# Fusing Ground-Penetrating Radar Images for Improving Image Characteristics Fidelity
## 4 Local Binary Pattern Theory  
The simplicity of the LBP algorithm in assigning a binary value (0 or 1) to each pixel based on the comparison between the selected central pixel and its neighboring pixels makes it one of the most widely used algorithms. The process is governed by the definition of a circular neighborhood as defined in Figure 5, usually of size 3 \(\times\) 3 or 5 \(\times\) 5, and by defining a threshold with the value of which the comparison is made, it is appropriately matched. In this way, combining the received binary values results in a binary string based on which the histogram of the resulting image is constructed [30].  
Figure 4: GPR systems are equipped with two antennas: one as a transmitter and one as a receiver. The transmitter emits electromagnetic waves into the ground, which reflect off subsurface structures. These reflections are captured by the receiver, generating detailed images of hyperbolic responses.  
Based on the idea of this algorithm, variants have been developed, such as the Multilevel Local Pattern Histogram finding good application, for example, in the classification of SAR images [24] and Completed Local Binary Patterns (CLBP), which overcome some limitations, such as sensitivity to rotation. This procedure finds application both in the classification of satellite images and in the evaluation of texture for the classification of vegetation of coastal wetlands [31] and in pattern recognition, as in GPR technology, enabling more accurate subsurface imaging [32; 33].  
The equation that was applied in the proposed method to evaluate the LBP is defined as  
\[\mathrm{LBP_{P}R(x_{c},y_{c})}=\sum_{p=0}^{P-1}s(i_{p}-i_{c})\cdot 2^{p} \tag{4}\]  
where \((x_{c},\ y_{c})\) is the center pixel, \(P\) is the number of sampling points, \(R\) is the radius, \(i_{c}\) is the gray value of the center pixel, \(i_{p}\) is the gray value of the \(p_{th}\) sampling point, and \(s(x)\) is the sign function that converts the difference between the gray values \(i_{p}\) and \(i_{c}\) into binary form and defined as:  
\[s(x)=\begin{cases}1&if\ x\geq 0\\ 0&if\ x<0\end{cases} \tag{5}\]  
The binary values are then weighted by \(2^{p}\) to form the LBP.  
We need to know if a binary pattern is uniform and if it is, it has at most two bit-wise transitions (0 to 1 or 1 to 0), which are useful for texture analysis as they capture fundamental texture information. To check the above condition, an equation is applied:  
\[\mathrm{U}(\mathrm{LBP_{P,R}})=\sum_{p=0}^{P-1}\left|s(i_{p+1}-i_{c})\cdot s( i_{p}-i_{c})\right| \tag{6}\]  
If \(\mathrm{U}(\mathrm{LBP_{P,R}})\leq 2\), the LBP pattern is considered uniform. Once the LBP values are computed for all pixels in an image or a region of interest, these values can be summarized in a histogram:  
\[H_{j}=\sum_{(x,y)}I(\mathrm{LBP_{P,R}}(x,y)=j),\ j=0,\ 2^{0},2^{1},\ldots,2^{P-1} \tag{7}\]  
where \(H_{j}\) represents the frequency of the LBP in the image, and \(I\) is an indicator function that equals 1 if the condition is true and 0 otherwise.  
Figure 5: (**a**) Indicative of the pixels of a part of the image above in exaggerated response for the representation of one of the neighborhoods where the local binary pattern was realized. (**b**) The \(3\times 3\) neighborhood of pixels.