# Line Matching Based on Viewpoint-Invariance for Stereo Wide-Baseline Aerial Images
## 4 Experiment and Analysis
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Data** & **Resolution** & **Pixel Size (um)** & **Focal Length (mm)** \\ \hline \multirow{2}{*}{Image pair 1} & Down-looking & 1326 \(\times\) 1988 & 4.52 & 35.0 \\  & Back-looking & 1988 \(\times\) 1326 & 4.52 & 50.0 \\ \hline \multirow{2}{*}{Image pair 2} & Down-looking & 2817 \(\times\) 1795 & 6.8 & 47.2 \\  & Back -looking & 2184 \(\times\) 1620 & 6.8 & 80.2 \\ \hline \multirow{2}{*}{Image pair 3} & Left-looking & 2622 \(\times\) 1944 & 6.8 & 80.1 \\  & Forward-looking & 2571 \(\times\) 1916 & 6.8 & 80.1 \\ \hline \multirow{2}{*}{Image pair 4} & Left-looking & 2622 \(\times\) 1944 & 6.8 & 80.1 \\  & Right-looking & 2613 \(\times\) 1933 & 6.8 & 80.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of the four groups of data. Figure 8: _Cont._  
Figure 7: Four pairs of original images. (**a**) Image pair 1; (**b**) Image pair 2; (**c**) Image pair 3; (**d**) Image pair 4. The red rectangle indicates a rectangular building and the red circle indicates a round object, respectively, on the original images. The quadrilateral areas formed by green lines and the image boundary are flat areas and outer areas are fluctuant areas. From the above rectified images, it can be seen that the geographic orientation of every two images in each rectified image pair is the same; that is to say, perspective projections unify the images into the geodetic coordinate system. As a whole, the effective contents of the original images changed into trapezoids in rectified images. Especially for several side-looking images, the perspective distortion effects are large and the trapezoidal effects are obvious. It can also be seen that scenes close to cameras are compressed. The effective contents of down-looking images are approximate parallelograms due to the small viewing angles. Paying attention to the local details, it is observed that the trapezoidal or parallelogram structure (represented by a red rectangle) in the original side-looking image (image pair 3 in Figure 7) becomes an approximate rectangle (Figure 9a) in the rectified image (image pair 3* in Figure 8), and the ellipse (represented by a red circle) becomes a nearly perfect circle (Figure 9b). Next, the original and rectified images were processed using the LJL algorithm to obtain line matching results. We use several different colors to help distinguish whether one match is correct. The number of correct matches, the total matching, and the matching accuracy rates are displayed directly in Figures 10-13, respectively. Figure 8: Rectified images with perspective projection transformation. (**a**) Image pair 1*; (**b**) Image pair 2*; (**c**) Image pair 3*; (**d**) Image pair 4*. The red rectangle indicates a rectangular building and the red circle indicates a round object, respectively, on the rectified images. Figure 9: Partial perspective rectification: (**a**) a trapezoid becomes a rectangle after rectification; (**b**) an ellipse becomes a circle after rectification. Figure 11: Comparison of the line matching results of the second image pair between original images and rectified images: (**a**) original images, \(130/166/78.3\%\); (**b**) rectified images, \(520/558/93.2\%\). Figure 12: Comparison of the line matching results of the third image pair between original images and rectified images: (**a**) original images, \(0/14/0\%\); (**b**) rectified images, \(345/397/86.9\%\). Figure 10: Comparison of the line matching results of the first image pair between original images and rectified images: (**a**) original images, \(117/186/62.9\%\); (**b**) rectified images, \(238/301/79.1\%\). Figure 13: Comparison of the line matching results of the fourth image pair between original images and rectified images: (**a**) original images, \(2/15/15\%\); (**b**) rectified images, \(332/374/88.8\%\). Finally, line segments matched on rectified images are back-projected to the original images, as shown in Figure 14. It can be seen that the accuracy and effect of the back-projected line segments are very good.