## 4 Experimental Results
### Datasets Analysis  
In this study, a typical steel surface defect dataset, namely Northeastern University (NEU) dataset [1], was utilized to evaluate the performance of the proposed method. The NEU dataset consists of six typical surface defects, viz., crazing (Cr), inclusion (In), patches, (Pa), pitted surface (PS), rolled-in scale (RS), and scratches (Sc). In total, the NEU dataset contains 1800 grayscale images with a spatial resolution of 200 \(\times\) 200 pixels, and approximately 300 defect images were collected in each class. The examples of the NEU dataset are shown in Figure 4. From these examples, it can be seen that the complex variance of the surface defects and the influence of the illumination are challenging issues for describing the dataset.  
To illustrate the complex variance of defects, [PERSON] et al. [2] demonstrated the ratio distribution and size distribution of steel surface defects based on the NEU-DET dataset. Intuitively, up to about three-quarters of the surface defects were measured to have a ratio of the long side to the short side between one to three. Meanwhile, most of the surface defects were small in scale according to the distribution of the ratio of the defect area to the image area. In short, these results indicated that the inter-class defects had a limited diverse appearance. Besides, defects such as pitted surface, inclusion, and scratches contain large differences in appearance. For instance, according to Figure 4, it is obvious that the inclusion and pitted surface defects contained noticeable changes in their size and grayscale. Moreover, the appearance of the scratches defect might be horizontal, vertical, or slanting stripes. Hence, the intra-class diversity and inter-class similarity might exacerbate the misleading of the training model.  
Furthermore, the disturbance defect dataset is constructed herein to evaluate the robustness of the MRFFN. The interference defect dataset involves two common noises in the actual production environment, which are Gaussian white noise and salt and pepper noise. According to [PERSON] et al. [46], due to the high temperature of the image sensor or the lack of illuminance, the occurrence of Gaussian noise will occur during data collection. Besides, the transmission error by the camera will generate random black or white points (salt and pepper noise) and disturb the feature learning progress. Moreover, the high speed of the production line should be considered as it may cause a motion blur effect while capturing images. Hence, this study provides three common interference situations in the image acquisition process, including Gaussian white noise, salt and pepper noise, and motion blur. First, the variance of the zero-mean Gaussian white noise is set as 0.01, 0.05, 0.1, and 0.5 accordingly. Second, the density of salt and pepper noise is set as 0.01, 0.05, 0.1, and 0.5. Lastly, the length of the motion is set as 5, 10, 15, and 20 with a stochastic angle between 0\({}^{\circ}\) and 360\({}^{\circ}\), as shown in Figure 5. For the interference defect dataset, 50 samples for each type of defect are randomly picked as the training samples and the remaining samples are regarded as the testing samples.