# Development of Height Indicators using Omnidirectional Images and Global Appearance Descriptors
## 5 Experiments and Results
### Results
This effect is specially pronounced when using panoramic images, both with the central cell correlation (Figure 16a,b), and with the CRS movement methods (Figure 16f,g). A high variance in the results means that the indicator is not reliable in those height gap ranges. On the other side, the configurations that use orthographic projections tend to present a relatively low variance. The results of the 2D-DFT Vertical Phase method (Figure 16c) present a high variance for those test images which are distant from the reference image. It is important to highlight that, as presented in Section 3.2, this method is based on the DFT shift theorem, which assumes that a pure circular shift of rows occurs. However, when the visual system moves vertically, new information is introduced and other existing disappears. This fact produces a difference in the 2D-DFT coefficients that implies an intrinsic error on the vertical phase estimation. As the height gap between images increases, this error tends to be more significant. As far as description methods are concerned, in the case of panoramic and orthographic projections, results do not present remarkable differences between the FS and the 2D-DFT, although the variance is slightly lower using the first descriptor. About the unit sphere projection, no comparative can be carried out as the only method to describe this projection is the SFT. Its results show a clear linear tendency, whereas deviation of the results is high for vertical gaps higher than 60 cm. As a conclusion, the techniques that use the orthographic view tend to present a quite linear behaviour with a relatively low variance in outdoor environments. Also, no relevant differences can be found in the linearity of global-appearance methods comparing to local-features methods. However, some global-appearance configurations present an improved deviation. Figure 17 shows the results obtained indoors in conditions (**c1**) and (**c2**) (considering \(h=1\) and \(h=5\) as reference images, blue continuous and green dashed curves respectively). To make it possible a homogeneous comparison, the same scale is used in the equivalent subfigures in Figures 16 and 17. Compared to the outdoors results, the sensitivity of the height indicators is higher as the slope of the curves is greater, specially when using the panoramic projection. The main reason for this behaviour is the relative distance of the elements with respect to the catadioptric vision sensor. Indoors, the elements of the environment are generally closer to the catadioptric system than outdoors. For this reason, when the height of the visual system changes, the distribution of the elements in the image suffers a greater variation, since the angle of incidence of the rays that represent the objects has also a higher variation. Figure 18 presents the variation of the angle of incidence of two world points \(P_{1}\) and \(P_{2}\) whose distance to the vision system is different, when the height of this system changes. The figure shows that \(\alpha_{1}\), which represents the change of the angle of projection of the closest point (\(P1\)) is higher than the angle of \(P2\) (\(\alpha_{2}\)). Moreover, the objects in an indoor scene generally present a greater range of distances with respect to the visual system. For that reason, when the catadioptric system moves vertically, the objects contained in the scenes experience movements with different magnitude depending on the distance from these objects to the catadioptric system. Figure 19 shows the panoramic view of two images captured from the same ground point but with different heights. We can observe that the element highlighted in red suffers a greater height variation in the scene (\(h_{1}^{\prime}-h_{1}\)) comparing to the object highlighted in green (\(h_{2}^{\prime}-h_{2}\)), which is more distant to the sensor. Also, when the camera is near the ceiling, there is a loss of visual information as the ceiling is more present in the scene.