# Color Point Cloud Registration Algorithm Based on [PERSON]
## 2 Color Theory Analysis  
RGB color space contains three independent basic colors and is currently the most widely used color space in computer vision. However, it does not reflect human visual perception very well, so it is not efficient when dealing with'real world' images. For point cloud collected from different locations, it is required that the color is the same, otherwise, the optimization will be led in the wrong direction, producing the wrong results. However, due to the influence of lighting conditions, the color represented by red, green, and blue usually change a lot when the lighting changes. In order to use color information correctly, the difference caused by lighting conditions should be reduced.  
HSV color space is based on three components, hue (H), saturation (S), and value (V), and is used to approximate how people perceive and understand colors [15; 16; 17; 18]. Hue is represented by an angle between 0 and 360 degrees, and its normalized formula from RGB color space is as follows:  
\[H=\begin{cases}0,&if\quad max(R,G,B)=min(R,G,B)\\ \frac{1}{6}\frac{G-B}{max(R,G,B)-min(R,G,B)},&if\quad max(R,G,B)=R\quad and \quad G\geq B\\ \frac{1}{6}\frac{G-B}{max(R,G,B)-min(R,G,B)}+1,&if\quad max(R,G,B)=R\quad and \quad G<B\\ \frac{1}{6}\frac{B-R}{max(R,G,B)-min(R,G,B)}+\frac{1}{3},&if\quad max(R,G,B)=G \\ \frac{1}{6}\frac{R-G}{max(R,G,B)-min(R,G,B)}+\frac{2}{3},&if\quad max(R,G,B)=B \end{cases} \tag{1}\]It can be seen that for each case, the hue information maps the ratio of the difference between the two smaller components of the RGB, which represents a kind of proportional information. When the ratio of the three color components of the RGB is fixed, the hue information does not change with the intensity of the color component, so it represents the relative brightness of the image. Because the changes caused by lighting conditions affect each component of RGB equally and the ratio of each component's change is fixed, using the relative brightness of RGB to represent color information can reduce the impact of lighting condition, so the hue has better robust than the gray information when representing absolute shading in different lighting conditions. This theory is then proved through experiments.  
Figure 1 shows the gray and hue of the same scene under different lighting conditions. The difference map represents how much it would change under different lighting conditions. It is obvious that hue information changes much less than gray, which demonstrates that hue has better lighting robustness than gray. We choose the sum square distance (SSD) of two point clouds to measure the color similarity between them. It can be calculated by the following formula:  
\[SSD(P,Q)=\frac{1}{N}\sum_{i=1}^{N}(C(p_{i})-C(q_{i}))^{2} \tag{2}\]  
where \(p_{i}\) and \(q_{i}\) represent the corresponding point in two point clouds \(P\) and \(Q\), respectively, and \(C(\cdot)\) represents the color information used. Since the point clouds collected are the same scene and only the lighting conditions are different, the color information at the same location should theoretically be the same, so a smaller SSD represents better robustness.  
We used the ASTRA Pro RGBD Scanner depth camera to collect the data. The camera position and the layout of the scene are kept unchanged, and different lighting conditions are simulated by changing the exposure time of the camera. First, take a frame as a reference  
Figure 1: The comparison of the same scene at different lighting conditions.  
point cloud, then change the camera exposure time to take multiple pictures under different lighting conditions.  
Figure 2 shows the SSD of gray and hue under different lighting conditions. The x-axis of the figure represents the exposure time of the camera, representing different lighting conditions. It can be seen that the SSD of hue is three orders of magnitude lower than gray, which fully demonstrates that the hue is more robust to lighting conditions than gray.