# GPS-Induced Disparity Correction for Accurate Object Placement in Augmented Reality
## 3 Results
### Results of 3D Object AR Rendering App Implementation and Location Correction  
We focused on the development results of the AR rendering features of 3D objects rather than the server and building updates previously described. Figure 3 illustrates a promotional balloon floating between buildings. The server API retrieves the building's GPS coordinates and height information corresponding to the coordinates of the object, which are then rendered by the application. Invisible barriers are set in the application to ensure proper object rendering. In the sequence of images presented in Figure 3a-d, the balloon's apparent reduction in size as it moves leftward is not due to an actual decrease in size but rather a perspective effect caused by the balloon being obscured by buildings. This visual effect is a result of the viewing angle, where parts of the balloon become hidden, giving the illusion of shrinking. However, GPS inaccuracies contribute to further discrepancies, making the balloon seem partially cut off from the viewer's perspective. The next step was to correct the appearance of the truncated balloon and adjust the location of the device. There are two methods to correct this: recalculating the location of the device, and using semantic segmentation to recognize different buildings and move the balloon accordingly. The selected method involved object segmentation, building recognition, and balloon movement. As shown in Figure 4, object segmentation is specifically applied to isolate each building. Then, we established barriers corresponding to these segmented buildings to ensure that the balloon was correctly displayed. As shown, the building identified in (a) is segmented, as shown in (b), leading us to set up an arbitrary barrier, as depicted in (c). This step is crucial for maneuvering the balloon, culminating in the outcomes shown in (d). This sequence clearly demonstrates the precise alignment of the balloon with the buildings, illustrating the practical application of our segmentation and barrier setup process in enhancing the AR object display. Figure 4: Sequence illustrating the augmented reality object display enhancement process: (**a**) initial segmentation of a building from the urban environment; (**b**) the segmented building is outlined for clarity; (**c**) setting of a virtual barrier around the segmented building; and (**d**) the augmented reality balloon accurately positioned in relation to the building, demonstrating an effective alignment with the urban landscape  
Figure 3: Sequence displaying the movement of an advertising balloon being obscured by buildings. The series from (**a–d**) shows the balloon moving and becoming partially hidden behind buildings, demonstrating the occurrence of distance discrepancies due to occlusion. The proposed equations are used to validate the positional error correction method through numerical analysis. Figure 5 shows the procedure to validate these equations using MATLAB R2022, showcasing a distance and positioning relative to the camera, objects, and buildings for numerical analysis. The left side of the image displays a camera without errors, depicting its position and angle and how the image projects, as described above. Conversely, the right-hand camera shows the projection of the lower image affected by GPS errors, which serve as the basis for our numerical analysis. The rectangles in the left image symbolize buildings, representing real structures. In this depiction, we calculate the projections of \(P(x,y,z)\) into \((x_{\text{pixel}},y_{\text{pixel}})\) and \((x_{\text{pixel\_error}},y_{\text{pixel\_error}})\). Given the world coordinates of object \(P(x,y,z)\) as (21.6, 17.3, 8.4), this point is projected onto the camera space under both error-prone and error-free scenarios. The erroneous and correct image plane coordinates were determined to be \((739.5421,366.0855)\) and \((550.0000,360.0000)\), respectively. These coordinates allowed us to directly observe the influence of GPS errors.