, the pixel size of the image is $350 \times 350$ , while the fabric sample physical size is 380 mm × 380 mm (15 in. × 15 in.). Thus, the resolution in pixels per inch (ppi) of the image is 23.33. As given in Table 1, the lowest weave density of the fabric used in the experiment is 58 (thd/inch). It can be found that the pattern caused by the yarn has a much higher frequency than the pixel sampling frequency, which is difficult to see in the image (as shown in Figure 9). Although the ppi of our system is relatively low, it is enough to preserve the wrinkle information on the fabric surface.

Figure 9.

Fabric images for each fabric sample listed in Table 1: (a) fabric 1 in SA-1; (b) fabric 2 in SA-3; (c) fabric 3 in SA-1.5; (d) fabric 4 in SA-4.

Table 1.

Fabric sample information and the sample number in different smoothness appearances

Fabric						Number of samples in each smoothness degree (pieces)
Number	Weave	Fiber content	Yarn count	Weave density (thds/inch)	Square weight (g/m²)	SA-1	SA-1.5	SA-2	SA-2.5	SA-3	SA-3.5	SA-4	SA-5
1	Plain	100% C	40S × 40S	117 × 79	125.4	25	13	15	15	7	7	10	6
2	Plain	65% T 35% C	32S × 32S	75 × 60	118.7	2	1	3	4	7	25	25	29
3	Twill	100% C	50S × 50S	139 × 90	130.0	18	12	13	15	9	11	12	4
4	Twill	65% T 35% C	32S × 32S	77 × 58	111.9	3	2	1	4	6	24	23	34

C: cotton; T: terephthalate-polyester.

Training and testing process

In the experiments, we applied 10 × 10 nested cross-validation⁴⁸ to evaluate the classification performance. In such a process, the original data set is uniformly divided into 10 subsets as the outer loop, each of which is treated as the testing set in turn, with the others being treated as the training set. For every outer loop, the training set is also divided into 10 subsets as the inner loop. In the inner loop, every fold is treated as the validation set, while the others are treated as the inner training set in turn. The inner loop tunes the model parameters while the outer loop trains the model with the optimal parameters. The final result was computed by the average result across the folds in the outer loop. The process of nested cross-validation is illustrated in Figure 10. Differing from the nominal cross-validation, the nested cross-validation optimizes the parameters of the validated algorithm in the inner loop, and all the samples in the data set are tested within the outer loop. Although the outer loop significantly increases the operation cost, for a data set without a large number of testing samples, the nested cross-validation can have more samples to be tested. It has a better ability to validate the generalization of the algorithm. In addition, as illustrated in Figure 8, the proposed OCF-LNE training has its own inner cross-validation loop, which makes it naturally adaptable to the nested cross-validation.

Figure 10.

Illustration of the nested cross-validation process and the specific operations of the proposed ordinal classification framework based on label noise estimation (in red; color online only).

Specifically, for the proposed OCF-LNE, the inner loop performs the label noise estimation and implements the label adjustment strategies for every sample in the validation set in turn. The outer loop trains the models with adjusted labels. The specific operation of the proposed OCF-LNE is illustrated in Figure 10 in red. Since the sample set size (number of samples in the sample data set) is 385, in 10 × 10 nested cross-validation, the number of training samples is 346 and the number of testing samples is 39 on average in the outer loops. In addition, the number of training samples is 311 and the number of validation samples is 35 on average in the outer loops.

Evaluation metrics

As an ordinal classification problem, the fabric smoothness evaluation problem values the results depending on the grade error. Thus, to evaluate the performance of the methods, accuracies named acc0, acc0.5, and acc1 are calculated as the classification accuracies under errors of 0, 0.5, and 1 degree, respectively.

Results and discussion

Comparison results

The objective evaluation results of the proposed method on the acquired data set by 10 × 10 nested cross-validation are given in Table 2. The testing results in the same condition of a series of fabric smoothness evaluation methods proposed in existing studies are included. In Table 2, edge features +k-NN¹⁰ used the image edge-based feature calculated as the number of statistical indicators of grayscale changes around the edges, and used the k-nearest neighbor (k-NN) classification model. GLCM Features+BPNN⁷ and GLCM Features+SVM⁸ used GLCM feature constructed by the texture consistency, texture contrast, texture entropy, and texture gray occurrence of the GLCM. They used the back-propagation neural network (BPNN) and SVM as classification models. In addition, Wavelet+SVM¹² and Fourier+SVM¹¹ used the feature extracted by the response energy in different frequency ranges in the wavelet decomposition space and Fourier frequency space, respectively. In addition, the performance of a group of famous deep learning models, that is, convolutional neural network (CNN)-based models, were compared, including AlexNet,⁴⁹ GoogLeNet: Inception V3,⁵⁰ ResNet,⁵¹ VGGNet,⁵² DenseNet,⁵³ InceptionResNet V2,⁵⁴ Xception,⁵⁵ and ResNext 101.⁵⁶ As the results of each training of the CNN models have a certain randomness, the CNN models were trained and tested three times and the results were recorded as the mean and standard deviation of the accuracies. As the training of CNN models is quite time-consuming, the typical 10-fold cross-validation was applied instead of nested cross-validation. By the implementation of the typical 10-fold cross-validation, the performance of the CNNs is expected to be better than that of the nested cross-validation.

Table 2.

The comparison results of different methods

Method	acc0 (%)	acc0.5 (%)	acc1 (%)	Execution time (s/per sample)
Edge features + k-NN¹⁰	68.83	92.21	99.74	0.1178
GLCM Features + BPNN⁷	71.69	90.13	99.74	0.0121
GLCM Features + SVM⁸	73.25	92.73	100	0.0136
Wavelet + SVM¹²	73.51	91.95	100	0.0243
Fourier + SVM¹¹	76.10	92.99	100	0.0269
Visual masking + SVM¹³	80.78	93.77	100	1.0916
AlexNet⁴⁹	76.27 ± 1.30	91.11 ± 0.76	99.74	0.0459
Inception V3⁵⁰	80.00 ± 1.64	90.93 ± 1.78	99.56	0.3569
ResNet 18⁵¹	79.56 ± 2.31	92.89 ± 1.98	100	0.1180
VGGNet⁵²	77.78 ± 1.98	92.36 ± 2.41	100	0.7738
DenseNet⁵³	68.19 ± 0.07	87.72 ± 0.31	98.94	0.9642
InceptionResNet V2⁵⁴	64.38 ± 0.28	85.33 ± 0.79	98.30	1.3521
Xception⁵⁵	66.98 ± 0.36	87.52 ± 0.48	97.60	0.6458
ResNext 101⁵⁶	72.56 ± 0.23	91.04 ± 0.42	99.57	1.1722
Visual masking + OCF-LNE	82.86	94.29	100	1.0746

k-NN: k-nearest neighbor; GLCM: gray-level co-occurrence matrix; BPNN: back-propagation neural network; SVM: support vector machine; OCF-LNE: ordinal classification framework based on label noise estimation.

As shown in Table 2, the proposed method shows an 82.86% acc0, which is the best compared with the other methods and demonstrates the good performance of the proposed method on fabric smoothness evaluation. On the other hand, the acc0.5 of the proposed method also takes the best place in the comparison experiment, and the near 95% value is acceptable in practical use. In the aspect of execution time, as fabric smoothness evaluation is not a strong time-dependent issue, the testing time of around 1 second of the proposed method is acceptable.

Discussion on different fabric image features

In order to evaluate the image feature adaption of the proposed OCF-LNE, we tested the framework with the SVM as a basic classifier on different image features extracted from the same fabric image set. The results of the framework were compared with the nominal multi-class SVM model (basic classifier), as shown in Table 3. In the table, every row describes a comparison of one feature set, and the better ones are in bold. For most of the feature sets, the proposed framework showed higher acc0. Although it reduces the acc0 on Fourier and wavelet features, the performance degradation is slight (around 0.4% in accuracy). More generally, the proposed framework improved the acc0.5 performance of the basic classifier for all the feature sets. Thus, the experiment verifies the general effectiveness of the ordinal framework.

Table 3.

The performance of the proposed ordinal classification framework based on label noise estimation (OCF-LNE) and the basic model on different feature sets

Feature sets	Basic model only			Within OCF-LNE
Feature sets	acc0 (%)	acc0.5 (%)	acc1 (%)	acc0 (%)	acc0.5 (%)	acc1 (%)
Edge-based¹⁰	72.73	92.99	100	73.77	93.51	100
Fourier¹¹	76.10	92.99	100	75.58	93.77	100
Wavelet¹²	73.51	91.95	100	73.25	93.25	100
GLCM^7,8	73.25	92.73	100	75.06	92.73	100
Visual masking¹³	80.78	93.76	100	82.86	94.29	100

GLCM: gray-level co-occurrence matrix.

Discussion of different basic models

In this paper, the proposed OCF-LNE can be applied with different basic classification models. To verify the basic model adaptation of the framework, in this experiment, we applied it with the SVM,⁴⁶, BPNN,⁷, k-NN, ⁵⁷ and random forest (RF)⁵⁸ as the basic model, respectively. The BPNN classification is a kind of model inspired by the biological neural networks that constitute animal brains, which are constructed by an interconnected group of nonlinear computing nodes. In addition, k-NN is also a widely used machine learning method for classification. In k-NNs, a sample is classified by the label mode of its k-NNs in the feature space. The RF is another widely used machine learning classification model, which is an ensemble by constructing a number of decision trees at training time and outputting the class that is the mode of the classes.

As given in Table 4, for every basic model, the performance of the basic model and the proposed framework are compared; the better ones are shown in bold. In general, the proposed framework improves the performance of all the basic models both on acc0 and acc0.5. The only one that does not seem to be improved is the k-NN. However, the acc0 reduction introduced by the framework is small (0.26%). In summary, the basic model adaption of the proposed framework is desirable.

Table 4.

The performance of the proposed ordinal classification framework based on label noise estimation (OCF-LNE) with different basic models

Basic model	Basic model only			Within OCF-LNE
Basic model	acc0 (%)	acc0.5 (%)	acc1 (%)	acc0 (%)	acc0.5 (%)	acc1 (%)
SVM	80.78	93.76	100	82.86	94.29	100
BPNN	74.29	92.47	100	75.84	93.25	100
k-NN	77.40	92.99	100	77.14	92.99	100
RF	80.52	96.10	100	80.78	96.36	100

SVM: support vector machine; BPNN: back-propagation neural network; k-NN: k-nearest neighbor; RF: random forest.

Comparison with different ordinal classification models

In this paper, we defined the fabric smoothness evaluation problem as an ordinal classification problem, differing from the general problem formulation in the area. By analyzing the characteristics of the problem, we propose an OCF-LNE, which builds a strategy for the ordinal classification problem. In this experiment, the proposed framework was compared with other ordinal classification models proposed in existing studies. As introduced in the previous part of this paper, the general ordinal classification models can be divided into two types, that is, binary decomposition-based models from the classification perspective and threshold-based models from the regression perspective. In this experiment, we selected ordinal classification methods with different basic models for both types, that is, SVMOP,⁴² NNOP,⁴³ and ELMOP⁴⁴ for the binary decomposition-based models and NNPOM⁴¹ and SVORIM⁴⁰ for the threshold-based models. The comparison result is given in Table 5, which verifies the best acc0 of the proposed framework. However, the acc0.5 of the proposed framework is not the best, which is lower than both the threshold-based models.

Table 5.

Comparison results of the proposed ordinal classification framework based on label noise estimation (OCF-LNE) with different ordinal classification models

Method		acc0 (%)	acc0.5 (%)	acc1 (%)
Binary decomposition-based	SVMOP⁴²	78.96	94.03	100
	NNOP⁴³	78.44	94.03	100
	ELMOP⁴⁴	73.25	91.43	99.22
Threshold-based	NNPOM⁴¹	78.70	94.81	99.74
Threshold-based	SVORIM⁴⁰	76.36	95.58	100
The proposed OCF-LNE		82.86	94.29	100

SVMOP: support vector machines with ordered-partitions; NNOP: neural network with ordered-partitions; ELMOP: extreme learning machine with ordered-partitions; NNPOM: neural network based on proportional odd model; SVORIM: support vector ordinal regression with implicit constraints.

From the perspective of ordinal information classification, the proposed OCF-LNE is also a category of binary decomposition-based methods. Compared with the other binary decomposition-based methods, OCF-LNE showed a superior general performance with the highest acc0 and acc0.5. This indicates that error estimation can effectively improve the model training by avoiding the interference of the label error. On the other hand, comparing with the threshold-based methods, although the acc0 of OCF-LNE is the highest, the acc0.5 of it is the lowest. Considering the internal mechanism of the methods, the threshold-based methods dealing with the ordinal classification from the regression perspective. Their high acc0.5 values reveal that their regression process can improve the model’s ability to describe the problem in a macro scope. Thus, in further research, we will try to introduce the regression model into the OCF-LNE to improve the macro performance (evaluated by acc0.5).

Conclusion

In this study, differing from traditional studies, the fabric smoothness evaluation was defined as an ordinal classification problem. To solve this ordinal classification problem, we proposed an OCF-LNE with the SVM as the basic classifier and MS-SMF as the fabric image feature. The proposed OCF-LNE for ordinal classification firstly introduces the label error estimation to improve the model performance. In our experiments, the methods were tested on a fabric image set including 385 graded fabric specimens. Within a 10 × 10 nested cross-validation, the proposed framework outperformed the state-of-the-art methods in the area with 82.86%, 94.29%, and 100% average accuracies under errors of 0, 0.5, and 1 degree, respectively. In addition, the image feature adaptability and image basic model adaptability of the OCF-LNE were verified by the experiments. Further, compared with the existing ordinal classification methods, the proposed OCF-LNE showed better adaptability to the fabric smoothness evaluation in this study. Generally, the proposed method meets the needs of the industrial application.

There are some limitations in this study. Firstly, compared with the existing ordinal classification methods from the regression perspective, the proposed OCF-LNE showed lower accuracy under 0.5 degrees, which means the proposed framework’s ability to learn the overall trend of data can be further improved. Secondly, for the final industrial application of the system, we must further increase the number of samples and the variety of samples (in different fiber contents and weaving structures) in our data set. In addition, the system illumination adaptation to fabrics with complex fabric structure needs further discussion. Finally, limited by the character 2D image, only light and solid color fabrics are used and discussed in this study. We are also working on a method to decolor multi-color fabric images.

Footnotes

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported in part by the National Key Research and Development Program of China under Grant 2017YFB0309200, in part by the National Natural Science Foundation of China under Grant 61802152, in part by the Natural Science Foundation of Jiangsu Province under Grant BK20180602 and Grant BK20180589, in part by the Fundamental Research Funds for the Central Universities under Grant JUSRP52007A, and in part by the Graduate Innovation Project of Jiangsu Province (KYLX16_0789).

ORCID iDs

Jingan Wang

Meng Shuo

Lei Wang

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