A Novel Feature Extraction Method Based on Legendre Multi-Wavelet Transform and Auto-Encoder for Steel Surface Defect Classification

Effective steel surface defect classification with low computational cost is essential for online quality inspection. The challenge of this task is large intra-class differences and unclear inter-class distances shown in various surface defects. This paper proposes a novel feature extraction method based on Legendre multi-wavelet transform and Auto-Encoder network (LWT-AE) for effectively recognizing the steel surface defects categories. More precisely, the finite element approximation theory is implemented to address the strong capacity of LW bases with various regularities and vanish moments for thoroughly matching the complex geometry characteristics of the steel surface defects, which provides strict theory foundation for the feature extraction in LWT frequency domain without losing any defect information due to its orthogonality. Then, the statistical and texture parameters are utilized to sparsely extract the defect features from LWT frequency domain, resulting in removing the redundancy components corresponding to the defects. AE network is utilized to further reduce the dimension of the extracted features and automatically select the most valuable defect features. Furthermore, two classifiers (SVM and BPNN) are used to rectify the generalization ability of the proposed method. Finally, extensive experiments are conducted on two datasets to verify the effectiveness and robustness of the proposed method. The highest classification accuracies 99.44% and 95.37% compared with other methods are attained on the NEU-CLS dataset and X-SDD dataset, respectively. To summary, the proposed method not only has simple structure, but also can reliably identify different types of the steel surface defects, which provides a suitable online application technique for the actual steel surface defect classification.


I. INTRODUCTION
Steel has various applications in numerous fields, such as the aerospace, machinery manufacturing, chemical industry, automotive industry and light industry [1], resulting in high quality standard requirements for the steel product [2].During the manufacturing process, the steel surfaces often come into being various defects due to technical and raw material issues and more [3].These defects can affect the quality and performance of the steel product in different aspects.Therefore, developing an efficient and fast classification method for the steel surface defects is great importance in improving the steel product quality [4].
It is known that the traditional method based on manual defect detection and classification suffer from some limitations such as subjectivity, low reliability and susceptibility to environmental influences [5], [6], [7], [8].Consequently, their practical application in the defect classification tasks are very limited.In contrast, the intelligent methods are becoming popular increasingly, which consist of three main aspects: machine vision-based, machine learning-based and deep learning-based methods for recognizing the steel surface defect detection and classification.
For example, Luo et al. [10] proposed a rapid classification method for the steel surface defects and achieved classification accuracy 99.11% on NEU-CLS dataset.Chu et al. [11] developed a method based on multi-type statistical features and an enhanced double SVM classifier to classify the surface defect data collected from the production line of a large steel mill in China.The experimental results demonstrated that this method attained both anti-noise ability and high classification efficiency.Martins et al. [12] used computer vision and artificial neural network techniques to classify the steel surface defect data provided by an ArcelorMittal steel company, resulting in classification accuracy 87% on this dataset through a lot of experiments.Song and Yan [14] used a noise robust method to identify the surface defects of NEU-CLS data, and this method achieved defect recognition accuracy 98.93% with strong anti-noise ability.Although these methods attained good performance in recognition accuracy and robust noise immunity with simple structure and ease of design and application.They necessitate manual feature extraction and selection, wherein the quality of these extracted features significantly influences the detection and classification accuracy and overall performance of the defect detection methods.Consequently, the most valuable feature selection remains a critical aspect of the methods based on the machine vision and machine learning [15].
It is noted that the automatic defect detection methods based on the deep learning network have significantly improved the recognition accuracy and precision of the steel surface defects, outperforming the traditional machine vision and machine learning-based methods [19], [20], [21], [22], [23], [24], [25], [26], [27].For example, Deshpande et al. [20] utilized a fully convolutional neural network for one-shot recognition of manufacturing defects in steel surfaces and achieved a classification accuracy of 92.55% on NEU-CLS dataset.He et al. [21] designed an end-to-end defect detection network fused the multi-level features and attained a defect classification accuracy of 99.67% on the same dataset.Li et al. [24] improved YOLO for defect detection on steel surfaces, achieving 97.55% mAP and a recall rate of 95.87%.To summary, these deep learning-based methods leverage the powerful learning ability of neural network structures to automatically learn features from the defect data and classify them without the need for the manual feature extraction, reducing the difficulty of algorithm design for the feature extraction.However, the deep learning-based methods have some limitations to recognition the steel surface defect categories.Due to their complex network structure and numerous configuration parameters, the training and tuning process requires substantial computational resources and cost [6].Furthermore, the deep learning models require a significant amount of data for training, and a lack of sufficient training data can largely impact the model's performance.Finally, the current complex computational demands of these methods prevent their impractical applications in the online defect detection systems [24].
To overcome the difficulties mentioned above and enhance the recognition accuracy with low computational cost, this paper proposes a new feature extraction method based on LWT-AE for recognition the steel surface defect categories.The advantages of the proposed method are elaborately described as follows: Compared with the traditional wavelet transform, LW bases with various regularities and vanish moments are thoroughly implemented to extract the salient characteristics of the steel surface defects.Compared with the machine vision and machine learning methods, the proposed method integrates the statistical features and texture features of defects to effectively remove the redundant components of defects in the LWT frequency domain.It is noted that AE network block is utilized to automatically extract the most valuable defect features, resulting in the dimensionality reduction of the extracted features.Finally, compared with the deep learning methods, the proposed method combines the simple classifier (SVM) to effectively recognize the various defect categories with a simpler structure and lower computational cost.The experimental results conducted on NEU-CLS and X-SDD steel surface defect datasets demonstrate that the presented method has some merits such as a simpler structure, easy implementation and high classification accuracy than other methods.The main contributions of this article are summarized as follows.
1) This paper devises the two dimensional LWT specific process for the steel surface defect image processing as illustrated in Fig. 1 in detail.The pro-processing involved is simpler than other multi-wavelet transformations, and it avoids the need to pad zeros to match the length of the original data [28], resulting in high accuracy on the edges.2) The finite element approximation theory is implemented to demonstrate the strong ability of matching the complex defect characteristics of the original images by LW bases.Then, the compressed feature space reduces the computational burden of the most value features selection.
3) The fusion of the statistical features and texture features in LWT frequency domain is utilized to effectively remove redundant information about the defects.Furthermore, AE network block is designed to automatically select the most valuable defect features, resulting in the dimension of the defect feature extraction reduction significantly, which is easy implementation to the online steel surface defect classification.4) The effectiveness and generalization of the proposed method are validated by using NEU-CLS and X-SDD datasets.Extensive experiment results show that the presented method has good classification performance and provides a promising method for designing the steel surface defect online detection and classification system.
The remaining of this article is formed as follows: Section II introduces the strong approximation ability of LW bases, and devises the specific the decomposition process of the steel surface defect image by LWT.Section III elaborately describes the proposed method for recognition the steel surface defects categories.In Section IV, the proposed method is implemented to recognize the steel surface detects on NEU-CLS and X-SDD datasets, and the classification results are compared with other defect classification methods.Section V gives a few conclusions of this research and prospects for future work.

II. REPRESENTATION ABILITY OF DEFECT CHARACTERISTICS BY LW BASES
In this section, the difficulties in effectively approximating the complex geometry characteristics of the steel surface defects are summarized.Then, the finite element analysis is utilized to address the strong capability of LW bases.Finally, LWT is devised to compute the approximation coefficients of LW bases, which can be utilized to extract the salient features of the steel surface defects.

A. THE TRADITIONAL WAVELET TRANSFORM
It is known that wavelet transform offers a comprehensive approach for image processing, which provides lots of advantages such as multi-scale analysis, efficient data representation, precise edge detection, powerful compression capabilities, effective noise reduction, feature extraction and pattern recognition [28], [29], [30], [31], [32], [33], [34].For example, Nejad and Zakeri [28] combined DWT with radon neural network for pavement distress classification.Li et al. [30] constructed Marginal Distribution Covariance Model (MDCM) in multiple orthogonal wavelet transform domains to describe the texture features of the image and represent the similarity of two images, resulting in effective recognition the images.
However, it is worth noting the limitations that should exist in these wavelet methods.For instance, Haar wavelet exhibits weak frequency localization characteristics, which is implemented to deal with the complex textured images, resulting in information loss [35].Similarly, although Daubechies wavelet performs well in terms of smoothness and compact support, it should have limitations in representing non-stationary signals and complex geometry image characteristics [36].Additionally, some wavelet methods should be sensitive to noise, leading to significant errors for the uncertain noise characteristic images [37].Therefore, to address these limitations and further enhance the accuracy and robustness of image processing and analysis, LWT with rich properties, especial various regularities, is thoroughly implemented to recognize the steel surface defect categories.
There are several reasons for using LWT to process images.First, since the multiple wavelet base functions of LW are orthogonal with each other, the obtained feature images by LWT do not lose any defect characteristic information.Second, the rich regularities of LW bases can be implemented to effectively extract more salient defect features of the original images.Finally, the process of the convolution does not need to pad zeros to make the length of the data be same as the original data as the traditional wavelet transform [28], [42], which can effectively reduce the computational burden and enhance the accuracy of LWT.

B. STRONG APPROXIMATION ABILITY OF LW BASES
It is known that LW bases are constructed by Alpert with the property that a variety of integral operators are represented in these bases as sparse matrices, to high precision, and the dissertation of the present author gives an earlier report of the work [38].Then, LW bases are mainly utilized to effectively compute integral and differential operators and solve corresponding partial differential equations [39].The corresponding results of this multi-wavelet bases can be explained by two-scale relationship as where ϕ k and ψ k denote the scale bases and wavelet bases respectively, and k = 0, 1, • • • , p − 1 is the order of LW bases.In addition, LW bases not only have rich properties as the traditional wavelet bases such as compact support, vanishing moments and orthogonality, but also contain various regularities discontinuity at some notes, different differentiability shown by different scale bases and wavelet bases [40].
Usually, an image can be explained as the values of a two dimensional function u at grid point.For the steel surface image with various defect characteristics, it is very important to adopt appropriate wavelet bases to effectively represent its features.This paper utilizes the approximation theorem in finite element analysis to address the strong approximation capability of LW bases described as follows.
Approximation theorem: Let K ⊂ R d be any regular element in the sense that ρ x ≤ diam(K ) ≤ x for some constant 0 < ρ < 1.Let u ∈ W k+1,p 1 (R d ) and Pu be the L 2 projection of u.Then, the finite element approximation theorem [43] is demonstrated as where It is noted that the representation in ( 4) is essentially explained that the linear combination of orthogonal polynomials approximates the surface on the parted rectangle I nl × I nl ′ , where I nl = [2 −n l, 2 −n (l + 1)).Then, the finite element approximation theory can be applied to the special situation p 1 = q 1 = 2, m 1 = 0 in (4), the approximation error in (3) is specifically described by where C is a constant depending on p, for more details refer to [44].
The approximation result demonstrates that the approximation error converges exponentially with the finest resolution level n and order p of LW bases, which means that the approximation coefficients in (3) can effectively represent the complex geometry characteristics of the steel surface defects, which provides strict theory foundation for the feature extraction from the LWT frequency domain.This paper devises the convolution operations of the original images by the filters 1),(2) to effectively solve the above approximation coefficients, which is very convenient to effectively extract the comprehensive features of the steel surface defects.

C. SPECIFIC PROCESS OF LEGENDRE MULTI-WAVELET DECOMPOSITION
According to multi-resolution analysis theory [40] and literatures [41] and [42], the j + 1 → j resolution level of LW decomposition procedure is elaborately described as follows: ki g (1) ki h (1) ki g (1) For clarity, let LL n k HL n k , LH n k , HH n k denote the coefficient matrices s kk ′ ,nll ′ , α kk ′ ,nll ′ , β kk ′ ,nll ′ , γ kk ′ ,nll ′ at the resolution level n respectively, which are usually used to represent the feature maps of the steel surface original image.
The essence of LW decomposition of the steel surface defect image is to project the original image into the four subspaces.Usually, the effectiveness of wavelet transform for image processing mainly depends on the size of the error between the projected image and the original image [41].The larger error means that more details are lost in the feature maps, and the smaller the error means that less details are lost in the feature maps.Fortunately, the decomposition feature maps by LWT based on the approximation results in (3) can be implemented to extract the salient defect characteristics of the steel surface.
Finally, it is known that the difficulty in image processing field by wavelet methods is the choice of two important parameters, which are the number of the wavelet function and the decomposition level [28], [40], [41].There is no commonly accepted method for determining these appropriate parameters [40].Based on the experience and knowledge provided in the literatures [40], [41], and [42] and the experimental results in Section IV.The decomposition level and the order of LW bases are adopted as one and two in this paper, respectively.In addition, for the sake of clarity in the flowchart, the resolution level n → n − 1 is replaced by the first decomposition level.Then, the specific procedure of LW decomposition level 1 is elaborately demonstrated in Figure 1 as follows.
As shown in Figure 1, the specific steps for LW decomposition are described as follows: Step 1: Double the original image according to the order of the chosen LW bases p = 2.
Step 2: Perform row pro-processing on the doubled images.Decompose the images into 2m, 2m+1 parts in the horizontal direction, where m = 0, 1, Step 3: Convolve the row pro-processed images by using filters H 0 , H 1 , G 0 and G 1 in (1), (2).Then obtain four convolved images, and combine the four convolved images into two feature images, respectively.
Step 4: Decompose the two feature images into 2m, 2m + 1 parts in the vertical direction.
Step 5: Convolve the column pro-processed images by using filters H 0 , H 1 , G 0 and G 1 in (1), (2), then the convolved images are combined into two feature image.
Step 6: Divide the above two feature images into eight feature sub-images , where k = 0, 1.
Then, the obtained feature sub-images are implemented to effectively extract the high resolution defect features.

III. THE PROPOSED METHOD
In this section, the advantages of LW decomposition are first combined the statistical features and texture features commonly used in image recognition field [2] to remove the redundant components corresponding to the defects.In the second step, AE network block is devised to select the most valuable defect features, resulting in the dimension of the features reduction largely.Finally, in order to verify the stability and generalization ability of the proposed LWT-AE feature extraction method, two classifiers (SVM and BPNN) are applied to the comparative experiments.Furthermore, how to choose the configuration parameters of SVM is described in details.In addition, the experiments are performed in a computer with Intel (R) i7-12700H CPU @2.30GHz and 16 GB RAM memory.All codes developed for the studies are implemented in Python.

A. FEATURE EXTRACTION BASED ON LWT-AE
Since the geometry characteristics of the steel surface defects are very complex and diverse, thus developing an effective and fast feature extraction method is crucial to reliably verify the steel surface defect categories.In this subsection, the statistical features and texture features, such as standard deviation, entropy, root mean square, skewness, kurtosis and Hu's invariant moments [45], [46], [47], are first selected to sparsely extract the defect features from LW decomposition frequency domain.It is noted that the statistical and texture features are all effective sparse metrics, which leads to easy calculation and application, resulting in avoiding complex feature extraction method based on optimal algorithms and a large amount of expert knowledge [10], [14].Then, AE network block is designed to automatically learn the most significant defect features, resulting in the dimension and computational cost reduction largely.Finally, the extracted most valuable defect features are inputted into SVM to accomplish the steel surface defect recognition.

B. LWT-AE+ SVM METHOD
This subsection mainly explains how to combine LWT-AE with SVM classifier for the steel surface defect classification.Then, for clarity, the decomposition level and the order of LW bases in the flowchart are adopted as n = 2 and p = 2, respectively.The detailed flowchart of the proposed method is illustrated in Figure .2 as follows.
As demonstrated in Figure 2, the specific steps of the flowchart are elaborately as follows.
Step 1: The original images are acquired.Then, LWT is performed on a specific steel surface defect image from NEU-CLS dataset.For two LW bases, 8 feature images in total LL 1 0 , HL 1 0 , LH 1 0 , HH 1 0 , LL 1 1 , HL 1 1 , LH 1 1 and HH 1  1 are obtained at the first decomposition level.Similarly, the low-frequency feature images LL 1 0 and LL 1 1 are further decomposed at the second decomposition level, then 16 high resolution feature images in total are attained.Finally, 22 feature images including 6 high frequency feature images at the first decomposition level and 16 feature images at the second decomposition level are implemented to sparsely extract defect features.

VOLUME 12, 2024
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.Step 2: The statistical and texture parameters are utilized to remove the redundant components from the extracted 22 frequency domain feature images.Then, AE network is used to further extract the most valuable defect features and reduce the dimension of the feature vectors.Finally, the extracted sensitive defect features are normalized to between 0 and 1, and the recognition labels are adopted as one-hot encoded.
Step 3: The normalized feature vector is utilized to train the SVM classifier by the corresponding training samples, and then the testing samples are fed into the input of the trained classifier to verify the steel surface defect categories.Finally, ten-fold cross validation method is implemented to verify the robustness and generalization capability of the proposed method.
SVM has many advantages in image multi-classification tasks, which can effectively deal with high-dimensional feature space and nonlinear classification problems, and has good robustness and generalization performance [48], [49].It is known that SVM generalization performance depends on a good setting of meta parameters such as C, gamma and kernel function.Then, the optimal selection of these configuration parameters is further addressed by the high effective grid search algorithm [50], [51].To be specific, the ranges of the configuration parameters C, gamma and kernel function are illustrated in Table 1 in details to effectively find the optimal parameter setting for SVM.
Furthermore, BPNN is an effective and reliable image classification method with the strong adaptability and generalization ability in multiple image classification tasks [52].In order to verify the generalization ability of the proposed feature extraction method, BPNN classifier is used to rec-ognize the steel surface defect categories as a comparative experiment.

IV. EXPERIMENTAL VALIDATION AND RESULTS ANALYSIS
In this section, two steel surface defect datasets used in the experiment are introduced, and the existing difficulties in the classification tasks of the surface defects are described in details.Then, the effectiveness and robustness of the proposed method are verified on the two steel surface defect datasets.Furthermore, to further illustrate the advantages of the proposed method, the experimental results are compared with the state-of-the-art intelligent defect recognition methods such as SqueezeNet method, ResNet50 method and YOLO method and more [24].

A. NEU-CLS AND X-SDD DATASETS
NEU-CLS is a steel surface defect dataset established by Northeastern University [14].The dataset includes six typical kinds of the hot-rolled steel surface defects, i.e., crazing (Cr), inclusion (In), patches (Pa), pitted surface (Ps), rolled in scale (RS) and scratches (Sc).There are a total of 1800 defective images, of which 300 are in each category, and the resolution of each defective image is 200 × 200 pixels.An example image of a typical surface defect is shown in Figure .3 in detail.
As demonstrated in Figure 3, it can be found that the rolled-in scale and crazing defects have high inter-class similarity, and the pitted surface intra-class defects are scattered [14], which lead to low recognition accuracy by the traditional methods [21].X-SDD is a hot rolled strip surface defect dataset from the field of hot rolled strips [4].Different from NEU-CLS dataset, each defect image in X-SDD dataset has a resolution of 128 × 128 pixels and the images are 3-channel JPG format.The X-SDD dataset contains 1360 defect images with 7 categories, including 238 slag inclusions (Si), 397 red iron sheets (Ri), 122 iron sheet ash (Isa), 134 surface scratches (Ss), 63 oxide scale of plate system (Osps), 203 finishing roll prints (Frp), and 203 oxide scale of temperature system (Osts).In this paper, the image format of X-SDD dataset is transformed into grayscale image format with pixels, which is the same as that of NEU-CLS dataset.Then, Figure . 4 shows an example image of a typical surface defect of this dataset as follows.
As demonstrated in Figure .4, the similar difficulties to NEU-CLS dataset are the high inter-class similarity between oxide scale of plate system and red iron sheets defects, and more scattered defects within red iron sheets classes.In addition, the defect samples in X-SDD dataset are imbalanced, thus the classifier is not able to fully learn the relationship between the internal feature space and the defect space to a extent, resulting in poor recognition performance in this dataset [4].

B. EXPERIMENTAL RESULTS ON NEU-CLS
The optimal configuration parameters of SVM classifier and BPNN classifier are obtained by using the grid search algorithm on NEU-CLS dataset, and the optimal structure of AE network is attained by extensive experiments as other existing methods [18], [21], [24].Then, the specific results are described in Table 2 in details as follows.Then, the detailed recognition results of the proposed method for the steel surface defects on NEU-CLS dataset LWT are described in Table 3 and in Figure .5, respectively.
As illustrated in Table 3, the proposed method can effectively identify different defect types of the steel surface on NEU-CLS dataset.To be specific, the average testing accuracy can achieve over 99% by only using the simple classifiers, which is 99.44% by SVM and 99.06% by BPNN, respectively.In addition, the results of ten-fold cross validation method shows that the proposed LWT-AE+SVM attains the smallest variation 0.21 than other methods, which demonstrates that the proposed method has good stability and generalization in the recognition steel surface defects on NEU-CLS dataset.
Furthermore, to explore which feature extraction module gives the best recognition accuracy improvement, this paper compares the classification performance of different feature extraction modules, such as the statistical features, the texture     As shown in Table 4, the combination of the statistical and texture features only attains 96.11% recognition accuracy.However, the proposed LWT-AE feature extraction method has obvious improvement in classification accuracy for the steel surface defect recognition on NEU-CLS dataset, which achieves the highest recognition accuracy and shows the effectiveness of the proposed method for the online defect recognition application.
Finally, in order to further show the superiority and effectiveness of the proposed method, other popular methods such as the fusion network of ResNet34 and multilevel-feature (ResNet34+MFN) [21], adjacent evaluation completed local binary patterns (AECLBP) [14], combing RelationNet and ProtoNet (RPNet) [22] and more, are also utilized to compare with the proposed method.Then, the comparison results are listed in Figure .6 in details as follows.As shown in Figure 6, the specific comparison results are summarized as follows: (1) Compared with the machine vision and machine learning methods such as Generalized completed local binary patterns (GCLBP), Adjacent evaluation completed local binary patterns (AECLBP) and OVERFEAT methods, the proposed method has the highest classification accuracy.
(2) Compared with the methods based on deep learning such as ResNet34+MFN [21] and Decaf [21] methods, the proposed method still has the highest recognition accuracy.It is noted that the proposed method has simpler structure, fewer configuration parameters and lower computational cost, which is very easy to design and implement to online steel surface defect classification.
(3) The classification accuracy of the method base on DWT can reach 98%, which is lower than that of the proposed method 99.44% and 99.06%.
To summarize, the above experimental results show that the proposed method can effectively identify different steel surface defect categories and obtains good stability and robustness compared with other existing methods.

C. EXPERIMENTAL RESULTS ON X-SDD
In this subsection, the optimal configuration parameters and experimental results of the proposed method are summarized in Table 5, TABLE 6 and Figure 7 as follows.As illustrated in Table 6 and Figure .7, the proposed method can effectively identify different defect types of the steel surface defects on X-SDD dataset shown imbalanced defect samples, and the average testing accuracies by using the SVM classifier and the BPNN classifier achieve 95.37% and 94.06%, respectively.It is noted that the proposed LWT-AE+BPNN obtains the smallest variation compared with other methods.The experimental results show that the method proposed also has good stability and high recognition accuracy in the steel surface defect classification tasks on the imbalanced defect samples dataset.
Furthermore, in order to further show the advantages of the proposed method compared with other existing methods, the following evaluation measures are also calculated on X-SDD dataset: Macro-Recall, Macro-Precision and Macro-F1, which offer a more holistic and overall evaluation of the steel surface defect categorization performance for different recognition methods.More specifically, Macro-Recall is the ratio of correctly predicted positive observations to the total actual positives.In a classification task, it measures the ability of the model to capture all positive instances.Macro-Precision is the ratio of correctly predicted positive observations to the total predicted positives.It measures the accuracy of the positive predictions made by the model.Macro-F1 is the harmonic mean of precision and recall.It provides a balance between precision and recall and is often used when there is an uneven class distribution.The formulas of these measures can be found in literature [4].The classification results of the proposed method are utilized to compare with different methods such as combing Squeeze and excitation block (SE) and deep ResNet (SEResNet34) [33], fusing RepVGG and spatial attention (SA) (RepVGG_B3g4+SA) [4], SqueezeNet [4], ResNet50 [4] and more.The comparison results are listed in Table 7 in details.
From the comparative results in TABLE 7, it is obvious that the proposed method attains the highest recognition accuracy 95.37% than the existing methods described in Table 7.It is noted that the accuracy of RepVGG_B3g4 is improved from 91.67% to 95.10% with the integration of SA blocks.The experimental results on X-SDD dataset demonstrate that the proposed method has the excellent feature learning capability of the imbalanced steel surface defect samples compared with other methods.
In summary, the presented method is powerful and robust to recognize different steel surface defect categories based on the experimental results of the two datasets.The highest testing accuracy is achieved by the proposed method with the simplest structure and lest configuration parameters, which provides a promising method for the online steel surface defect recognition implementation.

V. CONCLUSION
An effective and reliable method for the steel surface defect recognition is developed in this paper.Compared with the methods based on deep learning, such as ResNet, VGG, SqueezeNet and more, the proposed method achieves the highest classification accuracy of 99.44% and 95.37% on NEU-CLS and X-SDD datasets, respectively.Especially, the sparse representation by using the statistical features, texture features and AE network is able to remove the redundant components of the frequency domain feature maps, resulting in the dimension of the extracted features reduction largely, but should losing less defect components.In future work, LWT should be combined with other deep convolutional neural networks to extract the steel surface defect features with the situation of the imbalanced samples more comprehensively.

FIGURE 1 .
FIGURE 1.The decomposition of the original image by LWT.
d is the dimension of space variable, the constant C solely depends on k, and |•| denotes the semi-norm of Sobolev space W k+1,p 1 (K ).

FIGURE 2 .
FIGURE 2. Flowchart of the proposed method for the steel surface defect recognition.

FIGURE 3 .
FIGURE 3.An example image of NEU-CLS dataset.

FIGURE 4 .
FIGURE 4.An example image of X-SDD dataset.

FIGURE 6 .
FIGURE 6. Comparative results of different methods on NEU-CLS dataset.

TABLE 1 .
The range of the configuration parameter for SVM.

TABLE 2 .
The optimal configuration parameters of the proposed method on NEU-CLS dataset.

TABLE 3 .
Experimental results of different methods on NEU-CLS dataset (%).

TABLE 4 .
Recognition improvement by the combinations of different feature extraction methods.

TABLE 5 .
The optimal configuration parameters of the proposed method on X-SDD dataset.

TABLE 6 .
Experimental results of different methods on X-SDD dataset (%).

TABLE 7 .
Recognition results of different existing methods on X-SDD dataset.