## 4 Results and Discussion
### Measuring Changes in Camera's Position and Orientation  
The features in two images can transfer (i.e., displace) if the position and orientation of the camera that captured those pictures change. In this research study, to understand what type of transformation results in a certain type of change in a camera's position and orientation, some methods were determined. These methods could assist the authors in assessing the causes of image transformation in different pictures. These methods are described in the following paragraphs:  
**Change in the position of the camera in the Y direction** To be able to measure any change in the position of the camera in the Y direction, the method illustrated in Figure 14 was used. In this method, the position of the scene is fixed, but the camera's position changes. The distance between the current images in the scene can be estimated where \((y-y^{\prime}=y\times i\dot{i}^{\prime})\). In this equation, \(y\) is the distance between the scene to the camera that captured the reference picture, \(i\) is the distance between two points in the reference image, \(i^{\prime}\) is the distance between similar points in the current image, and \(y^{\prime}\) is the distance between the reference camera and the current one. After estimating the distance of the camera to the scene for all pictures, to find the change in position of the camera, the average distances should be compared with the distance measured regarding the reference picture (i.e., accuracy) and also with each other (i.e., precision). **Change in the position of the camera in the X direction** To measure the change in position of the camera in the X direction, a reference point was selected at the center of the board installed on the scene. The distance between this point and the center of the camera lens (i.e., the center of the picture) was measured for all pictures (Figure 15). Since the scales of the pictures were different, these distances were converted into a single scale to become comparable. To find the change in position of the camera, the average distances were compared with the distance measured in the reference picture (i.e., accuracy) and also with each other (i.e., precision). **Change in the orientation of the camera around the Y-axis (roll)** To measure the orientation of the camera around the Y-axis, a horizontal line that crossed the center of image was drawn. Then, a protractor was used, and the angle that this line made with the image was measured as rotation around the Y-axis. To find the change in orientation of the camera around the Y-axis, the average rotations for each group were compared with the reference rotation (i.e., accuracy) and also with each other (i.e., precision). **Change in the orientation of the camera around the Z-axis (head)** Since the images were two-dimensional, the rotation angle of the camera around the Z-axis was not easy to measure. Therefore, other variables were considered. These variables are the length of the left and right sides of an image that change when the rotation around the X-axis occurs. Turning the camera to the left expands the left side and reduces the right side, and vice versa (Figure 16). Knowing these principles, the left and right sides for all pictures from both groups were measured, and then the ratio for each one was measured (i.e., ratio = smaller vertical side/larger vertical side). Figure 14: The method used to calculate the camera distance to the scene (adapted from [57]). Figure 15: Distance between center of lens and center of the board installed on the wall. To understand the relationship between the camera's orientation and these ratios, a separate test was conducted. In this test, a scene was provided, and a camera was installed on a tripod. The camera lens was leveled and located in a parallel position to the scene. The camera had only one degree of freedom around the Z-axis. In this condition, the first picture was captured. Next, the camera was rotated 10 degrees around the Z-axis, and the second picture was captured.