## 4 Results and Discussion
### Results of SIFT  
In order to test the improvements to our methodology to determine the homologous points in two DEMs versus standard keypoint matching algorithms, we propose the use of the SIFT algorithm [15]. Because the algorithm is extensively described and programmed in several environments, we have applied the algorithm using the OpenCV [25]. The results are shown in Table 2 using the standard values proposed by [PERSON] [15], without limits in the number of feature detections (octaves = 3; contrast threshold = 0.03; sigma of Gaussian = 1.6; edge threshold = 10). In addition, Table 3 shows the matching results obtained from the SIFT BFMatcher algorithm from OpenCV [25]. First, it is important to note that not all keypoints can be used in the search of homologous pixels between two DEMs of the same zone. With respect to the results, the comparison between DTM25 and DSM05 or DTM05 has a scale near 0.2 that reflects the difference in resolution of the pixel indicated in Section 3, while the comparison between DSM05 and DTM05 has a scale similar to 1. In addition, the precision of the transformation is good when the number of the match is low, which could represent a great dispersion in the keypoints' results and distribution. \begin{table}
\begin{tabular}{c c} \hline
**DEM-ID** & **\#Keypoints** \\ \hline DTM25-0946 & 11 \\ DTM05-0946 & 9 \\ DSM05-0946 & 8 \\ \hline DTM25-1008 & 40 \\ DTM05-1008 & 45 \\ DSM05-1008 & 41 \\ \hline DTM25-1027 & 27 \\ DTM05-1027 & 27 \\ DSM05-1027 & 27 \\ \hline DTM25-1034 & 22 \\ DTM05-1034 & 24 \\ DSM05-1034 & 23 \\ \hline \end{tabular}
\end{table} 
Table 2: Number of keypoints obtained from SIFT algorithm. Figure 5: Distances in rows and columns of the matched keypoints (red: vertical; blue: horizontal). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**DEM-ID 1** & \multirow{2}{*}{**DEM-ID 2**} & **Mean Scale** & \multirow{2}{*}{**Rotation**} & \multirow{2}{*}{\(\hat{\rho}_{\mathbf{0}}^{2}\)} \\ (Reference) & & **(X/Y)** & & \\ \hline DSM05-0946 & DTM05-0946 & \(1.00000771\) & \(-0.000273299\) & \(2.9712019\) \\ DTM25-0946 & DSM05-0946 & \(4.999898885\) & \(0.000460667\) & \(43.7015771\) \\ DTM25-0946 & DTM05-0946 & \(4.99976919\) & \(-0.001847645\) & \(42.6738983\) \\ \hline DSM05-1008 & DTM05-1008 & \(1.00001888\) & \(-0.000348352\) & \(2.98831609\) \\ DTM25-1008 & DSM05-1008 & \(4.99759005\) & \(-0.000261853\) & \(44.5912646\) \\ DTM25-1008 & DTM05-1008 & \(4.99858267\) & \(-0.00105328\) & \(40.2658607\) \\ \hline DSM05-1027 & DTM05-1027 & \(0.99997725\) & \(-4.98485\times 10^{-5}\) & \(2.56474212\) \\ DTM25-1027 & DSM05-1027 & \(4.99907199\) & \(-0.01462987\) & \(49.0939488\) \\ DTM25-1027 & DTM05-1027 & \(4.99895135\) & \(-0.016072889\) & \(46.0422685\) \\ \hline DSM05-1034 & DTM05-1034 & \(0.99999601\) & \(0.000655466\) & \(2.6222421\) \\ DTM25-1034 & DSM05-1034 & \(4.99897657\) & \(0.00246365\) & \(52.7526375\) \\ DTM25-1034 & DTM05-1034 & \(4.99930689\) & \(0.009161375\) & \(50.3271811\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Matching results of the proposed algorithm (\(\hat{\rho}_{\mathbf{0}}^{2}\) is the variance of the mean square adjustment between both DEMS). Figure 6: Total distance of matched keypoints. After reviewing the correlation values (see Figure 4) a great number of pixels that matched between both DEMs were observed; in fact, the majority of pixels from the DEM with the smaller size were obtained, and the number was always greater than 80%. In addition, most of the pixels were close to 1, except for zones 1008 and 1027 between DEMs of different resolutions. On the other hand, Figure 5 shows the pixel distance along each axis with different colors for the pixels in the image (not the reference image). A first look reveals that the match between DTM05 and DSM05 only had a maximum distance of 2 pixels, but the distance between DTM25 and the others was up to 10 pixels. These values are defined by the initial scale from the first transformation. Additionally, the graphics indicate a difference between each axis.