## 1 Introduction  
With improvements in manufacturing technology, nondestructive testing (NDT) has become an asset for supporting quality control and maintenance inspection processes. NDT is a noninvasive approach for providing actual results to determine the integrity and safety of an engineering system [1]. By implementing NDT assessments, the inspection process can be completed without destroying the target object, thereby increasing the economic and resource benefits. These advantages have led NDT to become the backbone of maintenance inspections in critical engineering industries such as aerospace, marine, railroad, and nuclear systems, as these industries require surface inspections to analyze and evaluate the defect risks for preventive and overhaul maintenance decisions [2; 3; 4; 5; 6]. In current NDT techniques, there are several methods of surface inspection commonly used to inspect material defects, including penetrant testing (PT), magnetic-particle inspection (MPI), and magnetic flux leakage (MFL) [7]. The PT method considers a capillary action based on filling a perforated surface with a penetrant based on a liquid or dye [8; 9]. When the penetrant is cleaned from the target surface, the penetrant filling the defect stacksinside the defect and can be quickly observed using visual or UV assessments, depending on the type of penetrant. The most significant advantages of PT are its high portability and high applicability to most materials [10]. Another approach (and one of the oldest) to NDT visual surface inspections is the MPI method, which uses a magnetization process with tiny magnetic particles as a coating to observe material defects [11; 12; 13]. MPI is widely used for detecting surface defects in ferromagnetic materials. This inspection utilizes an induction magnetic flux based on a permanent magnet or direct-current electromagnetic field. When a specimen containing a defect is magnetized, a magnetic flux leakage (MFL) appears around the crack gap [14], and the defect can be detected when powders containing ferromagnetic particles are applied to the material. The magnetic leak attracts the powder to form the defect shape [15]. However, MPI inspection has a lower reputation compared to advanced electromagnetic techniques, as it requires a subjective decision from a highly experienced observer and is strongly dependent on inspector concentration [11]. Aiming to improve on the MPI weaknesses, MFL-based inspections have been further developed by utilizing inductive magnetic sensors such as giant magnetoresistance, Hall, and magneto-optic (MO) sensors as the observers. The MFL is widely used to inspect material defects owing to volume losses caused by corrosion or erosion. One approach to MFL inspection comprises an MO nondestructive inspection (MONDI) system, which promises a high-sensitivity assessment with a magnetic domain width of approximately 3-50 \(\upmu\)m and a defect detection ability at up to 0.4 mm [16; 17; 18; 14]. The MONDI system works based on a principle of the Faraday rotation effect on the behavior of light propagation through a magnetized medium. An MO sensor is used to detect the MFL distribution around a crack, with a high spatial resolution. The defects can be observed by implementing an optical polarity system based on the Faraday effect. Furthermore, to increase the assessment efficiency and reliability, robotics-based nondestructive inspection systems have been developed to address fast and complex engineering systems in actual industrial inspections (Figure 1). To implement autonomous NDT inspections, a quantitative evaluation of the presence, locations, shapes, and sizes of defects must be performed. This capability is essential for training NDT robots to track material defects and evaluate defect severity. Several image processing algorithms have been proposed to address these challenges. [PERSON] et al. (2012) proposed crack image extraction by using radial basis functions based on an interpolation technique [19].