# Development of Height Indicators using Omnidirectional Images and Global Appearance Descriptors
## 3 Development of Height Indicators Using Global Appearance Descriptors
### Method 1: Central Cell Correlation of Panoramic Images  
In a panoramic image, the most distinctive information is usually in the central rows of the scene. In outdoor environments, the bottom rows normally correspond to the terrain, and the upper rows to the sky and in indoor environments they correspond to the floor and ceiling respectively. If the altitude of the catadioptric system changes whether upwards of downwards, the area constituted by the central rows of the panoramic image is less likely to go out of the camera field of view. Taking this fact into account, in this method, the global appearance of the central rows of the reference and test images is compared to estimate the relative height between their capture points.  
First, the algorithm computes a global appearance descriptor of the central cell of \(im_{R}\) (the portion composed by the central rows). To obtain this descriptor either the FS (Section 2.2.1) or the 2D-DFT (Section 2.2.2) can be used. This process is repeated for different cells situated above and below the central cell. In Figure 4 a sample image and some cells extracted from it are shown. The central cell is emphasized with a wider line, and some additional cells have been defined both above and below it. \(d\) is the vertical distance (measured in pixels) from each additional cell to the central one.  
Considering now a test image \(im_{T}\), the algorithm computes the descriptor of the central cell, compares it with all the descriptors of the cells extracted from \(im_{R}\) and retains the best match. The position (\(d\)) of the cell in \(im_{R}\) that best matches the central cell of \(im_{T}\) is a measurement of the relative altitude. Therefore, the displacement is measured in pixels and it can be considered as a topological distance  
To illustrate this method, two 128 \(\times\) 512 panoramic images captured from different heights are considered (Figure 5). On the one hand, Figure 5a is the reference image (\(im_{R}\)). On the other hand, Figure 5b is the test image (\(im_{T}\)) and it was captured from a height 60 cm higher than \(im_{R}\). In this example, the size of the cells is equal to 64 \(\times\) 512 pixels and FS is used to describe these cells.  
First, \(im_{R}\) is considered and its central cell is extracted. After that, the FS of this cell is calculated and its magnitudes matrix is obtained. The result is the descriptor \(A_{R}^{(0)}\), where the superscript \((0)\) indicates that this is the descriptor of the central cell. This process is repeated for different cells situated  
Figure 4: Set of cells defined in a reference panoramic image for height estimation using the central cell correlation technique.  
Figure 5: Two panoramic images captured from different heights, to illustrate method 1. (**a**) Reference image and (**b**) test image.  
above and below the central cell. To do it, a set of cells is considered, whose distances to the central cell are, in this example, \(d=[-25,-24,\ldots,-1]\cup[1,2,\ldots,25]\) pixels. After that, the descriptors of the cells \(A_{R}^{(d)}\) will be available, where the superscript \((d)\) indicates the distance to the central cell.  
Second, \(im_{T}\) is considered. Its central cell is extracted, the FS of this cell is calculated and the magnitudes matrix is obtained. The result is the descriptor \(A_{T}^{(0)}\).  
When all this information is available, the algorithm calculates the Euclidean distance (Equation (6)) between the descriptor \(A_{T}^{(0)}\) and each of the descriptors \(A_{R}^{(d)}\), considering \(d=[-25,-24,\ldots,-1,0,1,\ldots,24,25]\). The distance \(d\) associated to the descriptor \(A_{R}^{(d)}\) that best matches \(A_{T}^{(0)}\) can be considered as a height indicator. Figure 6 shows \(dist(A_{T}^{(0)},A_{R}^{(d)})\) versus \(d\). In this case, the minimum is produced at \(d=3\). Since \(d>0\), the height of \(im_{T}\) is higher than \(im_{R}\).