# SMILE: Segmentation-Based Centroid Matching for Image Rectification via Aligning Epipolar Lines
## 4 Experiments
### Experimental Results  
Conventional camera calibration algorithms utilize precise patterns such as checkerboards to perform feature point detection, matching, and iterative nonlinear optimization. As a result, their computational complexity depends on the number of feature points \(n\), ranging from \(O(n)\) to \(O(n^{2})\) in the worst case. In contrast, the proposed SMILE method employs YOLOv9-based object detection, followed by simple 2D transformations--rotation, translation, and padding--applied to each detected object region. These subsequent matrix operations operate linearly with respect to the number of pixels \(m\) in the segmented object regions, resulting in a complexity of \(O(m)\). In the actual experiments, the average total processing time was measured to be 0.07 s, confirming the feasibility of real-time application even in high-resolution image environments. Furthermore, theoretical FLOPs analysis also indicates that SMILE has lower computational complexity compared to traditional methods. Figure 3 shows the input images used in the experiments, the visualization of feature point matching, and the resulting disparity maps. These are presented sequentially, first with the original images and then with the images adjusted according to the method proposed in this paper. It can be observed that in the images rotated using the proposed method, the lines connecting the matching points are generally more horizontally aligned compared to the original images. In some cases, disparity maps could not be generated from the original images, but, after applying the proposed rotation and adjustment, disparity maps were successfully generated. Figure 3: _Cont._  
Table 2 shows the evaluation results of the experiment using the fundamental matrix. If the fundamental matrix takes on the value given in Equation (18), it was considered that the rectification was performed accurately. Compared to the original images, after applying the method proposed in this paper, it was observed that in some cases, large values such as one to two were reduced to below one. Overall, the matrix becomes more simplified and the scale of the values is reduced. This indicates that the epipolar geometry was rearranged into a simpler form. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Original** & \multicolumn{4}{c}{**Rectified**} \\ \hline  & A-1 & \multicolumn{4}{c}{A-2} \\ \hline \(-0.0000\) & \(0.0000\) & \(-0.0005\) & \(-0.0000\) & \(0.0000\) & \(-0.0  
Table 3 shows the average values of Y-disparity, X-disparity entropy, SSIM, feature matching accuracy, and area-based correlation for both the original images without preprocessing and the images processed using the method proposed in this paper. Y-disparity is further divided into Y-disparity mean and Y-disparity Std. For Y-disparity mean, the original images have a value of 34.61, while the images with the proposed rectification applied have a value of 24.79, indicating that the average y-value difference decreased. This suggested that overall alignment improved. Y-disparity Std, which represents consistency in alignment, actually increased from 46.19 to 56.32, implying that the alignment was not consistent. X-disparity entropy showed identical results of 1.31 for both cases, which is likely because the proposed method focuses on rotation based on the y-coordinate, not affecting the X-disparity entropy. The SSIM values are 0.4210 and 0.4412, indicating that the structural similarity becomes closer through the proposed image rectification. Feature matching accuracy decreased slightly from 0.2650 to 0.2599, but the difference was so small that it was likely not significant. Lastly, the area-based correlation values of 0.3616 and 0.3847 indicated that the correlation between the corresponding regions increased when the rectified images were divided into smaller areas. For most metrics, the image rectification method proposed in this paper demonstrates effectiveness without requiring a calibration pattern. It also achieves a fast average processing time of 0.07 s per image.