# Correlation Analysis between UBD and LST in Hefei, China, Using Luojia1-01 Night-Time Light Imagery
## 3 Methodology
### UBD Estimation Model and Verification
Step 2: For the binarized image, there is mainly interference from other artificial objects such as buildings, and the buildings are usually a combination of regular rectangular shapes, but the roads are strip-shaped. The shape feature processing should be conducted to the image because roads have a certain width. By calculating the area of the segmented region and setting a certain threshold, it is possible to effectively remove small patches that may exist after the binarization process. Rectangularity is a measure of the target rectangle, which is defined as the ratio of the area of the target graph to the smallest rectangle area surrounding the graph. The formula of rectangularity is as follows:  
\[S=S_{o}/S_{m}, \tag{3}\]  
where \(S_{o}\) is the area of the target graph; \(S_{m}\) is the area of the smallest rectangle surrounding the graph. \(S\) can indicate how close the target object is to the rectangle. The range of rectangularity is \((0,1)\). The aspect ratio can reflect the slenderness of the object, and it can be used to extract areas with significant length features. Aspect ratio is expressed as:  
\[R=L_{m}/W, \tag{4}\]  
where \(L_{m}\) the length of the minimum circumscribed rectangle; \(W\) is the width of the smallest circumscribed rectangle. In this paper, the area, the aspect ratio, and the rectangularity were respectively set to 20, 2.5, and 0.36. Extensive use of these features can effectively remove non-road targets that are isolated from the road. Furthermore, through further processing by morphological filtering, the road edge is refined and smoothed to obtain the final road information [53]. Step 3: As the brightness value around the road is higher than the actual values in the Luojia1-01 images, the extracted road information was used to cover the Luojia1-01 NTL imagery, and K-means clustering was used for Luojial-01. The principle is to cluster the brightness values around the road in order to take the average value and fill the brightness value of the road. From the comparison shown in Figure 6, we can see that eliminating the interference of road light sources improved the accuracy: the correlation between the sample area NTL and the actual UBD was raised from 0.6530 to 0.7806. Figure 6: Scatter diagrams of the polynomial fitting results of the actual UBD and night-time light (NTL) of the 320 sample areas: **(a)** Before stripping the road area; and **(b)** After stripping the road area. After stripping the road area of the sample area, the UBD values of samples of the 32 types of NTL intensity were averaged, and the calculation formula was as follows:  
\[\rho_{c}^{*}=\frac{\sum_{i=1}^{N}(S_{a_{i}}-S_{b_{i}})}{(S\times N)}=\frac{\sum_ {i=1}^{N}(\rho_{a_{i}}-\rho_{b_{i}})}{N} \tag{5}\]  
where \(\rho_{c}^{*}\) is the average UBD of the \(c\)-type NTL intensity sample area; \(N\) is the number of samples; \(\rho_{a_{i}}\) is the UBD of the \(i\)th sample in the \(c\)-type NTL intensity sample area; \(\rho_{b_{i}}\) is the density of the road in the \(i\)th sample area of the \(c\)-type NTL intensity sample area; \(S\) is the area of the sample area; \(S_{a_{i}}\) is the construction area of the \(i\)th sample area of the \(c\)-type NTL intensity sample area; and \(S_{b_{i}}\) is the road area of the \(i\)th sample area of the \(c\)-type NTL intensity sample area. A segmented linear regression was used to fit the relationship between the average building density and the light intensity in the 32 sample areas, and the average UBD estimation model under different NTL intensities was obtained by:  
\[\rho_{c}= \begin{cases}4.5053\text{g}+0.9323,&0<\text{g}\ll 14.319\\ 0.1599\text{g}+29.009,&\text{g}>14.319\end{cases}  \tag{6}\]  
where \(g\) is the brightness of Luojia1-01 NTL and \(\rho_{c}\) is the average UBD of the NTL intensity classification sample area. Figure 7 is a schematic diagram of the segmented linear regression with a coefficient \(R^{2}\) of 0.9616 and 0.8949.