# Development of Height Indicators using Omnidirectional Images and Global Appearance Descriptors
## 3 Development of Height Indicators Using Global Appearance Descriptors
### Method 5: Matching of SURF Features  
The last method makes use of local features extracted from the omnidirectional scenes to estimate topological height. SURF features are used with this aim [45]. This method has been introduced for comparative purposes, since using local features is a mature approach to solve the localisation problem. The method starts extracting and describing the SURF features of the reference and test omnidirectional scenes. After that, a matching process is carried out; the points of the test image are matched with the points of the reference image. Considering a purely vertical movement, the points of the test image will move along the radial direction, towards the centre of the image if the movement is upwards and towards the periphery if the movement is downwards. Taking this fact into account, the matching process can be optimized by searching the possible match along the radial line associated to each point in the test image. Figure 10a shows two sample omnidirectional images captured indoors and superimposed, with a relative vertical movement  
Figure 9: (**a**) Projection of a world point \(P\) onto the image plane before and after the simulated vertical movement and (**b**) omnidirectional images and their panoramic projections considering the two different CRS positions. between them. The SURF points have been extracted from the reference image (red points) and from the test one (green crosses), described, and matched (yellow lines show the matches). This figure shows a number of outliers (those matches which are not produced in the radial direction). Figure 10b shows the same two images, but the matches of the test image SURF points have been searched along the radial line in the reference image. In these sample images, the local features of the test image tend to be closer to the centre of the image. This means that the robot has moved upwards to capture the test image with respect to the reference one. If \(p^{R}=\{p^{R}_{1},p^{R}_{2},\ldots,p^{R}_{n}\}\) and \(p^{T}=\{p^{T}_{1},p^{T}_{2},\ldots,p^{T}_{n}\}\) are, respectively, the set of SURF points extracted and matched from the reference and the test image (where the point \(p^{R}_{j}\) matches the point \(p^{T}_{j}\)), then, the average distance between each pair of matched points (Figure 10b) can be considered as a topological measurement of the height difference between images:  
\[d_{1}=\frac{1}{n}\cdot\sum_{i=1}^{n}dist\{p^{T}_{i},p^{R}_{i}\}, \tag{14}\]  
where \(dist\{p^{T}_{i},p^{R}_{i}\}\) is the Euclidean distance between \(p^{T}_{i}\) and \(p^{R}_{i}\). This distance is considered positive when \(p^{T}_{i}\) is closer to the centre than \(p^{R}_{i}\) and negative otherwise. This indicator is expected to provide a topological estimation of height. Furthermore, its linearity will depend on how linear the average displacement of the corresponding SURF points is when the omnidirectional vision systems changes its altitude. A popular alternative to obtain more robust results from the corresponding landmarks is the use of RANSAC (RANdom SAmple Consensus) [46]. An example of application in mobile robotics can be found in [47]. This way, in this paper, we also propose using RANSAC to estimate the relative topological altitude. Initially, a random subset of matched points can be used to have an estimation of the relative altitude, \(d_{2}\), calculated using Equation (14). After that, the rest of matched points can be used to corroborate this estimation. A pair of matched points corroborates this estimation if the distance between them is equal to \(d_{2}\) plus or less a specific threshold. After repeating this process a number of times with different initial subsets of matched points, the estimation \(d_{2}\) which is corroborated by a higher number of matched points is considered a measurement of the relative altitude. During the experiments, both methods will be considered.