# Development of Height Indicators using Omnidirectional Images and Global Appearance Descriptors
## 5 Experiments and Results
### Results  
This subsection presents the results of the experiments. First, the computational cost of the altitude estimation process is shown. Second, the accuracy of the methods to estimate the altitude is analysed, according to the experimental configurations explained above. To study the computational cost, the experiments have been carried out using Matlab running on a 2.4 GHz Intel Core i5 processor. Table 5 shows the results. We analyse separately the necessary time to describe a reference image (column \(t_{Ref}\) in the table) and the necessary time to describe a test image, compare it with the reference image and estimate the relative height (column \(t_{Test}\) in the table). In general, in the case of global-appearance methods, \(t_{Ref}\) tends to be higher than \(t_{Test}\) because describing the reference image implies using different cells in the method 1 (Central Cell Correlation method), several scales in the method 3 (Multiscale Analysis) and a number of artificial movements in method 4 (CRS Movement). On the one hand, methods 1 and 2 are the computationally lighter methods. Both of them need less than 0.08 s to describe a reference image and to estimate the relative height of a test image. On the other hand, methods 3 and 4 are more expensive to describe each reference image. Comparing both methods \(t_{Test}\) is lower in the case of the method 4, except when using SFT to describe the images. The combination of the method 4 along with the SFT is, computationally, the most expensive global-appearance choice. Comparing with the local-features method (method 5), all the global-appearance methods present a lower \(t_{Test}\), except method 4 with the SFT. In typical applications, a set of images is usually available initially to create a model of the environment. Using this model, the height of the robot can be estimated subsequently. This way, the description of the reference image is a process that can be carried out offline, during the creation of the model. Also, we have given priority to the precision over the computational cost to describe the reference image in this work. In a real application, the number of scales, cells or artificial movements could be reduced depending on the accuracy required. Once the model is available, during the localization process, the necessary time to estimate the height is \(t_{Test}\). This time is critical so that the \begin{table}
\begin{tabular}{c c c c} \hline \hline \(\Delta h\) & \(\Delta z\) (cm) & **\# Experiments Outdoors** & **\# Experiments Indoors** \\ \hline
**2** & 30 & 100 & 90 \\
**4** & 60 & 80 & 68 \\
**6** & 90 & 60 & 46 \\
**8** & 120 & 40 & 25 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Configuration of the experiments considered in condition (**c3**). Height gaps considered and number of experiments for the outdoor and indoor sets of imagesrobot can navigate in real time. Table 5 shows that all the algorithms proposed present a reasonable \(t_{\mathit{Test}}\) to be implemented in a real application. The greatest part of this time is used to describe the test image. This implies that once described, comparing it with a number of reference images would be a very quick process. Table 6 shows the size of the descriptor for every configuration analysed. The table shows separately the necessary memory to store the descriptor of a reference image (\(Mem_{\mathit{Ref}}\)) and the descriptor of a test image (\(Mem_{\mathit{Test}}\)). In general, the size of the FS descriptor is similar to the SFT, and the 2D-DFT is the most compact descriptor. Global-appearance methods tend to produce more compact descriptors for the test image, compared to the local-features method. After studying the computational cost, the accuracy in height estimation will be analysed in the next paragraphs. The results will be represented graphically using the average value of the estimations \(vs\) the actual height of the test image \(h_{\mathit{test}}\), according to Table 2. Standard deviation bars are also shown on each data point.