## 1 Introduction  
Bearing rings are important parts of mechanical equipment, and their quality directly affects the performance and reliability of mechanical products. During the actual processing of bearing rings, it is critical to detect surface defects and prevent their failure, which is related to the quality of the whole product. Electromagnetic non-destructive testing plays an increasingly important role in safety and production quality [1, 2]. Because the human eyes cannot directly observe the cracks, fluorescent magnetic particle inspection (MPI) is widely used for the ring surface detection of railway bearings due to its high sensitivity and low cost [3, 4]. However, surface defects are always inspected by human experts, which invest considerable labor and time. Therefore, it is necessary to apply computer vision-based techniques for automatic crack defect identification in fluorescent magnetic particle inspection of bearing rings. With the development of computer vision science and technology, automated defect detection is becoming increasingly popular [5; 6; 7; 8; 9; 10]. Many scholars have carried out several defect detection algorithms in fluorescent magnetic particle inspection [11; 12; 13; 14]. The processing and analysis of surface defect images are common methods for detecting defects. Traditional methods are mainly used for the automatic detection of surface defects through image processing and machine learning techniques. Most of the image processing methods used smoothing and enhancement algorithms to preserve crack regions and filter the interference simultaneously [15; 16]. Furthermore, techniques, such as edge-detection [17; 18], thresholding in greyscale images [19; 20], and image segmentation are typically used to segment defect regions from the images. Because images collected in the production workshop usually contain noise or textured backgrounds, there are many non-defective regions in the segmented images. To suppress complex interference, defect identification is a crucial module of the defect detection algorithm, which is usually composed of feature extractors and machine learning algorithms. Feature extractors are often used to obtain hand-designed features that describe the geometric or texture information of cracks, such as Hu invariant moment features [21], local binary pattern (LBP) features [22], histogram of oriented gradients (HOG) features [23], and SIFT features [24]. These features are fed into a trained classifier to decide whether the input image contains defects. For example, in [12], a maximum entropy threshold segmentation algorithm was used to obtain crack regions, and geometric features, greyscale features, and texture features of the regions were extracted. Then, a sparse self-coding neural network was applied to identify cracks. [PERSON] et al. acquired the centerline of the continuous accumulations of magnetic particles in the inspection image and extracted the SIFT features of these regions. Based on these features, they used a support vector machine (SVM) classifier for defect classification [25]. However, these methods using hand-designed features extracted from images were less effective in distinguishing cracks under complex conditions. Any change in these conditions, such as illumination, may have affected the reliability of these methods. In recent years, deep learning algorithms such as convolutional neural networks (CNNs) have been used for the detection of fluorescent MPI procedures. CNN models can extract relevant features from the input image through multilayer neural networks, which are superior to traditional methods based on hand-designed features and machine learning algorithms [26]. They can automatically extract high-level features by using the prior knowledge of known image samples and reduce the dependence on expert knowledge. For example, [PERSON] et al. used the improved EfficientNet model to detect cracks in fluorescent MPI images of forgings [27]. [PERSON] et al.