## 4 Results
### 3D Reconstruction Results  
Once we have the matching points in both catadioptric cameras, the next step is to transform those points into the mirrors. Figure 8(a) shows the Harris corners (which was the runner-up method in terms of the number of features) on the upper parabolic mirror (PMU) and the lower panoramic mirror (PML). Similarly, Figure 8(b) shows the DeepMatching points on each of the mirrors. As described in Section 4.3, DeepMatching provides broader coverage and density than all the other methods (see Figures 6 and 7) shown in Table 3 resulting in a more well-rounded reconstruction. The third columns of Figures 6 and 7 show the reconstruction of an outdoor scenario with features obtained with the methods presented in Table 3. Figure 8(a)-c show the Harris corners matches and the reconstruction, Figure 8(d)-f using KAZE, Figure 8(g)-i applying SuperGlue, Figure 8(j)-l employing SURF, Figure 8(m)-o with SIFT, and Figure 7 with DeepMatching. For this challenging outdoor environment, we see that the reconstructions generated with the feature matches from all these methods are poor due to the lack of feature density and coverage except for the DeepMatching method, where the features can cover most of the image as shown in Figure 7.  
Although DeepMatching returns many feature matches, not all of them are correct. To fix this, we use epipolar constraints as described in Section 3.2. Figure 8(a),b show the unfiltered DeepMatching results along with the 3D reconstruction in Figure 8(c). Figure 8(d),e show the DeepMatching results filtered with \(d=30\) pixels. Figure 8(f) shows the reconstruction with these filtered features points. Figure 10 shows the point clouds reconstructed using the Deep features matches with the different filtering levels. As the images show, when we relax the filter (when \(d\) is larger), we get more features but also more errors in the background. Figure 10: 3D reconstruction using DeepMatching. Figures (**a**–**c**) show the reconstruction with features filtered at \(d=5\), \(d=10\), and \(d=20\) respectively. Figure 9: Matching points in the panoramic mirrors (best seen in color). Pink points denote the features in the panoramic upper mirror PMU, and blue points are the features on the panoramic lower mirror PML. (**a**) Shows Harris corners on the mirrors, and (**b**) shows the DeepMatching points on the mirrors. To quantify the reconstruction error, we reconstruct an object with known dimensions, in this case a rectangular pattern of size 50 cm \(\times\) 230 cm. Figure 11 shows the results obtained with DeepMatching. Figures 11a,b show the unfiltered DeepMatching features and Figure 11c shows the 3D reconstruction. Figures 11d,e show the filtered matches with \(d=15\) and Figure 11f shows the 3D reconstruction. From Figure 11 we see that the filtering of the features using epipolar constraints produces a cleaner reconstruction without compromising the density. Using the rectangular pattern with known dimensions, we calculate the reconstruction's error at the center of the pattern and the extremes. At the right extreme, the error correlates with a larger distortion on the periphery of the mirror. Table 4 shows the mean reconstruction error in millimeters and the standard deviation. To evaluate the qualitative results of the 3D reconstructions, we reconstructed three more objects shown in Figure 12. A squared box, a hat, and a clay pot. For the squared box shown in Figure 12a, we computed the angles between normal vectors of adjacent planes compared with 90\({}^{\circ}\). The results are shown in Table 5. In this table, we compared the angle errors with [4] achieving slightly better results with one stereo pair. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Mean Error (mm)** & **Standard Deviation (mm)** \\ \hline Pattern right & 20.59 & 2.23 \\ Pattern center & 8.74 & 4.89 \\ Pattern left & 9.57 & 5.56 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Reconstruction error in millimeters.