## 1 Introduction  
Because the era of the Internet of Things (IoT) has been accompanied by the rapid development of the semiconductor industry and communication technologies, the use of high-tech products, such as mobile phones and wearable devices, has been spreading widely in our daily lives. The printed circuit board (PCB) is one of the key components of such electronic devices. A PCB is a thin plate made by printing an electrically conductive circuit on an insulator. Figure 1 shows an image of a generic PCB. As shown in Figure 1, a PCB connects to different parts electrically through a point-to-point wiring process. In the past, handwork wiring led to frequent failures of the wire junctions and a short circuit as the wire insulation began to age. Furthermore, this type of work was conducted manually for inner-connecting components within the board. Such wiring, therefore, required a significant amount of time and effort. With advancements in technology, PCBs were developed for efficient and automated production. Because PCBs allow for the use of mass production, they allow devices to be smaller and lighter. In addition, they allow a high level of reliability at low production costs. Because of these advantages, most electronic devices use PCBs. According to the recent trend of miniaturized and high-performance electronic devices, the demand for PCBs has increased substantially. The current PCB market has shown an average annual growth rate of 4%. Based on increasing demand, electronics manufacturers require perfect quality and a high level of accuracy from their PCB inspections to assure their competitive edge. To meet these quality requirements, PCB manufacturers conduct an inspection before proceeding to the main process. The PCB manufacturing process consists of many steps: cutting, inner layer etching, an automatic optical inspection (AOI), lay-up, lamination, etching, drilling, solder masking, routing, a bare board test (BBT), quality control, packing, and shipping, in that order. Before proceeding to the main processes, such as lamination and etching, faults in a PCB are detected during the AOI stage. An AOI is an automated visual inspection using an image comparison method. Most PCB manufacturers inspect their PCBs through the AOI process. The types of defects detected during the AOI process include scratches, improper etching, and open circuits. In particular, scratches are fatal defects because they have the potential to change the electrical properties and can result in a malfunction of the completed product. There are typically three methods applied during the AOI process: a comparison reference (CR), non-reference verification (NV), and a hybrid approach (HA). The CR method compares an inspected image with a reference image. It measures any existing dissimilarities between the reference image and the inspected image. Thus, this method requires a reference image, and inspection is difficult without such an image. The NV approach tests the design rule of the PCB for detecting faults. It essentially verifies the widths of the insulators and conductors. However, this approach makes it difficult for users to design the rules as restrictions on the image features, and it cannot detect faults without such rules [1]. The HA approach combines various types of CR and NV methods. That is, the approach utilizes a reference image or design rules to inspect a PCB image. However, it still does not solve the limitation of being unable to conduct an inspection without reference information. Because the circuits used in a PCB are diverse and complex, the reference information increases significantly, thereby decreasing the inspection's efficiency. Therefore, additional studies are required to detect faults without reference information. Numerous algorithms have been proposed to improve the accuracy of a PCB inspection. Such algorithms can be categorized into two approaches: referential and non-referential methods. Figure 1: An illustrative image of a printed circuit board (PCB).