## 1 Introduction
A referential method is based on a comparison between the inspected image and a reference image. To measure the dissimilarity between these two images, image subtraction and template matching techniques are used. [PERSON] et al. proposed an inspection method based on a subtraction method [2]. The image subtraction method compares both images using an XOR logic operator [3]. The resulting image, which is obtained after this operation, contains only portions of a fault [4]. Therefore, the reference image and the inspected image should be placed in a fixed position to compare both images. In addition, a reference image of the same size is required. Template matching is a technique for identifying the parts of the image that match the reference image. This method extracts the features of both the reference and inspected images. It then calculates the similarities of these features. One of the major disadvantages of template matching is that a large amount of information regarding the reference image must be used. Therefore, this method requires a mass storage device that can store all of the information. Moreover, the inspected images also have to be precisely matched for a comparison with the reference image [5]. [PERSON] et al. suggested an inspection algorithm that extracts the wavelet and geometric features, and then detects a defect after learning the fault pattern using a neural network and k-nearest neighbors [6]. When extracting the features of a PCB image, this method uses the maximum value of the correlation coefficients between the features of the reference image and the inspected image. This approach of applying machine-learning algorithms is called the learning-based model. The aim of this approach is to automatically detect faults through pattern recognition [7]. In [8], the authors proposed a defect detection method using feature matching for non-repetitive patterned images. The method first extracts features of both the reference image and the inspected image using a modified corner detector. It then detects a fault by finding a correspondence between two feature sets. Thus, the methods [6,8] still require a reference image to detect a fault. A non-referential method, on the other hand, does not require a reference image. However, this method uses design rules. If the inspected image does not conform to the design specification standards, it is considered defective. [PERSON] and [PERSON] suggested a verifying algorithm for minimum conductive and insulator trace widths [9]. This algorithm uses morphological techniques, which are methods for processing binary and grayscale images based on shape. Morphological techniques do not require a predefined model of a perfect pattern because we can construct specific shapes in an image by choosing an appropriate neighborhood shape [10]. However, this method has a disadvantage in that we should apply different pre-processing algorithms to check for faults in a PCB. In addition, it automatically increases the inspection time [5]. [PERSON] et al. proposed a non-referential defect detection approach for bond pads [11]. This approach restores the shape of the bond pads using Fourier image reconstruction. The method then evaluates the similarities and differences in the pad shape. However, the method has difficulty in reconstructing an original image of a PCB in the absence of a reference image because the shape of a circuit is quite varied and complex. Thus, the method is not suitable for detecting faults on a PCB. As mentioned earlier, a non-referential image analysis has certain limitations. [PERSON] and [PERSON] proposed a very fast and high-quality corner detector using machine-learning techniques [12]. This algorithm uses a decision tree to learn the properties of the corner points and determine which point is a corner point instead of directly counting the number of consecutive points of the same type. [PERSON] proposed an approach for the detection of three-dimensional faults on scale-covered steel surfaces [13].