## 1 Introduction
### Problem Statement  
In general, there are three main types of algorithms for image matching. The first type is shape matching algorithms, which look for similarities in the shapes of objects in the images [5]. The secondtype is pixel matching algorithms, which look for similarities in the pixel's intensity [5]. The third type is called feature-based matching algorithms [5]. In this type, the algorithm detects the distinct local features of images, such as corresponding points, lines, and areas [5]. The challenge these algorithms need to deal with is the variation in the context of pictures that were captured from a scene from different viewpoints. When two pictures are not taken from the same viewpoint, the position, orientation, and scale of the features (e.g., objects and background) in the scene are transformed. Thus, these algorithms should detect the similarities between the features that have been displaced and deformed in the images, and then match them. In previous decades, to deal with these issues of extracting features, researchers have proposed many different techniques. Some of these techniques detect image features regardless of transformations (e.g., translation and rotation) and illumination but not scaling. This group of techniques is known as single-scale detectors. Techniques such as Moravec detector [25], [PERSON] detector [26], SUSAN detector [27], FAST detector [28; 29], and Hessian detector [30; 31] are examples of single-scale detectors. Other techniques known as multiscale detectors, including Laplacian of Gaussian [32], difference of Gaussian [33], Harris-Laplace [34], Hessian-Laplace [35], and Gabor-Wavelet detector [36] were later created. In addition to rotation, translation, and illumination, these techniques consider the impact of uniform scaling in detecting features, with the assumption that scale is not affected by an affine transformation of the image structures. Thus, to be able to detect the image features as accurately as possible, it was necessary to create techniques that could handle non-uniform scaling (change in scaling in different directions). Scale invariant feature transform (SIFT) is one of the most advanced versions of these algorithms [1]. SIFT can detect and describe image features [1]. In the first step, the SIFT algorithm detects the local distinct points on images. In the second step, these distinct points (keypoints) are converted into histogram vectors based on the image gradient of each point called keypoint descriptors. SIFT gives value to each of these vectors. In the third step, SIFT compares these values to match the keypoints. However, this is not the end of the process, as not all matches conducted by SIFT are correct. There could be some keypoints in two images with equal values but related to different parts of the scene. For instance, a keypoint on the top of a scene could have equal value with a point on the bottom of a scene. In this case, SIFT cannot distinguish between them. Therefore, incorrect matching occurs. These incorrect matches need to be filtered. For the purpose of filtering the incorrect matches, the fourth step is required. In this step, a technique called RANSAC or random sample consensus [37] is widely used. This approach divides the corresponding points into inlier and outlier sets and finds the best portion of points in inlier sets. To ensure this occurs, first, this algorithm randomly samples two keypoints. The width of the inlier boundary is already determined for this algorithm. RANSAC counts what fractions of points are located inside of this inlier boundary. This process is repeated several times for different keypoints. The largest number of points found as inlier is defined as the best matching pattern, and other matches are removed. Figure 1 illustrates the procedures that SIFT detects, describes, and matches the key points, while RANSAC filters incorrect matches. However, image matching algorithms are not fully successful when image transformation occurs and image viewpoint changes [5; 7; 38; 39; 40].