## 2 LEA Detection and Tracking
### ROI Selection for LEA Detection  
An image received by the camera is likely to include a complex background. In addition, the prominent features of LEA are that it has a rectangular shape and might also appear as a blob shape during LED light emission. However, these are very common features that other objects may also include. Therefore, it is not easy to detect the LEA over the entire image. To solve this problem, reference LEDs or reference LEA patterns can be used [3; 5]. However, the use of references can lower the data rate and the appearance of the LEA might not be good. To overcome this weakness, by using the principle of the color space, we specify the ROI for a desired LEA in a received image with a complex background. Because the color-independent visual-MIMO system uses a GCM that is based on a color space, the color information associated with the GCM can be an effective means of LEA detection. Figure 4 presents an example of a circle-type constellation diagram in the CIE1931 color space [15; 16]. The input data symbol is represented by a constellation point (x, y) and each constellation point in the constellation diagram represents a color in the color space. In Figure 4, the target color, i.e., the color perceivable to human eyes after modulation, is the average of all appropriate constellation points. Here, constellation points in the color space can be arranged using a similar arrangement to that used in RF circular quadrature amplitude modulation (QAM). Supposing an equiprobable symbol transmission, which is reasonable, due to the compensation and interleaving algorithms, the target color can be obtained as the averaged RGB value along a number of symbols as shown in Equation (1) [10]:  
\[(x_{t},\,y_{t})=\left(\frac{\sum_{i=1}^{N}x_{i}}{N},\,\,\frac{\sum_{i=1}^{N}y _{i}}{N}\right) \tag{1}\]  
where \((x_{t},\,y_{t})\) denotes the position of a target color and \((x_{i},\,y_{i})\) denotes the position of the \(i_{th}\) symbol. Note that the value of \((x_{t},\,y_{t})\) is closer to the true target color when N is increasing in the probability sense. Here, N is the number of total LEDs of the LED array. Figure 5 shows a received image example in the form of a lattice structure and the corresponding color distribution of the sliding search window area in the CIE1931 color space. In the experiment, we used a Windows 7 library image from Microsoft Corporation as a background. To select the ROI, we divided the image into a grid unit and used a sliding search window. The window consisting of four grids is indicated by the red box in Figure 5. This window is moved by the grid unit and the color distribution of the sliding search window area is analyzed in the CIE1931 color space to determine  
Figure 4: Example of circle-type constellation diagram in the CIE1931 color space. whether the desired LEA exists at that location. In a circle-type constellation diagram, it is important to note that the polygon formed by connecting the coordinate point of each symbol has a constant side ratio and symmetry property. Using these properties, in this paper, we propose an LEA detection method that analyzes the color distribution of a sliding search window area in a CIE color space. To classify the samples distributed in the two-dimensional color space, the \(k\)-means clustering algorithm is used [17]. Then, we select the desired ROI by checking the side ratio and the symmetry property of the polygon generated after the center of each cluster has been connected. Figure 6 shows examples for different locations of sliding search windows and the corresponding color distribution of a window area in the CIE1931 color space. We can see that the color is more uniformly distributed, when the window overlaps more with the desired LEA. To analyze the color distribution, we use the \(k\)-means clustering algorithm [17]. In these examples, the value of \(k\) is 4, and a quadrangle can be formed by connecting the center of each cluster.