## 2 Background Information for Method Development  
### Image Transformation  
According to [PERSON] [1], the first step in matching two images is to detect or extract the distinct features of these images. However, this is not easy. Feature detection is challenging because when two images (e.g., the key reference frame and current frame) have been captured from a scene at different viewpoints, their features such as position, orientation, and scale are not exactly the same. This phenomenon is called image transformation. Thus, image transformation is impacted based on the position and orientation of the camera. The position and orientation of a camera depends on six spatial degrees of freedom, including three degrees of freedom for position (i.e., X, Y, and Z), and three degrees of freedom for orientation (i.e., pitch, roll, and yaw/head) [43]. Figure 6 illustrates the coordinate system that can be defined based on six degrees of freedom. Image Transformation Scenarios: Illustrative Case Study (i.e., Examples of Image-Based Scene Transformations)  
To have a better understanding of camera position and orientation and their impact on image transformation, an illustrative case study has been conducted. In this case study, a camera was installed on a tripod with six degrees of freedom. In this first step, a reference picture was captured from a scene with a fixed camera's orientation and position. In the second step, the secondary pictures were captured from a different camera's position and orientation. For each capture, only one degree of freedom was applied. In other words, three pictures were captured when the position of the camera changed in the X, Y, or Z directions with a fixed orientation, and three pictures were captured while the position was fixed and the orientation changed in the X, Y, or Z directions. The six images captured in these ways were aligned over the reference picture separately to identify the transformation impacts and based on the observations, six conceptual diagrams were created, as shown in Figure 7.  
The first type is a linear transformation that occurs on the X-axis. This type occurs when the relative position of a camera changes in the X direction while producing two images. The second type is a linear transformation on the Z-axis. This transformation occurs when the camera is repositioned in the Z direction. The third type of linear transformation occurs on the Y-axis. In this type, which is correlated with scaling, the picture is captured when the position of the camera in the Y direction is changed. In this type, the size of objects in the image changes. The fourth type is an angular transformation that occurs around the X-axis. In this type, the orientation of the camera changes, and the camera is rotated around in the X direction. The fifth type is an angular transformation that occurs around the Y-axis. In this type, the camera rotates in the Y direction. The sixth type is an angular transformation that occurs on the Z-axis. In this type, the camera is rotated around in the Z direction. In the first and second types of transformations, only the locations of objects in the images change. In the third type, in addition to the locations of objects, the sizes of the objects change. In the fourth  
Figure 6: Coordinate system including six degrees of freedom, three linear and three angular (adapted from [44]). type of transformation, the locations of objects change. In the fifth and sixth types of transformations, due to changes in the orientation of the camera, the shapes of objects in the image change. In addition to these changes, in all these transformations, due to changes in the position of the camera or changes in orientation, some objects that are captured on the first image disappear and some new objects are captured. Advanced Transformations  
In real situations, without using a tripod, these fundamental transformations combine and create new types of transformations. For instance, if transformations on the X- and Z-axis coincide, it is called translation.