# Development of Height Indicators using Omnidirectional Images and Global Appearance Descriptors
## 5 Experiments and Results
### Results
Figure 16 presents the results obtained outdoors in conditions (**c1**) and (**c2**) (considering \(h=1\) and \(h=5\) as reference images, blue continuous and green dashed curves respectively). In all cases, the height measurement behaves monotonically increasing as the actual height of the test image rises. Moreover, when the height of the test image is below the reference image (in the case of \(h_{\mathit{ref}}=5\)), indicators are negative. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Height Estimation Method** & **Image Projection** & **Descriptor** & \(Mem_{\mathit{Ref}}\) **(KB)** & \(Mem_{\mathit{Test}}\) **(KB)** \\ \hline \multirow{2}{*}{**1. Central Cell Correlation**} & \multirow{2}{*}{Panoramic Image} & FS & 1312 & 32 \\ \cline{3-5}  & & 2D-DFT & 328 & 8 \\ \hline \multirow{2}{*}{**2. 2D-DFT Vertical Phase**} & \multirow{2}{*}{Panoramic Image} & 2D-DFT & 8 & 8 \\ \cline{3-5}  & & & & 8 \\ \hline \multirow{2}{*}{**3. Multiscale Analysis**} & \multirow{2}{*}{Orthographic View} & FS & 3904 & 64 \\ \cline{3-5}  & & 2D-DFT & 488 & 8 \\ \hline \multirow{2}{*}{**4. Camera Reference Movement**} & \multirow{2}{*}{Panoramic Image} & FS & 1296 & 16 \\ \cline{3-5}  & & 2D-DFT & 162 & 8 \\ \cline{3-5}  & & FS & 2496 & 64 \\ \cline{3-5}  & & 2D-DFT & 312 & 8 \\ \cline{3-5}  & & ViT & 1952 & 64 \\ \hline \multirow{2}{*}{**5. Matching Local Features**} & \multirow{2}{*}{Omnidirectional Scene} & SURF & 99 & 99 \\ \cline{3-5}  & & SURF-RANSAC & 99 & 99 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Necessary memory to store all the necessary information from a reference image, \(Mem_{\mathit{Ref}}\), and to store the information from a test image, \(Mem_{\mathit{Test}}\). \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Height Estimation Method** & **Image projection** & **Descriptor** & \(t_{\mathit{Ref}}\) **(s)** & \(t_{\mathit{Test}}\) **(s)** \\ \hline
**1. Central Cell Correlation** & \multirow{2}{*}{Panoramic Image} & FS & 0.0450 & 0.0011 \\ \cline{3-5}  & & 2D-DFT & 0.0709 & 0.0017 \\ \hline
**2. 2D-DFT Vertical Phase** & Panoramic Image & 2D-DFT & 0.0032 & 0.0662 \\ \hline \multirow{2}{*}{**3. Multiscale Analysis**} & \multirow{2}{*}{Orthographic View} & FS & 11.5117 & 0.1908 \\ \cline{3-5}  & & 2D-DFT & 10.6323 & 0.1800 \\ \hline \multirow{3}{*}{**4. Camera Reference Movement**} & \multirow{2}{*}{Panoramic Image} & FS & 11.8509 & 0.0405 \\ \cline{3-5}  & & 2D-DFT & 11.3911 & 0.0385 \\ \cline{3-5}  & & FS & 11.6408 & 0.0273 \\ \cline{3-5}  & & 2D-DFT & 11.3409 & 0.0241 \\ \cline{3-5}  & & & 17.8813 & 0.2985 \\ \hline \multirow{3}{*}{**5. Matching Local Features**} & \multirow{2}{*}{Omnidirectional Scene} & SURF & 0.0939 & 0.2354 \\ \cline{3-5}  & & SURF-RANSAC & 0.0978 & 0.3810 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Computational cost to describe a reference image, \(t_{\mathit{Ref}}\) and to describe a test image and estimate its relative height, \(t_{\mathit{Test}}\). Figure 16: Results of the experiments in conditions (**c1**) (blue continuous) and (**c2**) (green dashed curves), considering all the combinations _method-image projection-descriptor_ shown in Table 3. Outdoor images. (**a**) Method 1 + Pano. Im. + FS. (**b**) Method 1 + Pano. Im. + 2D-DFT. (**c**) Method 2 + Pano. Im. + 2D-DFT. (**d**) Method 3 + Orthogr. View + FS. (**e**) Method 3 + Orthogr. View + 2D-DFT. (**f**) Method 4 + Pano. Im. + FS. (**g**) Method 4 + Pano. Im. + 2D-DFT. (**h**) Method 4 + Orthogr. View + FS. (**i**) Method 4 + Orthogr. View + 2D-DFT. (**j**) Method 4 + Unit Sphere Proj. + FFT. (**k**) Method 5 + SURF. (**l**) Method 5 + SURF + RANSAC. When the actual height difference is lower than \(\Delta h=3\) (\(\Delta z=45\) cm), the standard deviation in all cases is low enough to determine the relative height between images unequivocally. In general, the variance of the results is high for test images that were captured far away of the reference image.